Matrix-Inversion-Free Compressed Sensing With Variable Orthogonal Multi-Matching Pursuit Based on Prior Information for ECG Signals.

PubMed

Cheng, Yih-Chun; Tsai, Pei-Yun; Huang, Ming-Hao

2016-05-19

Low-complexity compressed sensing (CS) techniques for monitoring electrocardiogram (ECG) signals in wireless body sensor network (WBSN) are presented. The prior probability of ECG sparsity in the wavelet domain is first exploited. Then, variable orthogonal multi-matching pursuit (vOMMP) algorithm that consists of two phases is proposed. In the first phase, orthogonal matching pursuit (OMP) algorithm is adopted to effectively augment the support set with reliable indices and in the second phase, the orthogonal multi-matching pursuit (OMMP) is employed to rescue the missing indices. The reconstruction performance is thus enhanced with the prior information and the vOMMP algorithm. Furthermore, the computation-intensive pseudo-inverse operation is simplified by the matrix-inversion-free (MIF) technique based on QR decomposition. The vOMMP-MIF CS decoder is then implemented in 90 nm CMOS technology. The QR decomposition is accomplished by two systolic arrays working in parallel. The implementation supports three settings for obtaining 40, 44, and 48 coefficients in the sparse vector. From the measurement result, the power consumption is 11.7 mW at 0.9 V and 12 MHz. Compared to prior chip implementations, our design shows good hardware efficiency and is suitable for low-energy applications.

Sparse Matrix for ECG Identification with Two-Lead Features.

PubMed

Tseng, Kuo-Kun; Luo, Jiao; Hegarty, Robert; Wang, Wenmin; Haiting, Dong

2015-01-01

Electrocardiograph (ECG) human identification has the potential to improve biometric security. However, improvements in ECG identification and feature extraction are required. Previous work has focused on single lead ECG signals. Our work proposes a new algorithm for human identification by mapping two-lead ECG signals onto a two-dimensional matrix then employing a sparse matrix method to process the matrix. And that is the first application of sparse matrix techniques for ECG identification. Moreover, the results of our experiments demonstrate the benefits of our approach over existing methods.

Spectral Calculation of ICRF Wave Propagation and Heating in 2-D Using Massively Parallel Computers

NASA Astrophysics Data System (ADS)

Jaeger, E. F.; D'Azevedo, E.; Berry, L. A.; Carter, M. D.; Batchelor, D. B.

2000-10-01

Spectral calculations of ICRF wave propagation in plasmas have the natural advantage that they require no assumption regarding the smallness of the ion Larmor radius ρ relative to wavelength λ. Results are therefore applicable to all orders in k_bot ρ where k_bot = 2π/λ. But because all modes in the spectral representation are coupled, the solution requires inversion of a large dense matrix. In contrast, finite difference algorithms involve only matrices that are sparse and banded. Thus, spectral calculations of wave propagation and heating in tokamak plasmas have so far been limited to 1-D. In this paper, we extend the spectral method to 2-D by taking advantage of new matrix inversion techniques that utilize massively parallel computers. By spreading the dense matrix over 576 processors on the ORNL IBM RS/6000 SP supercomputer, we are able to solve up to 120,000 coupled complex equations requiring 230 GBytes of memory and achieving over 500 Gflops/sec. Initial results for ASDEX and NSTX will be presented using up to 200 modes in both the radial and vertical dimensions.

Recursive inverse factorization.

PubMed

Rubensson, Emanuel H; Bock, Nicolas; Holmström, Erik; Niklasson, Anders M N

2008-03-14

A recursive algorithm for the inverse factorization S(-1)=ZZ(*) of Hermitian positive definite matrices S is proposed. The inverse factorization is based on iterative refinement [A.M.N. Niklasson, Phys. Rev. B 70, 193102 (2004)] combined with a recursive decomposition of S. As the computational kernel is matrix-matrix multiplication, the algorithm can be parallelized and the computational effort increases linearly with system size for systems with sufficiently sparse matrices. Recent advances in network theory are used to find appropriate recursive decompositions. We show that optimization of the so-called network modularity results in an improved partitioning compared to other approaches. In particular, when the recursive inverse factorization is applied to overlap matrices of irregularly structured three-dimensional molecules.

Efficient diagonalization of the sparse matrices produced within the framework of the UK R-matrix molecular codes

NASA Astrophysics Data System (ADS)

Galiatsatos, P. G.; Tennyson, J.

2012-11-01

The most time consuming step within the framework of the UK R-matrix molecular codes is that of the diagonalization of the inner region Hamiltonian matrix (IRHM). Here we present the method that we follow to speed up this step. We use shared memory machines (SMM), distributed memory machines (DMM), the OpenMP directive based parallel language, the MPI function based parallel language, the sparse matrix diagonalizers ARPACK and PARPACK, a variation for real symmetric matrices of the official coordinate sparse matrix format and finally a parallel sparse matrix-vector product (PSMV). The efficient application of the previous techniques rely on two important facts: the sparsity of the matrix is large enough (more than 98%) and in order to get back converged results we need a small only part of the matrix spectrum.

Fast and Adaptive Sparse Precision Matrix Estimation in High Dimensions

PubMed Central

Liu, Weidong; Luo, Xi

2014-01-01

This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse Column-wise Inverse Operator, to address these two issues. We analyze an adaptive procedure based on cross validation, and establish its convergence rate under the Frobenius norm. The convergence rates under other matrix norms are also established. This method also enjoys the advantage of fast computation for large-scale problems, via a coordinate descent algorithm. Numerical merits are illustrated using both simulated and real datasets. In particular, it performs favorably on an HIV brain tissue dataset and an ADHD resting-state fMRI dataset. PMID:25750463

Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

DOE PAGES

Li, Ruipeng; Saad, Yousef

2017-08-01

This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisonsmore » with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.« less

Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Ruipeng; Saad, Yousef

This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisonsmore » with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.« less

Underdetermined blind separation of three-way fluorescence spectra of PAHs in water

NASA Astrophysics Data System (ADS)

Yang, Ruifang; Zhao, Nanjing; Xiao, Xue; Zhu, Wei; Chen, Yunan; Yin, Gaofang; Liu, Jianguo; Liu, Wenqing

2018-06-01

In this work, underdetermined blind decomposition method is developed to recognize individual components from the three-way fluorescent spectra of their mixtures by using sparse component analysis (SCA). The mixing matrix is estimated from the mixtures using fuzzy data clustering algorithm together with the scatters corresponding to local energy maximum value in the time-frequency domain, and the spectra of object components are recovered by pseudo inverse technique. As an example, using this method three and four pure components spectra can be blindly extracted from two samples of their mixture, with similarities between resolved and reference spectra all above 0.80. This work opens a new and effective path to realize monitoring PAHs in water by three-way fluorescence spectroscopy technique.

Sparse matrix methods research using the CSM testbed software system

NASA Technical Reports Server (NTRS)

Chu, Eleanor; George, J. Alan

1989-01-01

Research is described on sparse matrix techniques for the Computational Structural Mechanics (CSM) Testbed. The primary objective was to compare the performance of state-of-the-art techniques for solving sparse systems with those that are currently available in the CSM Testbed. Thus, one of the first tasks was to become familiar with the structure of the testbed, and to install some or all of the SPARSPAK package in the testbed. A suite of subroutines to extract from the data base the relevant structural and numerical information about the matrix equations was written, and all the demonstration problems distributed with the testbed were successfully solved. These codes were documented, and performance studies comparing the SPARSPAK technology to the methods currently in the testbed were completed. In addition, some preliminary studies were done comparing some recently developed out-of-core techniques with the performance of the testbed processor INV.

Sparse nonnegative matrix factorization with ℓ0-constraints

PubMed Central

Peharz, Robert; Pernkopf, Franz

2012-01-01

Although nonnegative matrix factorization (NMF) favors a sparse and part-based representation of nonnegative data, there is no guarantee for this behavior. Several authors proposed NMF methods which enforce sparseness by constraining or penalizing the ℓ1-norm of the factor matrices. On the other hand, little work has been done using a more natural sparseness measure, the ℓ0-pseudo-norm. In this paper, we propose a framework for approximate NMF which constrains the ℓ0-norm of the basis matrix, or the coefficient matrix, respectively. For this purpose, techniques for unconstrained NMF can be easily incorporated, such as multiplicative update rules, or the alternating nonnegative least-squares scheme. In experiments we demonstrate the benefits of our methods, which compare to, or outperform existing approaches. PMID:22505792

Analysis of Monte Carlo accelerated iterative methods for sparse linear systems: Analysis of Monte Carlo accelerated iterative methods for sparse linear systems

DOE PAGES

Benzi, Michele; Evans, Thomas M.; Hamilton, Steven P.; ...

2017-03-05

Here, we consider hybrid deterministic-stochastic iterative algorithms for the solution of large, sparse linear systems. Starting from a convergent splitting of the coefficient matrix, we analyze various types of Monte Carlo acceleration schemes applied to the original preconditioned Richardson (stationary) iteration. We expect that these methods will have considerable potential for resiliency to faults when implemented on massively parallel machines. We also establish sufficient conditions for the convergence of the hybrid schemes, and we investigate different types of preconditioners including sparse approximate inverses. Numerical experiments on linear systems arising from the discretization of partial differential equations are presented.

Learning Low-Rank Class-Specific Dictionary and Sparse Intra-Class Variant Dictionary for Face Recognition.

PubMed

Tang, Xin; Feng, Guo-Can; Li, Xiao-Xin; Cai, Jia-Xin

2015-01-01

Face recognition is challenging especially when the images from different persons are similar to each other due to variations in illumination, expression, and occlusion. If we have sufficient training images of each person which can span the facial variations of that person under testing conditions, sparse representation based classification (SRC) achieves very promising results. However, in many applications, face recognition often encounters the small sample size problem arising from the small number of available training images for each person. In this paper, we present a novel face recognition framework by utilizing low-rank and sparse error matrix decomposition, and sparse coding techniques (LRSE+SC). Firstly, the low-rank matrix recovery technique is applied to decompose the face images per class into a low-rank matrix and a sparse error matrix. The low-rank matrix of each individual is a class-specific dictionary and it captures the discriminative feature of this individual. The sparse error matrix represents the intra-class variations, such as illumination, expression changes. Secondly, we combine the low-rank part (representative basis) of each person into a supervised dictionary and integrate all the sparse error matrix of each individual into a within-individual variant dictionary which can be applied to represent the possible variations between the testing and training images. Then these two dictionaries are used to code the query image. The within-individual variant dictionary can be shared by all the subjects and only contribute to explain the lighting conditions, expressions, and occlusions of the query image rather than discrimination. At last, a reconstruction-based scheme is adopted for face recognition. Since the within-individual dictionary is introduced, LRSE+SC can handle the problem of the corrupted training data and the situation that not all subjects have enough samples for training. Experimental results show that our method achieves the state-of-the-art results on AR, FERET, FRGC and LFW databases.

Learning Low-Rank Class-Specific Dictionary and Sparse Intra-Class Variant Dictionary for Face Recognition

PubMed Central

Tang, Xin; Feng, Guo-can; Li, Xiao-xin; Cai, Jia-xin

2015-01-01

Face recognition is challenging especially when the images from different persons are similar to each other due to variations in illumination, expression, and occlusion. If we have sufficient training images of each person which can span the facial variations of that person under testing conditions, sparse representation based classification (SRC) achieves very promising results. However, in many applications, face recognition often encounters the small sample size problem arising from the small number of available training images for each person. In this paper, we present a novel face recognition framework by utilizing low-rank and sparse error matrix decomposition, and sparse coding techniques (LRSE+SC). Firstly, the low-rank matrix recovery technique is applied to decompose the face images per class into a low-rank matrix and a sparse error matrix. The low-rank matrix of each individual is a class-specific dictionary and it captures the discriminative feature of this individual. The sparse error matrix represents the intra-class variations, such as illumination, expression changes. Secondly, we combine the low-rank part (representative basis) of each person into a supervised dictionary and integrate all the sparse error matrix of each individual into a within-individual variant dictionary which can be applied to represent the possible variations between the testing and training images. Then these two dictionaries are used to code the query image. The within-individual variant dictionary can be shared by all the subjects and only contribute to explain the lighting conditions, expressions, and occlusions of the query image rather than discrimination. At last, a reconstruction-based scheme is adopted for face recognition. Since the within-individual dictionary is introduced, LRSE+SC can handle the problem of the corrupted training data and the situation that not all subjects have enough samples for training. Experimental results show that our method achieves the state-of-the-art results on AR, FERET, FRGC and LFW databases. PMID:26571112

Algorithms for solving large sparse systems of simultaneous linear equations on vector processors

NASA Technical Reports Server (NTRS)

David, R. E.

1984-01-01

Very efficient algorithms for solving large sparse systems of simultaneous linear equations have been developed for serial processing computers. These involve a reordering of matrix rows and columns in order to obtain a near triangular pattern of nonzero elements. Then an LU factorization is developed to represent the matrix inverse in terms of a sequence of elementary Gaussian eliminations, or pivots. In this paper it is shown how these algorithms are adapted for efficient implementation on vector processors. Results obtained on the CYBER 200 Model 205 are presented for a series of large test problems which show the comparative advantages of the triangularization and vector processing algorithms.

Underdetermined blind separation of three-way fluorescence spectra of PAHs in water.

PubMed

Yang, Ruifang; Zhao, Nanjing; Xiao, Xue; Zhu, Wei; Chen, Yunan; Yin, Gaofang; Liu, Jianguo; Liu, Wenqing

2018-06-15

In this work, underdetermined blind decomposition method is developed to recognize individual components from the three-way fluorescent spectra of their mixtures by using sparse component analysis (SCA). The mixing matrix is estimated from the mixtures using fuzzy data clustering algorithm together with the scatters corresponding to local energy maximum value in the time-frequency domain, and the spectra of object components are recovered by pseudo inverse technique. As an example, using this method three and four pure components spectra can be blindly extracted from two samples of their mixture, with similarities between resolved and reference spectra all above 0.80. This work opens a new and effective path to realize monitoring PAHs in water by three-way fluorescence spectroscopy technique. Copyright © 2018 Elsevier B.V. All rights reserved.

Point-source inversion techniques

NASA Astrophysics Data System (ADS)

Langston, Charles A.; Barker, Jeffrey S.; Pavlin, Gregory B.

1982-11-01

A variety of approaches for obtaining source parameters from waveform data using moment-tensor or dislocation point source models have been investigated and applied to long-period body and surface waves from several earthquakes. Generalized inversion techniques have been applied to data for long-period teleseismic body waves to obtain the orientation, time function and depth of the 1978 Thessaloniki, Greece, event, of the 1971 San Fernando event, and of several events associated with the 1963 induced seismicity sequence at Kariba, Africa. The generalized inversion technique and a systematic grid testing technique have also been used to place meaningful constraints on mechanisms determined from very sparse data sets; a single station with high-quality three-component waveform data is often sufficient to discriminate faulting type (e.g., strike-slip, etc.). Sparse data sets for several recent California earthquakes, for a small regional event associated with the Koyna, India, reservoir, and for several events at the Kariba reservoir have been investigated in this way. Although linearized inversion techniques using the moment-tensor model are often robust, even for sparse data sets, there are instances where the simplifying assumption of a single point source is inadequate to model the data successfully. Numerical experiments utilizing synthetic data and actual data for the 1971 San Fernando earthquake graphically demonstrate that severe problems may be encountered if source finiteness effects are ignored. These techniques are generally applicable to on-line processing of high-quality digital data, but source complexity and inadequacy of the assumed Green's functions are major problems which are yet to be fully addressed.

1-norm support vector novelty detection and its sparseness.

PubMed

Zhang, Li; Zhou, WeiDa

2013-12-01

This paper proposes a 1-norm support vector novelty detection (SVND) method and discusses its sparseness. 1-norm SVND is formulated as a linear programming problem and uses two techniques for inducing sparseness, or the 1-norm regularization and the hinge loss function. We also find two upper bounds on the sparseness of 1-norm SVND, or exact support vector (ESV) and kernel Gram matrix rank bounds. The ESV bound indicates that 1-norm SVND has a sparser representation model than SVND. The kernel Gram matrix rank bound can loosely estimate the sparseness of 1-norm SVND. Experimental results show that 1-norm SVND is feasible and effective. Copyright © 2013 Elsevier Ltd. All rights reserved.

Comparing implementations of penalized weighted least-squares sinogram restoration.

PubMed

Forthmann, Peter; Koehler, Thomas; Defrise, Michel; La Riviere, Patrick

2010-11-01

A CT scanner measures the energy that is deposited in each channel of a detector array by x rays that have been partially absorbed on their way through the object. The measurement process is complex and quantitative measurements are always and inevitably associated with errors, so CT data must be preprocessed prior to reconstruction. In recent years, the authors have formulated CT sinogram preprocessing as a statistical restoration problem in which the goal is to obtain the best estimate of the line integrals needed for reconstruction from the set of noisy, degraded measurements. The authors have explored both penalized Poisson likelihood (PL) and penalized weighted least-squares (PWLS) objective functions. At low doses, the authors found that the PL approach outperforms PWLS in terms of resolution-noise tradeoffs, but at standard doses they perform similarly. The PWLS objective function, being quadratic, is more amenable to computational acceleration than the PL objective. In this work, the authors develop and compare two different methods for implementing PWLS sinogram restoration with the hope of improving computational performance relative to PL in the standard-dose regime. Sinogram restoration is still significant in the standard-dose regime since it can still outperform standard approaches and it allows for correction of effects that are not usually modeled in standard CT preprocessing. The authors have explored and compared two implementation strategies for PWLS sinogram restoration: (1) A direct matrix-inversion strategy based on the closed-form solution to the PWLS optimization problem and (2) an iterative approach based on the conjugate-gradient algorithm. Obtaining optimal performance from each strategy required modifying the naive off-the-shelf implementations of the algorithms to exploit the particular symmetry and sparseness of the sinogram-restoration problem. For the closed-form approach, the authors subdivided the large matrix inversion into smaller coupled problems and exploited sparseness to minimize matrix operations. For the conjugate-gradient approach, the authors exploited sparseness and preconditioned the problem to speed up convergence. All methods produced qualitatively and quantitatively similar images as measured by resolution-variance tradeoffs and difference images. Despite the acceleration strategies, the direct matrix-inversion approach was found to be uncompetitive with iterative approaches, with a computational burden higher by an order of magnitude or more. The iterative conjugate-gradient approach, however, does appear promising, with computation times half that of the authors' previous penalized-likelihood implementation. Iterative conjugate-gradient based PWLS sinogram restoration with careful matrix optimizations has computational advantages over direct matrix PWLS inversion and over penalized-likelihood sinogram restoration and can be considered a good alternative in standard-dose regimes.

Convergence of Chahine's nonlinear relaxation inversion method used for limb viewing remote sensing

NASA Technical Reports Server (NTRS)

Chu, W. P.

1985-01-01

The application of Chahine's (1970) inversion technique to remote sensing problems utilizing the limb viewing geometry is discussed. The problem considered here involves occultation-type measurements and limb radiance-type measurements from either spacecraft or balloon platforms. The kernel matrix of the inversion problem is either an upper or lower triangular matrix. It is demonstrated that the Chahine inversion technique always converges, provided the diagonal elements of the kernel matrix are nonzero.

Preconditioner-free Wiener filtering with a dense noise matrix

NASA Astrophysics Data System (ADS)

Huffenberger, Kevin M.

2018-05-01

This work extends the Elsner & Wandelt (2013) iterative method for efficient, preconditioner-free Wiener filtering to cases in which the noise covariance matrix is dense, but can be decomposed into a sum whose parts are sparse in convenient bases. The new method, which uses multiple messenger fields, reproduces Wiener-filter solutions for test problems, and we apply it to a case beyond the reach of the Elsner & Wandelt (2013) method. We compute the Wiener-filter solution for a simulated Cosmic Microwave Background (CMB) map that contains spatially varying, uncorrelated noise, isotropic 1/f noise, and large-scale horizontal stripes (like those caused by atmospheric noise). We discuss simple extensions that can filter contaminated modes or inverse-noise-filter the data. These techniques help to address complications in the noise properties of maps from current and future generations of ground-based Microwave Background experiments, like Advanced ACTPol, Simons Observatory, and CMB-S4.

[Formula: see text]-regularized recursive total least squares based sparse system identification for the error-in-variables.

PubMed

Lim, Jun-Seok; Pang, Hee-Suk

2016-01-01

In this paper an [Formula: see text]-regularized recursive total least squares (RTLS) algorithm is considered for the sparse system identification. Although recursive least squares (RLS) has been successfully applied in sparse system identification, the estimation performance in RLS based algorithms becomes worse, when both input and output are contaminated by noise (the error-in-variables problem). We proposed an algorithm to handle the error-in-variables problem. The proposed [Formula: see text]-RTLS algorithm is an RLS like iteration using the [Formula: see text] regularization. The proposed algorithm not only gives excellent performance but also reduces the required complexity through the effective inversion matrix handling. Simulations demonstrate the superiority of the proposed [Formula: see text]-regularized RTLS for the sparse system identification setting.

Efficient preconditioning of the electronic structure problem in large scale ab initio molecular dynamics simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schiffmann, Florian; VandeVondele, Joost, E-mail: Joost.VandeVondele@mat.ethz.ch

2015-06-28

We present an improved preconditioning scheme for electronic structure calculations based on the orbital transformation method. First, a preconditioner is developed which includes information from the full Kohn-Sham matrix but avoids computationally demanding diagonalisation steps in its construction. This reduces the computational cost of its construction, eliminating a bottleneck in large scale simulations, while maintaining rapid convergence. In addition, a modified form of Hotelling’s iterative inversion is introduced to replace the exact inversion of the preconditioner matrix. This method is highly effective during molecular dynamics (MD), as the solution obtained in earlier MD steps is a suitable initial guess. Filteringmore » small elements during sparse matrix multiplication leads to linear scaling inversion, while retaining robustness, already for relatively small systems. For system sizes ranging from a few hundred to a few thousand atoms, which are typical for many practical applications, the improvements to the algorithm lead to a 2-5 fold speedup per MD step.« less

Sparse Gaussian elimination with controlled fill-in on a shared memory multiprocessor

NASA Technical Reports Server (NTRS)

Alaghband, Gita; Jordan, Harry F.

1989-01-01

It is shown that in sparse matrices arising from electronic circuits, it is possible to do computations on many diagonal elements simultaneously. A technique for obtaining an ordered compatible set directly from the ordered incompatible table is given. The ordering is based on the Markowitz number of the pivot candidates. This technique generates a set of compatible pivots with the property of generating few fills. A novel heuristic algorithm is presented that combines the idea of an order-compatible set with a limited binary tree search to generate several sets of compatible pivots in linear time. An elimination set for reducing the matrix is generated and selected on the basis of a minimum Markowitz sum number. The parallel pivoting technique presented is a stepwise algorithm and can be applied to any submatrix of the original matrix. Thus, it is not a preordering of the sparse matrix and is applied dynamically as the decomposition proceeds. Parameters are suggested to obtain a balance between parallelism and fill-ins. Results of applying the proposed algorithms on several large application matrices using the HEP multiprocessor (Kowalik, 1985) are presented and analyzed.

Exploring Deep Learning and Sparse Matrix Format Selection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Y.; Liao, C.; Shen, X.

We proposed to explore the use of Deep Neural Networks (DNN) for addressing the longstanding barriers. The recent rapid progress of DNN technology has created a large impact in many fields, which has significantly improved the prediction accuracy over traditional machine learning techniques in image classifications, speech recognitions, machine translations, and so on. To some degree, these tasks resemble the decision makings in many HPC tasks, including the aforementioned format selection for SpMV and linear solver selection. For instance, sparse matrix format selection is akin to image classification—such as, to tell whether an image contains a dog or a cat;more » in both problems, the right decisions are primarily determined by the spatial patterns of the elements in an input. For image classification, the patterns are of pixels, and for sparse matrix format selection, they are of non-zero elements. DNN could be naturally applied if we regard a sparse matrix as an image and the format selection or solver selection as classification problems.« less

Effects of partitioning and scheduling sparse matrix factorization on communication and load balance

NASA Technical Reports Server (NTRS)

Venugopal, Sesh; Naik, Vijay K.

1991-01-01

A block based, automatic partitioning and scheduling methodology is presented for sparse matrix factorization on distributed memory systems. Using experimental results, this technique is analyzed for communication and load imbalance overhead. To study the performance effects, these overheads were compared with those obtained from a straightforward 'wrap mapped' column assignment scheme. All experimental results were obtained using test sparse matrices from the Harwell-Boeing data set. The results show that there is a communication and load balance tradeoff. The block based method results in lower communication cost whereas the wrap mapped scheme gives better load balance.

Solving large sparse eigenvalue problems on supercomputers

NASA Technical Reports Server (NTRS)

Philippe, Bernard; Saad, Youcef

1988-01-01

An important problem in scientific computing consists in finding a few eigenvalues and corresponding eigenvectors of a very large and sparse matrix. The most popular methods to solve these problems are based on projection techniques on appropriate subspaces. The main attraction of these methods is that they only require the use of the matrix in the form of matrix by vector multiplications. The implementations on supercomputers of two such methods for symmetric matrices, namely Lanczos' method and Davidson's method are compared. Since one of the most important operations in these two methods is the multiplication of vectors by the sparse matrix, methods of performing this operation efficiently are discussed. The advantages and the disadvantages of each method are compared and implementation aspects are discussed. Numerical experiments on a one processor CRAY 2 and CRAY X-MP are reported. Possible parallel implementations are also discussed.

Solving large tomographic linear systems: size reduction and error estimation

NASA Astrophysics Data System (ADS)

Voronin, Sergey; Mikesell, Dylan; Slezak, Inna; Nolet, Guust

2014-10-01

We present a new approach to reduce a sparse, linear system of equations associated with tomographic inverse problems. We begin by making a modification to the commonly used compressed sparse-row format, whereby our format is tailored to the sparse structure of finite-frequency (volume) sensitivity kernels in seismic tomography. Next, we cluster the sparse matrix rows to divide a large matrix into smaller subsets representing ray paths that are geographically close. Singular value decomposition of each subset allows us to project the data onto a subspace associated with the largest eigenvalues of the subset. After projection we reject those data that have a signal-to-noise ratio (SNR) below a chosen threshold. Clustering in this way assures that the sparse nature of the system is minimally affected by the projection. Moreover, our approach allows for a precise estimation of the noise affecting the data while also giving us the ability to identify outliers. We illustrate the method by reducing large matrices computed for global tomographic systems with cross-correlation body wave delays, as well as with surface wave phase velocity anomalies. For a massive matrix computed for 3.7 million Rayleigh wave phase velocity measurements, imposing a threshold of 1 for the SNR, we condensed the matrix size from 1103 to 63 Gbyte. For a global data set of multiple-frequency P wave delays from 60 well-distributed deep earthquakes we obtain a reduction to 5.9 per cent. This type of reduction allows one to avoid loss of information due to underparametrizing models. Alternatively, if data have to be rejected to fit the system into computer memory, it assures that the most important data are preserved.

Comparing implementations of penalized weighted least-squares sinogram restoration

PubMed Central

Forthmann, Peter; Koehler, Thomas; Defrise, Michel; La Riviere, Patrick

2010-01-01

Purpose: A CT scanner measures the energy that is deposited in each channel of a detector array by x rays that have been partially absorbed on their way through the object. The measurement process is complex and quantitative measurements are always and inevitably associated with errors, so CT data must be preprocessed prior to reconstruction. In recent years, the authors have formulated CT sinogram preprocessing as a statistical restoration problem in which the goal is to obtain the best estimate of the line integrals needed for reconstruction from the set of noisy, degraded measurements. The authors have explored both penalized Poisson likelihood (PL) and penalized weighted least-squares (PWLS) objective functions. At low doses, the authors found that the PL approach outperforms PWLS in terms of resolution-noise tradeoffs, but at standard doses they perform similarly. The PWLS objective function, being quadratic, is more amenable to computational acceleration than the PL objective. In this work, the authors develop and compare two different methods for implementing PWLS sinogram restoration with the hope of improving computational performance relative to PL in the standard-dose regime. Sinogram restoration is still significant in the standard-dose regime since it can still outperform standard approaches and it allows for correction of effects that are not usually modeled in standard CT preprocessing. Methods: The authors have explored and compared two implementation strategies for PWLS sinogram restoration: (1) A direct matrix-inversion strategy based on the closed-form solution to the PWLS optimization problem and (2) an iterative approach based on the conjugate-gradient algorithm. Obtaining optimal performance from each strategy required modifying the naive off-the-shelf implementations of the algorithms to exploit the particular symmetry and sparseness of the sinogram-restoration problem. For the closed-form approach, the authors subdivided the large matrix inversion into smaller coupled problems and exploited sparseness to minimize matrix operations. For the conjugate-gradient approach, the authors exploited sparseness and preconditioned the problem to speed up convergence. Results: All methods produced qualitatively and quantitatively similar images as measured by resolution-variance tradeoffs and difference images. Despite the acceleration strategies, the direct matrix-inversion approach was found to be uncompetitive with iterative approaches, with a computational burden higher by an order of magnitude or more. The iterative conjugate-gradient approach, however, does appear promising, with computation times half that of the authors’ previous penalized-likelihood implementation. Conclusions: Iterative conjugate-gradient based PWLS sinogram restoration with careful matrix optimizations has computational advantages over direct matrix PWLS inversion and over penalized-likelihood sinogram restoration and can be considered a good alternative in standard-dose regimes. PMID:21158306

An exact formulation of the time-ordered exponential using path-sums

DOE Office of Scientific and Technical Information (OSTI.GOV)

Giscard, P.-L., E-mail: p.giscard1@physics.ox.ac.uk; Lui, K.; Thwaite, S. J.

2015-05-15

We present the path-sum formulation for the time-ordered exponential of a time-dependent matrix. The path-sum formulation gives the time-ordered exponential as a branched continued fraction of finite depth and breadth. The terms of the path-sum have an elementary interpretation as self-avoiding walks and self-avoiding polygons on a graph. Our result is based on a representation of the time-ordered exponential as the inverse of an operator, the mapping of this inverse to sums of walks on a graphs, and the algebraic structure of sets of walks. We give examples demonstrating our approach. We establish a super-exponential decay bound for the magnitudemore » of the entries of the time-ordered exponential of sparse matrices. We give explicit results for matrices with commonly encountered sparse structures.« less

Newmark-Beta-FDTD method for super-resolution analysis of time reversal waves

NASA Astrophysics Data System (ADS)

Shi, Sheng-Bing; Shao, Wei; Ma, Jing; Jin, Congjun; Wang, Xiao-Hua

2017-09-01

In this work, a new unconditionally stable finite-difference time-domain (FDTD) method with the split-field perfectly matched layer (PML) is proposed for the analysis of time reversal (TR) waves. The proposed method is very suitable for multiscale problems involving microstructures. The spatial and temporal derivatives in this method are discretized by the central difference technique and Newmark-Beta algorithm, respectively, and the derivation results in the calculation of a banded-sparse matrix equation. Since the coefficient matrix keeps unchanged during the whole simulation process, the lower-upper (LU) decomposition of the matrix needs to be performed only once at the beginning of the calculation. Moreover, the reverse Cuthill-Mckee (RCM) technique, an effective preprocessing technique in bandwidth compression of sparse matrices, is used to improve computational efficiency. The super-resolution focusing of TR wave propagation in two- and three-dimensional spaces is included to validate the accuracy and efficiency of the proposed method.

GPU-accelerated algorithms for compressed signals recovery with application to astronomical imagery deblurring

NASA Astrophysics Data System (ADS)

Fiandrotti, Attilio; Fosson, Sophie M.; Ravazzi, Chiara; Magli, Enrico

2018-04-01

Compressive sensing promises to enable bandwidth-efficient on-board compression of astronomical data by lifting the encoding complexity from the source to the receiver. The signal is recovered off-line, exploiting GPUs parallel computation capabilities to speedup the reconstruction process. However, inherent GPU hardware constraints limit the size of the recoverable signal and the speedup practically achievable. In this work, we design parallel algorithms that exploit the properties of circulant matrices for efficient GPU-accelerated sparse signals recovery. Our approach reduces the memory requirements, allowing us to recover very large signals with limited memory. In addition, it achieves a tenfold signal recovery speedup thanks to ad-hoc parallelization of matrix-vector multiplications and matrix inversions. Finally, we practically demonstrate our algorithms in a typical application of circulant matrices: deblurring a sparse astronomical image in the compressed domain.

Weighted low-rank sparse model via nuclear norm minimization for bearing fault detection

NASA Astrophysics Data System (ADS)

Du, Zhaohui; Chen, Xuefeng; Zhang, Han; Yang, Boyuan; Zhai, Zhi; Yan, Ruqiang

2017-07-01

It is a fundamental task in the machine fault diagnosis community to detect impulsive signatures generated by the localized faults of bearings. The main goal of this paper is to exploit the low-rank physical structure of periodic impulsive features and further establish a weighted low-rank sparse model for bearing fault detection. The proposed model mainly consists of three basic components: an adaptive partition window, a nuclear norm regularization and a weighted sequence. Firstly, due to the periodic repetition mechanism of impulsive feature, an adaptive partition window could be designed to transform the impulsive feature into a data matrix. The highlight of partition window is to accumulate all local feature information and align them. Then, all columns of the data matrix share similar waveforms and a core physical phenomenon arises, i.e., these singular values of the data matrix demonstrates a sparse distribution pattern. Therefore, a nuclear norm regularization is enforced to capture that sparse prior. However, the nuclear norm regularization treats all singular values equally and thus ignores one basic fact that larger singular values have more information volume of impulsive features and should be preserved as much as possible. Therefore, a weighted sequence with adaptively tuning weights inversely proportional to singular amplitude is adopted to guarantee the distribution consistence of large singular values. On the other hand, the proposed model is difficult to solve due to its non-convexity and thus a new algorithm is developed to search one satisfying stationary solution through alternatively implementing one proximal operator operation and least-square fitting. Moreover, the sensitivity analysis and selection principles of algorithmic parameters are comprehensively investigated through a set of numerical experiments, which shows that the proposed method is robust and only has a few adjustable parameters. Lastly, the proposed model is applied to the wind turbine (WT) bearing fault detection and its effectiveness is sufficiently verified. Compared with the current popular bearing fault diagnosis techniques, wavelet analysis and spectral kurtosis, our model achieves a higher diagnostic accuracy.

Harnessing data structure for recovery of randomly missing structural vibration responses time history: Sparse representation versus low-rank structure

NASA Astrophysics Data System (ADS)

Yang, Yongchao; Nagarajaiah, Satish

2016-06-01

Randomly missing data of structural vibration responses time history often occurs in structural dynamics and health monitoring. For example, structural vibration responses are often corrupted by outliers or erroneous measurements due to sensor malfunction; in wireless sensing platforms, data loss during wireless communication is a common issue. Besides, to alleviate the wireless data sampling or communication burden, certain accounts of data are often discarded during sampling or before transmission. In these and other applications, recovery of the randomly missing structural vibration responses from the available, incomplete data, is essential for system identification and structural health monitoring; it is an ill-posed inverse problem, however. This paper explicitly harnesses the data structure itself-of the structural vibration responses-to address this (inverse) problem. What is relevant is an empirical, but often practically true, observation, that is, typically there are only few modes active in the structural vibration responses; hence a sparse representation (in frequency domain) of the single-channel data vector, or, a low-rank structure (by singular value decomposition) of the multi-channel data matrix. Exploiting such prior knowledge of data structure (intra-channel sparse or inter-channel low-rank), the new theories of ℓ1-minimization sparse recovery and nuclear-norm-minimization low-rank matrix completion enable recovery of the randomly missing or corrupted structural vibration response data. The performance of these two alternatives, in terms of recovery accuracy and computational time under different data missing rates, is investigated on a few structural vibration response data sets-the seismic responses of the super high-rise Canton Tower and the structural health monitoring accelerations of a real large-scale cable-stayed bridge. Encouraging results are obtained and the applicability and limitation of the presented methods are discussed.

Atmospheric inverse modeling via sparse reconstruction

NASA Astrophysics Data System (ADS)

Hase, Nils; Miller, Scot M.; Maaß, Peter; Notholt, Justus; Palm, Mathias; Warneke, Thorsten

2017-10-01

Many applications in atmospheric science involve ill-posed inverse problems. A crucial component of many inverse problems is the proper formulation of a priori knowledge about the unknown parameters. In most cases, this knowledge is expressed as a Gaussian prior. This formulation often performs well at capturing smoothed, large-scale processes but is often ill equipped to capture localized structures like large point sources or localized hot spots. Over the last decade, scientists from a diverse array of applied mathematics and engineering fields have developed sparse reconstruction techniques to identify localized structures. In this study, we present a new regularization approach for ill-posed inverse problems in atmospheric science. It is based on Tikhonov regularization with sparsity constraint and allows bounds on the parameters. We enforce sparsity using a dictionary representation system. We analyze its performance in an atmospheric inverse modeling scenario by estimating anthropogenic US methane (CH4) emissions from simulated atmospheric measurements. Different measures indicate that our sparse reconstruction approach is better able to capture large point sources or localized hot spots than other methods commonly used in atmospheric inversions. It captures the overall signal equally well but adds details on the grid scale. This feature can be of value for any inverse problem with point or spatially discrete sources. We show an example for source estimation of synthetic methane emissions from the Barnett shale formation.

Implementation of hierarchical clustering using k-mer sparse matrix to analyze MERS-CoV genetic relationship

NASA Astrophysics Data System (ADS)

Bustamam, A.; Ulul, E. D.; Hura, H. F. A.; Siswantining, T.

2017-07-01

Hierarchical clustering is one of effective methods in creating a phylogenetic tree based on the distance matrix between DNA (deoxyribonucleic acid) sequences. One of the well-known methods to calculate the distance matrix is k-mer method. Generally, k-mer is more efficient than some distance matrix calculation techniques. The steps of k-mer method are started from creating k-mer sparse matrix, and followed by creating k-mer singular value vectors. The last step is computing the distance amongst vectors. In this paper, we analyze the sequences of MERS-CoV (Middle East Respiratory Syndrome - Coronavirus) DNA by implementing hierarchical clustering using k-mer sparse matrix in order to perform the phylogenetic analysis. Our results show that the ancestor of our MERS-CoV is coming from Egypt. Moreover, we found that the MERS-CoV infection that occurs in one country may not necessarily come from the same country of origin. This suggests that the process of MERS-CoV mutation might not only be influenced by geographical factor.

On-Chip Neural Data Compression Based On Compressed Sensing With Sparse Sensing Matrices.

PubMed

Zhao, Wenfeng; Sun, Biao; Wu, Tong; Yang, Zhi

2018-02-01

On-chip neural data compression is an enabling technique for wireless neural interfaces that suffer from insufficient bandwidth and power budgets to transmit the raw data. The data compression algorithm and its implementation should be power and area efficient and functionally reliable over different datasets. Compressed sensing is an emerging technique that has been applied to compress various neurophysiological data. However, the state-of-the-art compressed sensing (CS) encoders leverage random but dense binary measurement matrices, which incur substantial implementation costs on both power and area that could offset the benefits from the reduced wireless data rate. In this paper, we propose two CS encoder designs based on sparse measurement matrices that could lead to efficient hardware implementation. Specifically, two different approaches for the construction of sparse measurement matrices, i.e., the deterministic quasi-cyclic array code (QCAC) matrix and -sparse random binary matrix [-SRBM] are exploited. We demonstrate that the proposed CS encoders lead to comparable recovery performance. And efficient VLSI architecture designs are proposed for QCAC-CS and -SRBM encoders with reduced area and total power consumption.

Efficient sparse matrix-matrix multiplication for computing periodic responses by shooting method on Intel Xeon Phi

NASA Astrophysics Data System (ADS)

Stoykov, S.; Atanassov, E.; Margenov, S.

2016-10-01

Many of the scientific applications involve sparse or dense matrix operations, such as solving linear systems, matrix-matrix products, eigensolvers, etc. In what concerns structural nonlinear dynamics, the computations of periodic responses and the determination of stability of the solution are of primary interest. Shooting method iswidely used for obtaining periodic responses of nonlinear systems. The method involves simultaneously operations with sparse and dense matrices. One of the computationally expensive operations in the method is multiplication of sparse by dense matrices. In the current work, a new algorithm for sparse matrix by dense matrix products is presented. The algorithm takes into account the structure of the sparse matrix, which is obtained by space discretization of the nonlinear Mindlin's plate equation of motion by the finite element method. The algorithm is developed to use the vector engine of Intel Xeon Phi coprocessors. It is compared with the standard sparse matrix by dense matrix algorithm and the one developed by Intel MKL and it is shown that by considering the properties of the sparse matrix better algorithms can be developed.

A Performance Comparison of the Parallel Preconditioners for Iterative Methods for Large Sparse Linear Systems Arising from Partial Differential Equations on Structured Grids

NASA Astrophysics Data System (ADS)

Ma, Sangback

In this paper we compare various parallel preconditioners such as Point-SSOR (Symmetric Successive OverRelaxation), ILU(0) (Incomplete LU) in the Wavefront ordering, ILU(0) in the Multi-color ordering, Multi-Color Block SOR (Successive OverRelaxation), SPAI (SParse Approximate Inverse) and pARMS (Parallel Algebraic Recursive Multilevel Solver) for solving large sparse linear systems arising from two-dimensional PDE (Partial Differential Equation)s on structured grids. Point-SSOR is well-known, and ILU(0) is one of the most popular preconditioner, but it is inherently serial. ILU(0) in the Wavefront ordering maximizes the parallelism in the natural order, but the lengths of the wave-fronts are often nonuniform. ILU(0) in the Multi-color ordering is a simple way of achieving a parallelism of the order N, where N is the order of the matrix, but its convergence rate often deteriorates as compared to that of natural ordering. We have chosen the Multi-Color Block SOR preconditioner combined with direct sparse matrix solver, since for the Laplacian matrix the SOR method is known to have a nondeteriorating rate of convergence when used with the Multi-Color ordering. By using block version we expect to minimize the interprocessor communications. SPAI computes the sparse approximate inverse directly by least squares method. Finally, ARMS is a preconditioner recursively exploiting the concept of independent sets and pARMS is the parallel version of ARMS. Experiments were conducted for the Finite Difference and Finite Element discretizations of five two-dimensional PDEs with large meshsizes up to a million on an IBM p595 machine with distributed memory. Our matrices are real positive, i. e., their real parts of the eigenvalues are positive. We have used GMRES(m) as our outer iterative method, so that the convergence of GMRES(m) for our test matrices are mathematically guaranteed. Interprocessor communications were done using MPI (Message Passing Interface) primitives. The results show that in general ILU(0) in the Multi-Color ordering ahd ILU(0) in the Wavefront ordering outperform the other methods but for symmetric and nearly symmetric 5-point matrices Multi-Color Block SOR gives the best performance, except for a few cases with a small number of processors.

Fast Solution in Sparse LDA for Binary Classification

NASA Technical Reports Server (NTRS)

Moghaddam, Baback

2010-01-01

An algorithm that performs sparse linear discriminant analysis (Sparse-LDA) finds near-optimal solutions in far less time than the prior art when specialized to binary classification (of 2 classes). Sparse-LDA is a type of feature- or variable- selection problem with numerous applications in statistics, machine learning, computer vision, computational finance, operations research, and bio-informatics. Because of its combinatorial nature, feature- or variable-selection problems are NP-hard or computationally intractable in cases involving more than 30 variables or features. Therefore, one typically seeks approximate solutions by means of greedy search algorithms. The prior Sparse-LDA algorithm was a greedy algorithm that considered the best variable or feature to add/ delete to/ from its subsets in order to maximally discriminate between multiple classes of data. The present algorithm is designed for the special but prevalent case of 2-class or binary classification (e.g. 1 vs. 0, functioning vs. malfunctioning, or change versus no change). The present algorithm provides near-optimal solutions on large real-world datasets having hundreds or even thousands of variables or features (e.g. selecting the fewest wavelength bands in a hyperspectral sensor to do terrain classification) and does so in typical computation times of minutes as compared to days or weeks as taken by the prior art. Sparse LDA requires solving generalized eigenvalue problems for a large number of variable subsets (represented by the submatrices of the input within-class and between-class covariance matrices). In the general (fullrank) case, the amount of computation scales at least cubically with the number of variables and thus the size of the problems that can be solved is limited accordingly. However, in binary classification, the principal eigenvalues can be found using a special analytic formula, without resorting to costly iterative techniques. The present algorithm exploits this analytic form along with the inherent sequential nature of greedy search itself. Together this enables the use of highly-efficient partitioned-matrix-inverse techniques that result in large speedups of computation in both the forward-selection and backward-elimination stages of greedy algorithms in general.

Parallel pivoting combined with parallel reduction

NASA Technical Reports Server (NTRS)

Alaghband, Gita

1987-01-01

Parallel algorithms for triangularization of large, sparse, and unsymmetric matrices are presented. The method combines the parallel reduction with a new parallel pivoting technique, control over generations of fill-ins and a check for numerical stability, all done in parallel with the work being distributed over the active processes. The parallel technique uses the compatibility relation between pivots to identify parallel pivot candidates and uses the Markowitz number of pivots to minimize fill-in. This technique is not a preordering of the sparse matrix and is applied dynamically as the decomposition proceeds.

Efficient Storage Scheme of Covariance Matrix during Inverse Modeling

NASA Astrophysics Data System (ADS)

Mao, D.; Yeh, T. J.

2013-12-01

During stochastic inverse modeling, the covariance matrix of geostatistical based methods carries the information about the geologic structure. Its update during iterations reflects the decrease of uncertainty with the incorporation of observed data. For large scale problem, its storage and update cost too much memory and computational resources. In this study, we propose a new efficient storage scheme for storage and update. Compressed Sparse Column (CSC) format is utilized to storage the covariance matrix, and users can assign how many data they prefer to store based on correlation scales since the data beyond several correlation scales are usually not very informative for inverse modeling. After every iteration, only the diagonal terms of the covariance matrix are updated. The off diagonal terms are calculated and updated based on shortened correlation scales with a pre-assigned exponential model. The correlation scales are shortened by a coefficient, i.e. 0.95, every iteration to show the decrease of uncertainty. There is no universal coefficient for all the problems and users are encouraged to try several times. This new scheme is tested with 1D examples first. The estimated results and uncertainty are compared with the traditional full storage method. In the end, a large scale numerical model is utilized to validate this new scheme.

Exponentially more precise quantum simulation of fermions in the configuration interaction representation

NASA Astrophysics Data System (ADS)

Babbush, Ryan; Berry, Dominic W.; Sanders, Yuval R.; Kivlichan, Ian D.; Scherer, Artur; Wei, Annie Y.; Love, Peter J.; Aspuru-Guzik, Alán

2018-01-01

We present a quantum algorithm for the simulation of molecular systems that is asymptotically more efficient than all previous algorithms in the literature in terms of the main problem parameters. As in Babbush et al (2016 New Journal of Physics 18, 033032), we employ a recently developed technique for simulating Hamiltonian evolution using a truncated Taylor series to obtain logarithmic scaling with the inverse of the desired precision. The algorithm of this paper involves simulation under an oracle for the sparse, first-quantized representation of the molecular Hamiltonian known as the configuration interaction (CI) matrix. We construct and query the CI matrix oracle to allow for on-the-fly computation of molecular integrals in a way that is exponentially more efficient than classical numerical methods. Whereas second-quantized representations of the wavefunction require \\widetilde{{ O }}(N) qubits, where N is the number of single-particle spin-orbitals, the CI matrix representation requires \\widetilde{{ O }}(η ) qubits, where η \\ll N is the number of electrons in the molecule of interest. We show that the gate count of our algorithm scales at most as \\widetilde{{ O }}({η }2{N}3t).

Beyond Low Rank + Sparse: Multi-scale Low Rank Matrix Decomposition

PubMed Central

Ong, Frank; Lustig, Michael

2016-01-01

We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often exhibit local correlations in multiple scales. Concretely, we propose a multi-scale low rank modeling that represents a data matrix as a sum of block-wise low rank matrices with increasing scales of block sizes. We then consider the inverse problem of decomposing the data matrix into its multi-scale low rank components and approach the problem via a convex formulation. Theoretically, we show that under various incoherence conditions, the convex program recovers the multi-scale low rank components either exactly or approximately. Practically, we provide guidance on selecting the regularization parameters and incorporate cycle spinning to reduce blocking artifacts. Experimentally, we show that the multi-scale low rank decomposition provides a more intuitive decomposition than conventional low rank methods and demonstrate its effectiveness in four applications, including illumination normalization for face images, motion separation for surveillance videos, multi-scale modeling of the dynamic contrast enhanced magnetic resonance imaging and collaborative filtering exploiting age information. PMID:28450978

User's Manual for PCSMS (Parallel Complex Sparse Matrix Solver). Version 1.

NASA Technical Reports Server (NTRS)

Reddy, C. J.

2000-01-01

PCSMS (Parallel Complex Sparse Matrix Solver) is a computer code written to make use of the existing real sparse direct solvers to solve complex, sparse matrix linear equations. PCSMS converts complex matrices into real matrices and use real, sparse direct matrix solvers to factor and solve the real matrices. The solution vector is reconverted to complex numbers. Though, this utility is written for Silicon Graphics (SGI) real sparse matrix solution routines, it is general in nature and can be easily modified to work with any real sparse matrix solver. The User's Manual is written to make the user acquainted with the installation and operation of the code. Driver routines are given to aid the users to integrate PCSMS routines in their own codes.

Visual Tracking Based on Extreme Learning Machine and Sparse Representation

PubMed Central

Wang, Baoxian; Tang, Linbo; Yang, Jinglin; Zhao, Baojun; Wang, Shuigen

2015-01-01

The existing sparse representation-based visual trackers mostly suffer from both being time consuming and having poor robustness problems. To address these issues, a novel tracking method is presented via combining sparse representation and an emerging learning technique, namely extreme learning machine (ELM). Specifically, visual tracking can be divided into two consecutive processes. Firstly, ELM is utilized to find the optimal separate hyperplane between the target observations and background ones. Thus, the trained ELM classification function is able to remove most of the candidate samples related to background contents efficiently, thereby reducing the total computational cost of the following sparse representation. Secondly, to further combine ELM and sparse representation, the resultant confidence values (i.e., probabilities to be a target) of samples on the ELM classification function are used to construct a new manifold learning constraint term of the sparse representation framework, which tends to achieve robuster results. Moreover, the accelerated proximal gradient method is used for deriving the optimal solution (in matrix form) of the constrained sparse tracking model. Additionally, the matrix form solution allows the candidate samples to be calculated in parallel, thereby leading to a higher efficiency. Experiments demonstrate the effectiveness of the proposed tracker. PMID:26506359

Sparse Image Reconstruction on the Sphere: Analysis and Synthesis.

PubMed

Wallis, Christopher G R; Wiaux, Yves; McEwen, Jason D

2017-11-01

We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularization, exploiting sparsity in both axisymmetric and directional scale-discretized wavelet space. Denoising, inpainting, and deconvolution problems and combinations thereof, are considered as examples. Inverse problems are solved in both the analysis and synthesis settings, with a number of different sampling schemes. The most effective approach is that with the most restricted solution-space, which depends on the interplay between the adopted sampling scheme, the selection of the analysis/synthesis problem, and any weighting of the l 1 norm appearing in the regularization problem. More efficient sampling schemes on the sphere improve reconstruction fidelity by restricting the solution-space and also by improving sparsity in wavelet space. We apply the technique to denoise Planck 353-GHz observations, improving the ability to extract the structure of Galactic dust emission, which is important for studying Galactic magnetism.

Fast iterative image reconstruction using sparse matrix factorization with GPU acceleration

NASA Astrophysics Data System (ADS)

Zhou, Jian; Qi, Jinyi

2011-03-01

Statistically based iterative approaches for image reconstruction have gained much attention in medical imaging. An accurate system matrix that defines the mapping from the image space to the data space is the key to high-resolution image reconstruction. However, an accurate system matrix is often associated with high computational cost and huge storage requirement. Here we present a method to address this problem by using sparse matrix factorization and parallel computing on a graphic processing unit (GPU).We factor the accurate system matrix into three sparse matrices: a sinogram blurring matrix, a geometric projection matrix, and an image blurring matrix. The sinogram blurring matrix models the detector response. The geometric projection matrix is based on a simple line integral model. The image blurring matrix is to compensate for the line-of-response (LOR) degradation due to the simplified geometric projection matrix. The geometric projection matrix is precomputed, while the sinogram and image blurring matrices are estimated by minimizing the difference between the factored system matrix and the original system matrix. The resulting factored system matrix has much less number of nonzero elements than the original system matrix and thus substantially reduces the storage and computation cost. The smaller size also allows an efficient implement of the forward and back projectors on GPUs, which have limited amount of memory. Our simulation studies show that the proposed method can dramatically reduce the computation cost of high-resolution iterative image reconstruction. The proposed technique is applicable to image reconstruction for different imaging modalities, including x-ray CT, PET, and SPECT.

Approximate method of variational Bayesian matrix factorization/completion with sparse prior

NASA Astrophysics Data System (ADS)

Kawasumi, Ryota; Takeda, Koujin

2018-05-01

We derive the analytical expression of a matrix factorization/completion solution by the variational Bayes method, under the assumption that the observed matrix is originally the product of low-rank, dense and sparse matrices with additive noise. We assume the prior of a sparse matrix is a Laplace distribution by taking matrix sparsity into consideration. Then we use several approximations for the derivation of a matrix factorization/completion solution. By our solution, we also numerically evaluate the performance of a sparse matrix reconstruction in matrix factorization, and completion of a missing matrix element in matrix completion.

High-performance implementation of Chebyshev filter diagonalization for interior eigenvalue computations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pieper, Andreas; Kreutzer, Moritz; Alvermann, Andreas, E-mail: alvermann@physik.uni-greifswald.de

2016-11-15

We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is approximated with filter polynomials obtained from Chebyshev expansions of window functions. After the discussion of the conceptual foundations of Chebyshev filter diagonalization we analyze the impact of the choice of the damping kernel, search space size, and filter polynomial degree on the computational accuracy and effort, before we describe the necessary steps towards a parallel high-performance implementation. Because Chebyshev filter diagonalization avoids the need formore » matrix inversion it can deal with matrices and problem sizes that are presently not accessible with rational function methods based on direct or iterative linear solvers. To demonstrate the potential of Chebyshev filter diagonalization for large-scale problems of this kind we include as an example the computation of the 10{sup 2} innermost eigenpairs of a topological insulator matrix with dimension 10{sup 9} derived from quantum physics applications.« less

A Sparse Matrix Approach for Simultaneous Quantification of Nystagmus and Saccade

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.; Stone, Lee; Boyle, Richard D.

2012-01-01

The vestibulo-ocular reflex (VOR) consists of two intermingled non-linear subsystems; namely, nystagmus and saccade. Typically, nystagmus is analysed using a single sufficiently long signal or a concatenation of them. Saccade information is not analysed and discarded due to insufficient data length to provide consistent and minimum variance estimates. This paper presents a novel sparse matrix approach to system identification of the VOR. It allows for the simultaneous estimation of both nystagmus and saccade signals. We show via simulation of the VOR that our technique provides consistent and unbiased estimates in the presence of output additive noise.

Brief announcement: Hypergraph parititioning for parallel sparse matrix-matrix multiplication

DOE PAGES

Ballard, Grey; Druinsky, Alex; Knight, Nicholas; ...

2015-01-01

The performance of parallel algorithms for sparse matrix-matrix multiplication is typically determined by the amount of interprocessor communication performed, which in turn depends on the nonzero structure of the input matrices. In this paper, we characterize the communication cost of a sparse matrix-matrix multiplication algorithm in terms of the size of a cut of an associated hypergraph that encodes the computation for a given input nonzero structure. Obtaining an optimal algorithm corresponds to solving a hypergraph partitioning problem. Furthermore, our hypergraph model generalizes several existing models for sparse matrix-vector multiplication, and we can leverage hypergraph partitioners developed for that computationmore » to improve application-specific algorithms for multiplying sparse matrices.« less

HIGH DIMENSIONAL COVARIANCE MATRIX ESTIMATION IN APPROXIMATE FACTOR MODELS.

PubMed

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2011-01-01

The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied.

Adaptive OFDM Waveform Design for Spatio-Temporal-Sparsity Exploited STAP Radar

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sen, Satyabrata

In this chapter, we describe a sparsity-based space-time adaptive processing (STAP) algorithm to detect a slowly moving target using an orthogonal frequency division multiplexing (OFDM) radar. The motivation of employing an OFDM signal is that it improves the target-detectability from the interfering signals by increasing the frequency diversity of the system. However, due to the addition of one extra dimension in terms of frequency, the adaptive degrees-of-freedom in an OFDM-STAP also increases. Therefore, to avoid the construction a fully adaptive OFDM-STAP, we develop a sparsity-based STAP algorithm. We observe that the interference spectrum is inherently sparse in the spatio-temporal domain,more » as the clutter responses occupy only a diagonal ridge on the spatio-temporal plane and the jammer signals interfere only from a few spatial directions. Hence, we exploit that sparsity to develop an efficient STAP technique that utilizes considerably lesser number of secondary data compared to the other existing STAP techniques, and produces nearly optimum STAP performance. In addition to designing the STAP filter, we optimally design the transmit OFDM signals by maximizing the output signal-to-interference-plus-noise ratio (SINR) in order to improve the STAP performance. The computation of output SINR depends on the estimated value of the interference covariance matrix, which we obtain by applying the sparse recovery algorithm. Therefore, we analytically assess the effects of the synthesized OFDM coefficients on the sparse recovery of the interference covariance matrix by computing the coherence measure of the sparse measurement matrix. Our numerical examples demonstrate the achieved STAP-performance due to sparsity-based technique and adaptive waveform design.« less

Spatial operator factorization and inversion of the manipulator mass matrix

NASA Technical Reports Server (NTRS)

Rodriguez, Guillermo; Kreutz-Delgado, Kenneth

1992-01-01

This paper advances two linear operator factorizations of the manipulator mass matrix. Embedded in the factorizations are many of the techniques that are regarded as very efficient computational solutions to inverse and forward dynamics problems. The operator factorizations provide a high-level architectural understanding of the mass matrix and its inverse, which is not visible in the detailed algorithms. They also lead to a new approach to the development of computer programs or organize complexity in robot dynamics.

HIGH DIMENSIONAL COVARIANCE MATRIX ESTIMATION IN APPROXIMATE FACTOR MODELS

PubMed Central

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2012-01-01

The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied. PMID:22661790

Selected inversion as key to a stable Langevin evolution across the QCD phase boundary

NASA Astrophysics Data System (ADS)

Bloch, Jacques; Schenk, Olaf

2018-03-01

We present new results of full QCD at nonzero chemical potential. In PRD 92, 094516 (2015) the complex Langevin method was shown to break down when the inverse coupling decreases and enters the transition region from the deconfined to the confined phase. We found that the stochastic technique used to estimate the drift term can be very unstable for indefinite matrices. This may be avoided by using the full inverse of the Dirac operator, which is, however, too costly for four-dimensional lattices. The major breakthrough in this work was achieved by realizing that the inverse elements necessary for the drift term can be computed efficiently using the selected inversion technique provided by the parallel sparse direct solver package PARDISO. In our new study we show that no breakdown of the complex Langevin method is encountered and that simulations can be performed across the phase boundary.

Inverse modeling of the terrestrial carbon flux in China with flux covariance among inverted regions

NASA Astrophysics Data System (ADS)

Wang, H.; Jiang, F.; Chen, J. M.; Ju, W.; Wang, H.

2011-12-01

Quantitative understanding of the role of ocean and terrestrial biosphere in the global carbon cycle, their response and feedback to climate change is required for the future projection of the global climate. China has the largest amount of anthropogenic CO2 emission, diverse terrestrial ecosystems and an unprecedented rate of urbanization. Thus information on spatial and temporal distributions of the terrestrial carbon flux in China is of great importance in understanding the global carbon cycle. We developed a nested inversion with focus in China. Based on Transcom 22 regions for the globe, we divide China and its neighboring countries into 17 regions, making 39 regions in total for the globe. A Bayesian synthesis inversion is made to estimate the terrestrial carbon flux based on GlobalView CO2 data. In the inversion, GEOS-Chem is used as the transport model to develop the transport matrix. A terrestrial ecosystem model named BEPS is used to produce the prior surface flux to constrain the inversion. However, the sparseness of available observation stations in Asia poses a challenge to the inversion for the 17 small regions. To obtain additional constraint on the inversion, a prior flux covariance matrix is constructed using the BEPS model through analyzing the correlation in the net carbon flux among regions under variable climate conditions. The use of the covariance among different regions in the inversion effectively extends the information content of CO2 observations to more regions. The carbon flux over the 39 land and ocean regions are inverted for the period from 2004 to 2009. In order to investigate the impact of introducing the covariance matrix with non-zero off-diagonal values to the inversion, the inverted terrestrial carbon flux over China is evaluated against ChinaFlux eddy-covariance observations after applying an upscaling methodology.

Wavelet-sparsity based regularization over time in the inverse problem of electrocardiography.

PubMed

Cluitmans, Matthijs J M; Karel, Joël M H; Bonizzi, Pietro; Volders, Paul G A; Westra, Ronald L; Peeters, Ralf L M

2013-01-01

Noninvasive, detailed assessment of electrical cardiac activity at the level of the heart surface has the potential to revolutionize diagnostics and therapy of cardiac pathologies. Due to the requirement of noninvasiveness, body-surface potentials are measured and have to be projected back to the heart surface, yielding an ill-posed inverse problem. Ill-posedness ensures that there are non-unique solutions to this problem, resulting in a problem of choice. In the current paper, it is proposed to restrict this choice by requiring that the time series of reconstructed heart-surface potentials is sparse in the wavelet domain. A local search technique is introduced that pursues a sparse solution, using an orthogonal wavelet transform. Epicardial potentials reconstructed from this method are compared to those from existing methods, and validated with actual intracardiac recordings. The new technique improves the reconstructions in terms of smoothness and recovers physiologically meaningful details. Additionally, reconstruction of activation timing seems to be improved when pursuing sparsity of the reconstructed signals in the wavelet domain.

An Efficient Scheme for Updating Sparse Cholesky Factors

NASA Technical Reports Server (NTRS)

Raghavan, Padma

2002-01-01

Raghavan had earlier developed the software package DCSPACK which can be used for solving sparse linear systems where the coefficient matrix is symmetric and positive definite (this project was not funded by NASA but by agencies such as NSF). DSCPACK-S is the serial code and DSCPACK-P is a parallel implementation suitable for multiprocessors or networks-of-workstations with message passing using MCI. The main algorithm used is the Cholesky factorization of a sparse symmetric positive positive definite matrix A = LL(T). The code can also compute the factorization A = LDL(T). The complexity of the software arises from several factors relating to the sparsity of the matrix A. A sparse N x N matrix A has typically less that cN nonzeroes where c is a small constant. If the matrix were dense, it would have O(N2) nonzeroes. The most complicated part of such sparse Cholesky factorization relates to fill-in, i.e., zeroes in the original matrix that become nonzeroes in the factor L. An efficient implementation depends to a large extent on complex data structures and on techniques from graph theory to reduce, identify, and manage fill. DSCPACK is based on an efficient multifrontal implementation with fill-managing algorithms and implementation arising from earlier research by Raghavan and others. Sparse Cholesky factorization is typically a four step process: (1) ordering to compute a fill-reducing numbering, (2) symbolic factorization to determine the nonzero structure of L, (3) numeric factorization to compute L, and, (4) triangular solution to solve L(T)x = y and Ly = b. The first two steps are symbolic and are performed using the graph of the matrix. The numeric factorization step is of dominant cost and there are several schemes for improving performance by exploiting the nested and dense structure of groups of columns in the factor. The latter are aimed at better utilization of the cache-memory hierarchy on modem processors to prevent cache-misses and provide execution rates (operations/second) that are close to the peak rates for dense matrix computations. Currently, EPISCOPACY is being used in an application at NASA directed by J. Newman and M. James. We propose the implementation of efficient schemes for updating the LL(T) or LDL(T) factors computed in DSCPACK-S to meet the computational requirements of their project. A brief description is provided in the next section.

Multi-threaded Sparse Matrix Sparse Matrix Multiplication for Many-Core and GPU Architectures.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deveci, Mehmet; Trott, Christian Robert; Rajamanickam, Sivasankaran

Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scientific computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we develop parallel algorithms for sparse matrix- matrix multiplication with a focus on performance portability across different high performance computing architectures. The performance of these algorithms depend on the data structures used in them. We compare different types of accumulators in these algorithms and demonstrate the performance difference between these data structures. Furthermore, we develop a meta-algorithm, kkSpGEMM, to choose the right algorithm and datamore » structure based on the characteristics of the problem. We show performance comparisons on three architectures and demonstrate the need for the community to develop two phase sparse matrix-matrix multiplication implementations for efficient reuse of the data structures involved.« less

Error analysis applied to several inversion techniques used for the retrieval of middle atmospheric constituents from limb-scanning MM-wave spectroscopic measurements

NASA Technical Reports Server (NTRS)

Puliafito, E.; Bevilacqua, R.; Olivero, J.; Degenhardt, W.

1992-01-01

The formal retrieval error analysis of Rodgers (1990) allows the quantitative determination of such retrieval properties as measurement error sensitivity, resolution, and inversion bias. This technique was applied to five numerical inversion techniques and two nonlinear iterative techniques used for the retrieval of middle atmospheric constituent concentrations from limb-scanning millimeter-wave spectroscopic measurements. It is found that the iterative methods have better vertical resolution, but are slightly more sensitive to measurement error than constrained matrix methods. The iterative methods converge to the exact solution, whereas two of the matrix methods under consideration have an explicit constraint, the sensitivity of the solution to the a priori profile. Tradeoffs of these retrieval characteristics are presented.

Frequency-domain elastic full waveform inversion using encoded simultaneous sources

NASA Astrophysics Data System (ADS)

Jeong, W.; Son, W.; Pyun, S.; Min, D.

2011-12-01

Currently, numerous studies have endeavored to develop robust full waveform inversion and migration algorithms. These processes require enormous computational costs, because of the number of sources in the survey. To avoid this problem, the phase encoding technique for prestack migration was proposed by Romero (2000) and Krebs et al. (2009) proposed the encoded simultaneous-source inversion technique in the time domain. On the other hand, Ben-Hadj-Ali et al. (2011) demonstrated the robustness of the frequency-domain full waveform inversion with simultaneous sources for noisy data changing the source assembling. Although several studies on simultaneous-source inversion tried to estimate P- wave velocity based on the acoustic wave equation, seismic migration and waveform inversion based on the elastic wave equations are required to obtain more reliable subsurface information. In this study, we propose a 2-D frequency-domain elastic full waveform inversion technique using phase encoding methods. In our algorithm, the random phase encoding method is employed to calculate the gradients of the elastic parameters, source signature estimation and the diagonal entries of approximate Hessian matrix. The crosstalk for the estimated source signature and the diagonal entries of approximate Hessian matrix are suppressed with iteration as for the gradients. Our 2-D frequency-domain elastic waveform inversion algorithm is composed using the back-propagation technique and the conjugate-gradient method. Source signature is estimated using the full Newton method. We compare the simultaneous-source inversion with the conventional waveform inversion for synthetic data sets of the Marmousi-2 model. The inverted results obtained by simultaneous sources are comparable to those obtained by individual sources, and source signature is successfully estimated in simultaneous source technique. Comparing the inverted results using the pseudo Hessian matrix with previous inversion results provided by the approximate Hessian matrix, it is noted that the latter are better than the former for deeper parts of the model. This work was financially supported by the Brain Korea 21 project of Energy System Engineering, by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0006155), by the Energy Efficiency & Resources of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Knowledge Economy (No. 2010T100200133).

A High Performance Block Eigensolver for Nuclear Configuration Interaction Calculations

DOE PAGES

Aktulga, Hasan Metin; Afibuzzaman, Md.; Williams, Samuel; ...

2017-06-01

As on-node parallelism increases and the performance gap between the processor and the memory system widens, achieving high performance in large-scale scientific applications requires an architecture-aware design of algorithms and solvers. We focus on the eigenvalue problem arising in nuclear Configuration Interaction (CI) calculations, where a few extreme eigenpairs of a sparse symmetric matrix are needed. Here, we consider a block iterative eigensolver whose main computational kernels are the multiplication of a sparse matrix with multiple vectors (SpMM), and tall-skinny matrix operations. We then present techniques to significantly improve the SpMM and the transpose operation SpMM T by using themore » compressed sparse blocks (CSB) format. We achieve 3-4× speedup on the requisite operations over good implementations with the commonly used compressed sparse row (CSR) format. We develop a performance model that allows us to correctly estimate the performance of our SpMM kernel implementations, and we identify cache bandwidth as a potential performance bottleneck beyond DRAM. We also analyze and optimize the performance of LOBPCG kernels (inner product and linear combinations on multiple vectors) and show up to 15× speedup over using high performance BLAS libraries for these operations. The resulting high performance LOBPCG solver achieves 1.4× to 1.8× speedup over the existing Lanczos solver on a series of CI computations on high-end multicore architectures (Intel Xeons). We also analyze the performance of our techniques on an Intel Xeon Phi Knights Corner (KNC) processor.« less

A High Performance Block Eigensolver for Nuclear Configuration Interaction Calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aktulga, Hasan Metin; Afibuzzaman, Md.; Williams, Samuel

As on-node parallelism increases and the performance gap between the processor and the memory system widens, achieving high performance in large-scale scientific applications requires an architecture-aware design of algorithms and solvers. We focus on the eigenvalue problem arising in nuclear Configuration Interaction (CI) calculations, where a few extreme eigenpairs of a sparse symmetric matrix are needed. Here, we consider a block iterative eigensolver whose main computational kernels are the multiplication of a sparse matrix with multiple vectors (SpMM), and tall-skinny matrix operations. We then present techniques to significantly improve the SpMM and the transpose operation SpMM T by using themore » compressed sparse blocks (CSB) format. We achieve 3-4× speedup on the requisite operations over good implementations with the commonly used compressed sparse row (CSR) format. We develop a performance model that allows us to correctly estimate the performance of our SpMM kernel implementations, and we identify cache bandwidth as a potential performance bottleneck beyond DRAM. We also analyze and optimize the performance of LOBPCG kernels (inner product and linear combinations on multiple vectors) and show up to 15× speedup over using high performance BLAS libraries for these operations. The resulting high performance LOBPCG solver achieves 1.4× to 1.8× speedup over the existing Lanczos solver on a series of CI computations on high-end multicore architectures (Intel Xeons). We also analyze the performance of our techniques on an Intel Xeon Phi Knights Corner (KNC) processor.« less

Sparse Matrices in MATLAB: Design and Implementation

NASA Technical Reports Server (NTRS)

Gilbert, John R.; Moler, Cleve; Schreiber, Robert

1992-01-01

The matrix computation language and environment MATLAB is extended to include sparse matrix storage and operations. The only change to the outward appearance of the MATLAB language is a pair of commands to create full or sparse matrices. Nearly all the operations of MATLAB now apply equally to full or sparse matrices, without any explicit action by the user. The sparse data structure represents a matrix in space proportional to the number of nonzero entries, and most of the operations compute sparse results in time proportional to the number of arithmetic operations on nonzeros.

A Comparison between Model Base Hardconstrain, Bandlimited, and Sparse-Spike Seismic Inversion: New Insights for CBM Reservoir Modelling on Muara Enim Formation, South Sumatra

NASA Astrophysics Data System (ADS)

Mohamad Noor, Faris; Adipta, Agra

2018-03-01

Coal Bed Methane (CBM) as a newly developed resource in Indonesia is one of the alternatives to relieve Indonesia’s dependencies on conventional energies. Coal resource of Muara Enim Formation is known as one of the prolific reservoirs in South Sumatra Basin. Seismic inversion and well analysis are done to determine the coal seam characteristics of Muara Enim Formation. This research uses three inversion methods, which are: model base hard- constrain, bandlimited, and sparse-spike inversion. Each type of seismic inversion has its own advantages to display the coal seam and its characteristic. Interpretation result from the analysis data shows that the Muara Enim coal seam has 20 (API) gamma ray value, 1 (gr/cc) – 1.4 (gr/cc) from density log, and low AI cutoff value range between 5000-6400 (m/s)*(g/cc). The distribution of coal seam is laterally thinning northwest to southeast. Coal seam is seen biasedly on model base hard constraint inversion and discontinued on band-limited inversion which isn’t similar to the geological model. The appropriate AI inversion is sparse spike inversion which has 0.884757 value from cross plot inversion as the best correlation value among the chosen inversion methods. Sparse Spike inversion its self-has high amplitude as a proper tool to identify coal seam continuity which commonly appears as a thin layer. Cross-sectional sparse spike inversion shows that there are possible new boreholes in CDP 3662-3722, CDP 3586-3622, and CDP 4004-4148 which is seen in seismic data as a thick coal seam.

Total variation-based method for radar coincidence imaging with model mismatch for extended target

NASA Astrophysics Data System (ADS)

Cao, Kaicheng; Zhou, Xiaoli; Cheng, Yongqiang; Fan, Bo; Qin, Yuliang

2017-11-01

Originating from traditional optical coincidence imaging, radar coincidence imaging (RCI) is a staring/forward-looking imaging technique. In RCI, the reference matrix must be computed precisely to reconstruct the image as preferred; unfortunately, such precision is almost impossible due to the existence of model mismatch in practical applications. Although some conventional sparse recovery algorithms are proposed to solve the model-mismatch problem, they are inapplicable to nonsparse targets. We therefore sought to derive the signal model of RCI with model mismatch by replacing the sparsity constraint item with total variation (TV) regularization in the sparse total least squares optimization problem; in this manner, we obtain the objective function of RCI with model mismatch for an extended target. A more robust and efficient algorithm called TV-TLS is proposed, in which the objective function is divided into two parts and the perturbation matrix and scattering coefficients are updated alternately. Moreover, due to the ability of TV regularization to recover sparse signal or image with sparse gradient, TV-TLS method is also applicable to sparse recovering. Results of numerical experiments demonstrate that, for uniform extended targets, sparse targets, and real extended targets, the algorithm can achieve preferred imaging performance both in suppressing noise and in adapting to model mismatch.

Removing flicker based on sparse color correspondences in old film restoration

NASA Astrophysics Data System (ADS)

Huang, Xi; Ding, Youdong; Yu, Bing; Xia, Tianran

2018-04-01

In the long history of human civilization, archived film is an indispensable part of it, and using digital method to repair damaged film is also a mainstream trend nowadays. In this paper, we propose a sparse color correspondences based technique to remove fading flicker for old films. Our model, combined with multi frame images to establish a simple correction model, includes three key steps. Firstly, we recover sparse color correspondences in the input frames to build a matrix with many missing entries. Secondly, we present a low-rank matrix factorization approach to estimate the unknown parameters of this model. Finally, we adopt a two-step strategy that divide the estimated parameters into reference frame parameters for color recovery correction and other frame parameters for color consistency correction to remove flicker. Our method combined multi-frames takes continuity of the input sequence into account, and the experimental results show the method can remove fading flicker efficiently.

Tomographic PIV: particles versus blobs

NASA Astrophysics Data System (ADS)

Champagnat, Frédéric; Cornic, Philippe; Cheminet, Adam; Leclaire, Benjamin; Le Besnerais, Guy; Plyer, Aurélien

2014-08-01

We present an alternative approach to tomographic particle image velocimetry (tomo-PIV) that seeks to recover nearly single voxel particles rather than blobs of extended size. The baseline of our approach is a particle-based representation of image data. An appropriate discretization of this representation yields an original linear forward model with a weight matrix built with specific samples of the system’s point spread function (PSF). Such an approach requires only a few voxels to explain the image appearance, therefore it favors much more sparsely reconstructed volumes than classic tomo-PIV. The proposed forward model is general and flexible and can be embedded in a classical multiplicative algebraic reconstruction technique (MART) or a simultaneous multiplicative algebraic reconstruction technique (SMART) inversion procedure. We show, using synthetic PIV images and by way of a large exploration of the generating conditions and a variety of performance metrics, that the model leads to better results than the classical tomo-PIV approach, in particular in the case of seeding densities greater than 0.06 particles per pixel and of PSFs characterized by a standard deviation larger than 0.8 pixels.

Tensor-GMRES method for large sparse systems of nonlinear equations

NASA Technical Reports Server (NTRS)

Feng, Dan; Pulliam, Thomas H.

1994-01-01

This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.

Simultaneous analysis of large INTEGRAL/SPI1 datasets: Optimizing the computation of the solution and its variance using sparse matrix algorithms

NASA Astrophysics Data System (ADS)

Bouchet, L.; Amestoy, P.; Buttari, A.; Rouet, F.-H.; Chauvin, M.

2013-02-01

Nowadays, analyzing and reducing the ever larger astronomical datasets is becoming a crucial challenge, especially for long cumulated observation times. The INTEGRAL/SPI X/γ-ray spectrometer is an instrument for which it is essential to process many exposures at the same time in order to increase the low signal-to-noise ratio of the weakest sources. In this context, the conventional methods for data reduction are inefficient and sometimes not feasible at all. Processing several years of data simultaneously requires computing not only the solution of a large system of equations, but also the associated uncertainties. We aim at reducing the computation time and the memory usage. Since the SPI transfer function is sparse, we have used some popular methods for the solution of large sparse linear systems; we briefly review these methods. We use the Multifrontal Massively Parallel Solver (MUMPS) to compute the solution of the system of equations. We also need to compute the variance of the solution, which amounts to computing selected entries of the inverse of the sparse matrix corresponding to our linear system. This can be achieved through one of the latest features of the MUMPS software that has been partly motivated by this work. In this paper we provide a brief presentation of this feature and evaluate its effectiveness on astrophysical problems requiring the processing of large datasets simultaneously, such as the study of the entire emission of the Galaxy. We used these algorithms to solve the large sparse systems arising from SPI data processing and to obtain both their solutions and the associated variances. In conclusion, thanks to these newly developed tools, processing large datasets arising from SPI is now feasible with both a reasonable execution time and a low memory usage.

High-dimensional statistical inference: From vector to matrix

NASA Astrophysics Data System (ADS)

Zhang, Anru

Statistical inference for sparse signals or low-rank matrices in high-dimensional settings is of significant interest in a range of contemporary applications. It has attracted significant recent attention in many fields including statistics, applied mathematics and electrical engineering. In this thesis, we consider several problems in including sparse signal recovery (compressed sensing under restricted isometry) and low-rank matrix recovery (matrix recovery via rank-one projections and structured matrix completion). The first part of the thesis discusses compressed sensing and affine rank minimization in both noiseless and noisy cases and establishes sharp restricted isometry conditions for sparse signal and low-rank matrix recovery. The analysis relies on a key technical tool which represents points in a polytope by convex combinations of sparse vectors. The technique is elementary while leads to sharp results. It is shown that, in compressed sensing, delta kA < 1/3, deltak A+ thetak,kA < 1, or deltatkA < √( t - 1)/t for any given constant t ≥ 4/3 guarantee the exact recovery of all k sparse signals in the noiseless case through the constrained ℓ1 minimization, and similarly in affine rank minimization delta rM < 1/3, deltar M + thetar, rM < 1, or deltatrM< √( t - 1)/t ensure the exact reconstruction of all matrices with rank at most r in the noiseless case via the constrained nuclear norm minimization. Moreover, for any epsilon > 0, delta kA < 1/3 + epsilon, deltak A + thetak,kA < 1 + epsilon, or deltatkA< √(t - 1) / t + epsilon are not sufficient to guarantee the exact recovery of all k-sparse signals for large k. Similar result also holds for matrix recovery. In addition, the conditions delta kA<1/3, deltak A+ thetak,kA<1, delta tkA < √(t - 1)/t and deltarM<1/3, delta rM+ thetar,rM<1, delta trM< √(t - 1)/ t are also shown to be sufficient respectively for stable recovery of approximately sparse signals and low-rank matrices in the noisy case. For the second part of the thesis, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization method for stable recovery of low-rank matrices in the noisy case. The procedure is adaptive to the rank and robust against small perturbations. Both upper and lower bounds for the estimation accuracy under the Frobenius norm loss are obtained. The proposed estimator is shown to be rate-optimal under certain conditions. The estimator is easy to implement via convex programming and performs well numerically. The techniques and main results developed in the chapter also have implications to other related statistical problems. An application to estimation of spiked covariance matrices from one-dimensional random projections is considered. The results demonstrate that it is still possible to accurately estimate the covariance matrix of a high-dimensional distribution based only on one-dimensional projections. For the third part of the thesis, we consider another setting of low-rank matrix completion. Current literature on matrix completion focuses primarily on independent sampling models under which the individual observed entries are sampled independently. Motivated by applications in genomic data integration, we propose a new framework of structured matrix completion (SMC) to treat structured missingness by design. Specifically, our proposed method aims at efficient matrix recovery when a subset of the rows and columns of an approximately low-rank matrix are observed. We provide theoretical justification for the proposed SMC method and derive lower bound for the estimation errors, which together establish the optimal rate of recovery over certain classes of approximately low-rank matrices. Simulation studies show that the method performs well in finite sample under a variety of configurations. The method is applied to integrate several ovarian cancer genomic studies with different extent of genomic measurements, which enables us to construct more accurate prediction rules for ovarian cancer survival.

New Factorization Techniques and Fast Serial and Parrallel Algorithms for Operational Space Control of Robot Manipulators

NASA Technical Reports Server (NTRS)

Fijany, Amir; Djouani, Karim; Fried, George; Pontnau, Jean

1997-01-01

In this paper a new factorization technique for computation of inverse of mass matrix, and the operational space mass matrix, as arising in implementation of the operational space control scheme, is presented.

Efficient ICCG on a shared memory multiprocessor

NASA Technical Reports Server (NTRS)

Hammond, Steven W.; Schreiber, Robert

1989-01-01

Different approaches are discussed for exploiting parallelism in the ICCG (Incomplete Cholesky Conjugate Gradient) method for solving large sparse symmetric positive definite systems of equations on a shared memory parallel computer. Techniques for efficiently solving triangular systems and computing sparse matrix-vector products are explored. Three methods for scheduling the tasks in solving triangular systems are implemented on the Sequent Balance 21000. Sample problems that are representative of a large class of problems solved using iterative methods are used. We show that a static analysis to determine data dependences in the triangular solve can greatly improve its parallel efficiency. We also show that ignoring symmetry and storing the whole matrix can reduce solution time substantially.

A Strassen-Newton algorithm for high-speed parallelizable matrix inversion

NASA Technical Reports Server (NTRS)

Bailey, David H.; Ferguson, Helaman R. P.

1988-01-01

Techniques are described for computing matrix inverses by algorithms that are highly suited to massively parallel computation. The techniques are based on an algorithm suggested by Strassen (1969). Variations of this scheme use matrix Newton iterations and other methods to improve the numerical stability while at the same time preserving a very high level of parallelism. One-processor Cray-2 implementations of these schemes range from one that is up to 55 percent faster than a conventional library routine to one that is slower than a library routine but achieves excellent numerical stability. The problem of computing the solution to a single set of linear equations is discussed, and it is shown that this problem can also be solved efficiently using these techniques.

Dynamic data integration and stochastic inversion of a confined aquifer

NASA Astrophysics Data System (ADS)

Wang, D.; Zhang, Y.; Irsa, J.; Huang, H.; Wang, L.

2013-12-01

Much work has been done in developing and applying inverse methods to aquifer modeling. The scope of this paper is to investigate the applicability of a new direct method for large inversion problems and to incorporate uncertainty measures in the inversion outcomes (Wang et al., 2013). The problem considered is a two-dimensional inverse model (50×50 grid) of steady-state flow for a heterogeneous ground truth model (500×500 grid) with two hydrofacies. From the ground truth model, decreasing number of wells (12, 6, 3) were sampled for facies types, based on which experimental indicator histograms and directional variograms were computed. These parameters and models were used by Sequential Indicator Simulation to generate 100 realizations of hydrofacies patterns in a 100×100 (geostatistical) grid, which were conditioned to the facies measurements at wells. These realizations were smoothed with Simulated Annealing, coarsened to the 50×50 inverse grid, before they were conditioned with the direct method to the dynamic data, i.e., observed heads and groundwater fluxes at the same sampled wells. A set of realizations of estimated hydraulic conductivities (Ks), flow fields, and boundary conditions were created, which centered on the 'true' solutions from solving the ground truth model. Both hydrofacies conductivities were computed with an estimation accuracy of ×10% (12 wells), ×20% (6 wells), ×35% (3 wells) of the true values. For boundary condition estimation, the accuracy was within × 15% (12 wells), 30% (6 wells), and 50% (3 wells) of the true values. The inversion system of equations was solved with LSQR (Paige et al, 1982), for which coordinate transform and matrix scaling preprocessor were used to improve the condition number (CN) of the coefficient matrix. However, when the inverse grid was refined to 100×100, Gaussian Noise Perturbation was used to limit the growth of the CN before the matrix solve. To scale the inverse problem up (i.e., without smoothing and coarsening and therefore reducing the associated estimation uncertainty), a parallel LSQR solver was written and verified. For the 50×50 grid, the parallel solver sped up the serial solution time by 14X using 4 CPUs (research on parallel performance and scaling is ongoing). A sensitivity analysis was conducted to examine the relation between the observed data and the inversion outcomes, where measurement errors of increasing magnitudes (i.e., ×1, 2, 5, 10% of the total head variation and up to ×2% of the total flux variation) were imposed on the observed data. Inversion results were stable but the accuracy of Ks and boundary estimation degraded with increasing errors, as expected. In particular, quality of the observed heads is critical to hydraulic head recovery, while quality of the observed fluxes plays a dominant role in K estimation. References: Wang, D., Y. Zhang, J. Irsa, H. Huang, and L. Wang (2013), Data integration and stochastic inversion of a confined aquifer with high performance computing, Advances in Water Resources, in preparation. Paige, C. C., and M. A. Saunders (1982), LSQR: an algorithm for sparse linear equations and sparse least squares, ACM Transactions on Mathematical Software, 8(1), 43-71.

Wavelet-like bases for thin-wire integral equations in electromagnetics

NASA Astrophysics Data System (ADS)

Francomano, E.; Tortorici, A.; Toscano, E.; Ala, G.; Viola, F.

2005-03-01

In this paper, wavelets are used in solving, by the method of moments, a modified version of the thin-wire electric field integral equation, in frequency domain. The time domain electromagnetic quantities, are obtained by using the inverse discrete fast Fourier transform. The retarded scalar electric and vector magnetic potentials are employed in order to obtain the integral formulation. The discretized model generated by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix which have to be solved for each frequency of the Fourier spectrum of the time domain impressed source. Therefore, orthogonal wavelet-like basis transform is used to sparsify the moment matrix. In particular, dyadic and M-band wavelet transforms have been adopted, so generating different sparse matrix structures. This leads to an efficient solution in solving the resulting sparse matrix equation. Moreover, a wavelet preconditioner is used to accelerate the convergence rate of the iterative solver employed. These numerical features are used in analyzing the transient behavior of a lightning protection system. In particular, the transient performance of the earth termination system of a lightning protection system or of the earth electrode of an electric power substation, during its operation is focused. The numerical results, obtained by running a complex structure, are discussed and the features of the used method are underlined.

Exact recovery of sparse multiple measurement vectors by [Formula: see text]-minimization.

PubMed

Wang, Changlong; Peng, Jigen

2018-01-01

The joint sparse recovery problem is a generalization of the single measurement vector problem widely studied in compressed sensing. It aims to recover a set of jointly sparse vectors, i.e., those that have nonzero entries concentrated at a common location. Meanwhile [Formula: see text]-minimization subject to matrixes is widely used in a large number of algorithms designed for this problem, i.e., [Formula: see text]-minimization [Formula: see text] Therefore the main contribution in this paper is two theoretical results about this technique. The first one is proving that in every multiple system of linear equations there exists a constant [Formula: see text] such that the original unique sparse solution also can be recovered from a minimization in [Formula: see text] quasi-norm subject to matrixes whenever [Formula: see text]. The other one is showing an analytic expression of such [Formula: see text]. Finally, we display the results of one example to confirm the validity of our conclusions, and we use some numerical experiments to show that we increase the efficiency of these algorithms designed for [Formula: see text]-minimization by using our results.

Deflation as a method of variance reduction for estimating the trace of a matrix inverse

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gambhir, Arjun Singh; Stathopoulos, Andreas; Orginos, Kostas

Many fields require computing the trace of the inverse of a large, sparse matrix. The typical method used for such computations is the Hutchinson method which is a Monte Carlo (MC) averaging over matrix quadratures. To improve its convergence, several variance reductions techniques have been proposed. In this paper, we study the effects of deflating the near null singular value space. We make two main contributions. First, we analyze the variance of the Hutchinson method as a function of the deflated singular values and vectors. Although this provides good intuition in general, by assuming additionally that the singular vectors aremore » random unitary matrices, we arrive at concise formulas for the deflated variance that include only the variance and mean of the singular values. We make the remarkable observation that deflation may increase variance for Hermitian matrices but not for non-Hermitian ones. This is a rare, if not unique, property where non-Hermitian matrices outperform Hermitian ones. The theory can be used as a model for predicting the benefits of deflation. Second, we use deflation in the context of a large scale application of "disconnected diagrams" in Lattice QCD. On lattices, Hierarchical Probing (HP) has previously provided an order of magnitude of variance reduction over MC by removing "error" from neighboring nodes of increasing distance in the lattice. Although deflation used directly on MC yields a limited improvement of 30% in our problem, when combined with HP they reduce variance by a factor of over 150 compared to MC. For this, we pre-computated 1000 smallest singular values of an ill-conditioned matrix of size 25 million. Furthermore, using PRIMME and a domain-specific Algebraic Multigrid preconditioner, we perform one of the largest eigenvalue computations in Lattice QCD at a fraction of the cost of our trace computation.« less

Deflation as a method of variance reduction for estimating the trace of a matrix inverse

DOE PAGES

Gambhir, Arjun Singh; Stathopoulos, Andreas; Orginos, Kostas

2017-04-06

Many fields require computing the trace of the inverse of a large, sparse matrix. The typical method used for such computations is the Hutchinson method which is a Monte Carlo (MC) averaging over matrix quadratures. To improve its convergence, several variance reductions techniques have been proposed. In this paper, we study the effects of deflating the near null singular value space. We make two main contributions. First, we analyze the variance of the Hutchinson method as a function of the deflated singular values and vectors. Although this provides good intuition in general, by assuming additionally that the singular vectors aremore » random unitary matrices, we arrive at concise formulas for the deflated variance that include only the variance and mean of the singular values. We make the remarkable observation that deflation may increase variance for Hermitian matrices but not for non-Hermitian ones. This is a rare, if not unique, property where non-Hermitian matrices outperform Hermitian ones. The theory can be used as a model for predicting the benefits of deflation. Second, we use deflation in the context of a large scale application of "disconnected diagrams" in Lattice QCD. On lattices, Hierarchical Probing (HP) has previously provided an order of magnitude of variance reduction over MC by removing "error" from neighboring nodes of increasing distance in the lattice. Although deflation used directly on MC yields a limited improvement of 30% in our problem, when combined with HP they reduce variance by a factor of over 150 compared to MC. For this, we pre-computated 1000 smallest singular values of an ill-conditioned matrix of size 25 million. Furthermore, using PRIMME and a domain-specific Algebraic Multigrid preconditioner, we perform one of the largest eigenvalue computations in Lattice QCD at a fraction of the cost of our trace computation.« less

Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis.

PubMed

Kim, Hyunsoo; Park, Haesun

2007-06-15

Many practical pattern recognition problems require non-negativity constraints. For example, pixels in digital images and chemical concentrations in bioinformatics are non-negative. Sparse non-negative matrix factorizations (NMFs) are useful when the degree of sparseness in the non-negative basis matrix or the non-negative coefficient matrix in an NMF needs to be controlled in approximating high-dimensional data in a lower dimensional space. In this article, we introduce a novel formulation of sparse NMF and show how the new formulation leads to a convergent sparse NMF algorithm via alternating non-negativity-constrained least squares. We apply our sparse NMF algorithm to cancer-class discovery and gene expression data analysis and offer biological analysis of the results obtained. Our experimental results illustrate that the proposed sparse NMF algorithm often achieves better clustering performance with shorter computing time compared to other existing NMF algorithms. The software is available as supplementary material.

SPARSKIT: A basic tool kit for sparse matrix computations

NASA Technical Reports Server (NTRS)

Saad, Youcef

1990-01-01

Presented here are the main features of a tool package for manipulating and working with sparse matrices. One of the goals of the package is to provide basic tools to facilitate the exchange of software and data between researchers in sparse matrix computations. The starting point is the Harwell/Boeing collection of matrices for which the authors provide a number of tools. Among other things, the package provides programs for converting data structures, printing simple statistics on a matrix, plotting a matrix profile, and performing linear algebra operations with sparse matrices.

Detection of extracellular matrix modification in cancer models with inverse spectroscopic optical coherence tomography

NASA Astrophysics Data System (ADS)

Spicer, Graham L. C.; Azarin, Samira M.; Yi, Ji; Young, Scott T.; Ellis, Ronald; Bauer, Greta M.; Shea, Lonnie D.; Backman, Vadim

2016-10-01

In cancer biology, there has been a recent effort to understand tumor formation in the context of the tissue microenvironment. In particular, recent progress has explored the mechanisms behind how changes in the cell-extracellular matrix ensemble influence progression of the disease. The extensive use of in vitro tissue culture models in simulant matrix has proven effective at studying such interactions, but modalities for non-invasively quantifying aspects of these systems are scant. We present the novel application of an imaging technique, Inverse Spectroscopic Optical Coherence Tomography, for the non-destructive measurement of in vitro biological samples during matrix remodeling. Our findings indicate that the nanoscale-sensitive mass density correlation shape factor D of cancer cells increases in response to a more crosslinked matrix. We present a facile technique for the non-invasive, quantitative study of the micro- and nano-scale structure of the extracellular matrix and its host cells.

Sparse Matrix Software Catalog, Sparse Matrix Symposium 1982, Fairfield Glade, Tennessee, October 24-27, 1982,

DTIC Science & Technology

1982-10-27

are buried within * a much larger, special purpose package. We regret such omissions, but to have reached the practi- tioners in each of the diverse...sparse matrix (form PAQ ) 4. Method of solution: Distribution count sort 5. Programming language: FORTRAN g Precision: Single and double precision 7

Elastic-Waveform Inversion with Compressive Sensing for Sparse Seismic Data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Youzuo; Huang, Lianjie

2015-01-28

Accurate velocity models of compressional- and shear-waves are essential for geothermal reservoir characterization and microseismic imaging. Elastic-waveform inversion of multi-component seismic data can provide high-resolution inversion results of subsurface geophysical properties. However, the method requires seismic data acquired using dense source and receiver arrays. In practice, seismic sources and/or geophones are often sparsely distributed on the surface and/or in a borehole, such as 3D vertical seismic profiling (VSP) surveys. We develop a novel elastic-waveform inversion method with compressive sensing for inversion of sparse seismic data. We employ an alternating-minimization algorithm to solve the optimization problem of our new waveform inversionmore » method. We validate our new method using synthetic VSP data for a geophysical model built using geologic features found at the Raft River enhanced-geothermal-system (EGS) field. We apply our method to synthetic VSP data with a sparse source array and compare the results with those obtained with a dense source array. Our numerical results demonstrate that the velocity models produced with our new method using a sparse source array are almost as accurate as those obtained using a dense source array.« less

A study of the parallel algorithm for large-scale DC simulation of nonlinear systems

NASA Astrophysics Data System (ADS)

Cortés Udave, Diego Ernesto; Ogrodzki, Jan; Gutiérrez de Anda, Miguel Angel

Newton-Raphson DC analysis of large-scale nonlinear circuits may be an extremely time consuming process even if sparse matrix techniques and bypassing of nonlinear models calculation are used. A slight decrease in the time required for this task may be enabled on multi-core, multithread computers if the calculation of the mathematical models for the nonlinear elements as well as the stamp management of the sparse matrix entries are managed through concurrent processes. This numerical complexity can be further reduced via the circuit decomposition and parallel solution of blocks taking as a departure point the BBD matrix structure. This block-parallel approach may give a considerable profit though it is strongly dependent on the system topology and, of course, on the processor type. This contribution presents the easy-parallelizable decomposition-based algorithm for DC simulation and provides a detailed study of its effectiveness.

MATLAB Simulation of Gradient-Based Neural Network for Online Matrix Inversion

NASA Astrophysics Data System (ADS)

Zhang, Yunong; Chen, Ke; Ma, Weimu; Li, Xiao-Dong

This paper investigates the simulation of a gradient-based recurrent neural network for online solution of the matrix-inverse problem. Several important techniques are employed as follows to simulate such a neural system. 1) Kronecker product of matrices is introduced to transform a matrix-differential-equation (MDE) to a vector-differential-equation (VDE); i.e., finally, a standard ordinary-differential-equation (ODE) is obtained. 2) MATLAB routine "ode45" is introduced to solve the transformed initial-value ODE problem. 3) In addition to various implementation errors, different kinds of activation functions are simulated to show the characteristics of such a neural network. Simulation results substantiate the theoretical analysis and efficacy of the gradient-based neural network for online constant matrix inversion.

Multi-threaded Sparse Matrix-Matrix Multiplication for Many-Core and GPU Architectures.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deveci, Mehmet; Rajamanickam, Sivasankaran; Trott, Christian Robert

Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scienti c computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we develop parallel algorithms for sparse matrix-matrix multiplication with a focus on performance portability across different high performance computing architectures. The performance of these algorithms depend on the data structures used in them. We compare different types of accumulators in these algorithms and demonstrate the performance difference between these data structures. Furthermore, we develop a meta-algorithm, kkSpGEMM, to choose the right algorithm and datamore » structure based on the characteristics of the problem. We show performance comparisons on three architectures and demonstrate the need for the community to develop two phase sparse matrix-matrix multiplication implementations for efficient reuse of the data structures involved.« less

Sparse representation-based image restoration via nonlocal supervised coding

NASA Astrophysics Data System (ADS)

Li, Ao; Chen, Deyun; Sun, Guanglu; Lin, Kezheng

2016-10-01

Sparse representation (SR) and nonlocal technique (NLT) have shown great potential in low-level image processing. However, due to the degradation of the observed image, SR and NLT may not be accurate enough to obtain a faithful restoration results when they are used independently. To improve the performance, in this paper, a nonlocal supervised coding strategy-based NLT for image restoration is proposed. The novel method has three main contributions. First, to exploit the useful nonlocal patches, a nonnegative sparse representation is introduced, whose coefficients can be utilized as the supervised weights among patches. Second, a novel objective function is proposed, which integrated the supervised weights learning and the nonlocal sparse coding to guarantee a more promising solution. Finally, to make the minimization tractable and convergence, a numerical scheme based on iterative shrinkage thresholding is developed to solve the above underdetermined inverse problem. The extensive experiments validate the effectiveness of the proposed method.

Matrix differentiation formulas

NASA Technical Reports Server (NTRS)

Usikov, D. A.; Tkhabisimov, D. K.

1983-01-01

A compact differentiation technique (without using indexes) is developed for scalar functions that depend on complex matrix arguments which are combined by operations of complex conjugation, transposition, addition, multiplication, matrix inversion and taking the direct product. The differentiation apparatus is developed in order to simplify the solution of extremum problems of scalar functions of matrix arguments.

Reconstructing source terms from atmospheric concentration measurements: Optimality analysis of an inversion technique

NASA Astrophysics Data System (ADS)

Turbelin, Grégory; Singh, Sarvesh Kumar; Issartel, Jean-Pierre

2014-12-01

In the event of an accidental or intentional contaminant release in the atmosphere, it is imperative, for managing emergency response, to diagnose the release parameters of the source from measured data. Reconstruction of the source information exploiting measured data is called an inverse problem. To solve such a problem, several techniques are currently being developed. The first part of this paper provides a detailed description of one of them, known as the renormalization method. This technique, proposed by Issartel (2005), has been derived using an approach different from that of standard inversion methods and gives a linear solution to the continuous Source Term Estimation (STE) problem. In the second part of this paper, the discrete counterpart of this method is presented. By using matrix notation, common in data assimilation and suitable for numerical computing, it is shown that the discrete renormalized solution belongs to a family of well-known inverse solutions (minimum weighted norm solutions), which can be computed by using the concept of generalized inverse operator. It is shown that, when the weight matrix satisfies the renormalization condition, this operator satisfies the criteria used in geophysics to define good inverses. Notably, by means of the Model Resolution Matrix (MRM) formalism, we demonstrate that the renormalized solution fulfils optimal properties for the localization of single point sources. Throughout the article, the main concepts are illustrated with data from a wind tunnel experiment conducted at the Environmental Flow Research Centre at the University of Surrey, UK.

Joint Inversion of Body-Wave Arrival Times and Surface-Wave Dispersion Data in the Wavelet Domain Constrained by Sparsity Regularization

NASA Astrophysics Data System (ADS)

Zhang, H.; Fang, H.; Yao, H.; Maceira, M.; van der Hilst, R. D.

2014-12-01

Recently, Zhang et al. (2014, Pure and Appiled Geophysics) have developed a joint inversion code incorporating body-wave arrival times and surface-wave dispersion data. The joint inversion code was based on the regional-scale version of the double-difference tomography algorithm tomoDD. The surface-wave inversion part uses the propagator matrix solver in the algorithm DISPER80 (Saito, 1988) for forward calculation of dispersion curves from layered velocity models and the related sensitivities. The application of the joint inversion code to the SAFOD site in central California shows that the fault structure is better imaged in the new model, which is able to fit both the body-wave and surface-wave observations adequately. Here we present a new joint inversion method that solves the model in the wavelet domain constrained by sparsity regularization. Compared to the previous method, it has the following advantages: (1) The method is both data- and model-adaptive. For the velocity model, it can be represented by different wavelet coefficients at different scales, which are generally sparse. By constraining the model wavelet coefficients to be sparse, the inversion in the wavelet domain can inherently adapt to the data distribution so that the model has higher spatial resolution in the good data coverage zone. Fang and Zhang (2014, Geophysical Journal International) have showed the superior performance of the wavelet-based double-difference seismic tomography method compared to the conventional method. (2) For the surface wave inversion, the joint inversion code takes advantage of the recent development of direct inversion of surface wave dispersion data for 3-D variations of shear wave velocity without the intermediate step of phase or group velocity maps (Fang et al., 2014, Geophysical Journal International). A fast marching method is used to compute, at each period, surface wave traveltimes and ray paths between sources and receivers. We will test the new joint inversion code at the SAFOD site to compare its performance over the previous code. We will also select another fault zone such as the San Jacinto Fault Zone to better image its structure.

Kernel Recursive Least-Squares Temporal Difference Algorithms with Sparsification and Regularization

PubMed Central

Zhu, Qingxin; Niu, Xinzheng

2016-01-01

By combining with sparse kernel methods, least-squares temporal difference (LSTD) algorithms can construct the feature dictionary automatically and obtain a better generalization ability. However, the previous kernel-based LSTD algorithms do not consider regularization and their sparsification processes are batch or offline, which hinder their widespread applications in online learning problems. In this paper, we combine the following five techniques and propose two novel kernel recursive LSTD algorithms: (i) online sparsification, which can cope with unknown state regions and be used for online learning, (ii) L 2 and L 1 regularization, which can avoid overfitting and eliminate the influence of noise, (iii) recursive least squares, which can eliminate matrix-inversion operations and reduce computational complexity, (iv) a sliding-window approach, which can avoid caching all history samples and reduce the computational cost, and (v) the fixed-point subiteration and online pruning, which can make L 1 regularization easy to implement. Finally, simulation results on two 50-state chain problems demonstrate the effectiveness of our algorithms. PMID:27436996

Kernel Recursive Least-Squares Temporal Difference Algorithms with Sparsification and Regularization.

PubMed

Zhang, Chunyuan; Zhu, Qingxin; Niu, Xinzheng

2016-01-01

By combining with sparse kernel methods, least-squares temporal difference (LSTD) algorithms can construct the feature dictionary automatically and obtain a better generalization ability. However, the previous kernel-based LSTD algorithms do not consider regularization and their sparsification processes are batch or offline, which hinder their widespread applications in online learning problems. In this paper, we combine the following five techniques and propose two novel kernel recursive LSTD algorithms: (i) online sparsification, which can cope with unknown state regions and be used for online learning, (ii) L 2 and L 1 regularization, which can avoid overfitting and eliminate the influence of noise, (iii) recursive least squares, which can eliminate matrix-inversion operations and reduce computational complexity, (iv) a sliding-window approach, which can avoid caching all history samples and reduce the computational cost, and (v) the fixed-point subiteration and online pruning, which can make L 1 regularization easy to implement. Finally, simulation results on two 50-state chain problems demonstrate the effectiveness of our algorithms.

Tensor Sparse Coding for Positive Definite Matrices.

PubMed

Sivalingam, Ravishankar; Boley, Daniel; Morellas, Vassilios; Papanikolopoulos, Nikos

2013-08-02

In recent years, there has been extensive research on sparse representation of vector-valued signals. In the matrix case, the data points are merely vectorized and treated as vectors thereafter (for e.g., image patches). However, this approach cannot be used for all matrices, as it may destroy the inherent structure of the data. Symmetric positive definite (SPD) matrices constitute one such class of signals, where their implicit structure of positive eigenvalues is lost upon vectorization. This paper proposes a novel sparse coding technique for positive definite matrices, which respects the structure of the Riemannian manifold and preserves the positivity of their eigenvalues, without resorting to vectorization. Synthetic and real-world computer vision experiments with region covariance descriptors demonstrate the need for and the applicability of the new sparse coding model. This work serves to bridge the gap between the sparse modeling paradigm and the space of positive definite matrices.

Tensor sparse coding for positive definite matrices.

PubMed

Sivalingam, Ravishankar; Boley, Daniel; Morellas, Vassilios; Papanikolopoulos, Nikolaos

2014-03-01

In recent years, there has been extensive research on sparse representation of vector-valued signals. In the matrix case, the data points are merely vectorized and treated as vectors thereafter (for example, image patches). However, this approach cannot be used for all matrices, as it may destroy the inherent structure of the data. Symmetric positive definite (SPD) matrices constitute one such class of signals, where their implicit structure of positive eigenvalues is lost upon vectorization. This paper proposes a novel sparse coding technique for positive definite matrices, which respects the structure of the Riemannian manifold and preserves the positivity of their eigenvalues, without resorting to vectorization. Synthetic and real-world computer vision experiments with region covariance descriptors demonstrate the need for and the applicability of the new sparse coding model. This work serves to bridge the gap between the sparse modeling paradigm and the space of positive definite matrices.

BCYCLIC: A parallel block tridiagonal matrix cyclic solver

NASA Astrophysics Data System (ADS)

Hirshman, S. P.; Perumalla, K. S.; Lynch, V. E.; Sanchez, R.

2010-09-01

A block tridiagonal matrix is factored with minimal fill-in using a cyclic reduction algorithm that is easily parallelized. Storage of the factored blocks allows the application of the inverse to multiple right-hand sides which may not be known at factorization time. Scalability with the number of block rows is achieved with cyclic reduction, while scalability with the block size is achieved using multithreaded routines (OpenMP, GotoBLAS) for block matrix manipulation. This dual scalability is a noteworthy feature of this new solver, as well as its ability to efficiently handle arbitrary (non-powers-of-2) block row and processor numbers. Comparison with a state-of-the art parallel sparse solver is presented. It is expected that this new solver will allow many physical applications to optimally use the parallel resources on current supercomputers. Example usage of the solver in magneto-hydrodynamic (MHD), three-dimensional equilibrium solvers for high-temperature fusion plasmas is cited.

Approximate equiangular tight frames for compressed sensing and CDMA applications

NASA Astrophysics Data System (ADS)

Tsiligianni, Evaggelia; Kondi, Lisimachos P.; Katsaggelos, Aggelos K.

2017-12-01

Performance guarantees for recovery algorithms employed in sparse representations, and compressed sensing highlights the importance of incoherence. Optimal bounds of incoherence are attained by equiangular unit norm tight frames (ETFs). Although ETFs are important in many applications, they do not exist for all dimensions, while their construction has been proven extremely difficult. In this paper, we construct frames that are close to ETFs. According to results from frame and graph theory, the existence of an ETF depends on the existence of its signature matrix, that is, a symmetric matrix with certain structure and spectrum consisting of two distinct eigenvalues. We view the construction of a signature matrix as an inverse eigenvalue problem and propose a method that produces frames of any dimensions that are close to ETFs. Due to the achieved equiangularity property, the so obtained frames can be employed as spreading sequences in synchronous code-division multiple access (s-CDMA) systems, besides compressed sensing.

Nonlocal low-rank and sparse matrix decomposition for spectral CT reconstruction

NASA Astrophysics Data System (ADS)

Niu, Shanzhou; Yu, Gaohang; Ma, Jianhua; Wang, Jing

2018-02-01

Spectral computed tomography (CT) has been a promising technique in research and clinics because of its ability to produce improved energy resolution images with narrow energy bins. However, the narrow energy bin image is often affected by serious quantum noise because of the limited number of photons used in the corresponding energy bin. To address this problem, we present an iterative reconstruction method for spectral CT using nonlocal low-rank and sparse matrix decomposition (NLSMD), which exploits the self-similarity of patches that are collected in multi-energy images. Specifically, each set of patches can be decomposed into a low-rank component and a sparse component, and the low-rank component represents the stationary background over different energy bins, while the sparse component represents the rest of the different spectral features in individual energy bins. Subsequently, an effective alternating optimization algorithm was developed to minimize the associated objective function. To validate and evaluate the NLSMD method, qualitative and quantitative studies were conducted by using simulated and real spectral CT data. Experimental results show that the NLSMD method improves spectral CT images in terms of noise reduction, artifact suppression and resolution preservation.

Holographic implementation of a binary associative memory for improved recognition

NASA Astrophysics Data System (ADS)

Bandyopadhyay, Somnath; Ghosh, Ajay; Datta, Asit K.

1998-03-01

Neural network associate memory has found wide application sin pattern recognition techniques. We propose an associative memory model for binary character recognition. The interconnection strengths of the memory are binary valued. The concept of sparse coding is sued to enhance the storage efficiency of the model. The question of imposed preconditioning of pattern vectors, which is inherent in a sparsely coded conventional memory, is eliminated by using a multistep correlation technique an the ability of correct association is enhanced in a real-time application. A potential optoelectronic implementation of the proposed associative memory is also described. The learning and recall is possible by using digital optical matrix-vector multiplication, where full use of parallelism and connectivity of optics is made. A hologram is used in the experiment as a longer memory (LTM) for storing all input information. The short-term memory or the interconnection weight matrix required during the recall process is configured by retrieving the necessary information from the holographic LTM.

Interpretation of the Precision Matrix and Its Application in Estimating Sparse Brain Connectivity during Sleep Spindles from Human Electrocorticography Recordings

PubMed Central

Das, Anup; Sampson, Aaron L.; Lainscsek, Claudia; Muller, Lyle; Lin, Wutu; Doyle, John C.; Cash, Sydney S.; Halgren, Eric; Sejnowski, Terrence J.

2017-01-01

The correlation method from brain imaging has been used to estimate functional connectivity in the human brain. However, brain regions might show very high correlation even when the two regions are not directly connected due to the strong interaction of the two regions with common input from a third region. One previously proposed solution to this problem is to use a sparse regularized inverse covariance matrix or precision matrix (SRPM) assuming that the connectivity structure is sparse. This method yields partial correlations to measure strong direct interactions between pairs of regions while simultaneously removing the influence of the rest of the regions, thus identifying regions that are conditionally independent. To test our methods, we first demonstrated conditions under which the SRPM method could indeed find the true physical connection between a pair of nodes for a spring-mass example and an RC circuit example. The recovery of the connectivity structure using the SRPM method can be explained by energy models using the Boltzmann distribution. We then demonstrated the application of the SRPM method for estimating brain connectivity during stage 2 sleep spindles from human electrocorticography (ECoG) recordings using an 8 × 8 electrode array. The ECoG recordings that we analyzed were from a 32-year-old male patient with long-standing pharmaco-resistant left temporal lobe complex partial epilepsy. Sleep spindles were automatically detected using delay differential analysis and then analyzed with SRPM and the Louvain method for community detection. We found spatially localized brain networks within and between neighboring cortical areas during spindles, in contrast to the case when sleep spindles were not present. PMID:28095202

Addressing the computational cost of large EIT solutions.

PubMed

Boyle, Alistair; Borsic, Andrea; Adler, Andy

2012-05-01

Electrical impedance tomography (EIT) is a soft field tomography modality based on the application of electric current to a body and measurement of voltages through electrodes at the boundary. The interior conductivity is reconstructed on a discrete representation of the domain using a finite-element method (FEM) mesh and a parametrization of that domain. The reconstruction requires a sequence of numerically intensive calculations. There is strong interest in reducing the cost of these calculations. An improvement in the compute time for current problems would encourage further exploration of computationally challenging problems such as the incorporation of time series data, wide-spread adoption of three-dimensional simulations and correlation of other modalities such as CT and ultrasound. Multicore processors offer an opportunity to reduce EIT computation times but may require some restructuring of the underlying algorithms to maximize the use of available resources. This work profiles two EIT software packages (EIDORS and NDRM) to experimentally determine where the computational costs arise in EIT as problems scale. Sparse matrix solvers, a key component for the FEM forward problem and sensitivity estimates in the inverse problem, are shown to take a considerable portion of the total compute time in these packages. A sparse matrix solver performance measurement tool, Meagre-Crowd, is developed to interface with a variety of solvers and compare their performance over a range of two- and three-dimensional problems of increasing node density. Results show that distributed sparse matrix solvers that operate on multiple cores are advantageous up to a limit that increases as the node density increases. We recommend a selection procedure to find a solver and hardware arrangement matched to the problem and provide guidance and tools to perform that selection.

DNA melting profiles from a matrix method.

PubMed

Poland, Douglas

2004-02-05

In this article we give a new method for the calculation of DNA melting profiles. Based on the matrix formulation of the DNA partition function, the method relies for its efficiency on the fact that the required matrices are very sparse, essentially reducing matrix multiplication to vector multiplication and thus making the computer time required to treat a DNA molecule containing N base pairs proportional to N(2). A key ingredient in the method is the result that multiplication by the inverse matrix can also be reduced to vector multiplication. The task of calculating the melting profile for the entire genome is further reduced by treating regions of the molecule between helix-plateaus, thus breaking the molecule up into independent parts that can each be treated individually. The method is easily modified to incorporate changes in the assignment of statistical weights to the different structural features of DNA. We illustrate the method using the genome of Haemophilus influenzae. Copyright 2003 Wiley Periodicals, Inc.

Sparse matrix multiplications for linear scaling electronic structure calculations in an atom-centered basis set using multiatom blocks.

PubMed

Saravanan, Chandra; Shao, Yihan; Baer, Roi; Ross, Philip N; Head-Gordon, Martin

2003-04-15

A sparse matrix multiplication scheme with multiatom blocks is reported, a tool that can be very useful for developing linear-scaling methods with atom-centered basis functions. Compared to conventional element-by-element sparse matrix multiplication schemes, efficiency is gained by the use of the highly optimized basic linear algebra subroutines (BLAS). However, some sparsity is lost in the multiatom blocking scheme because these matrix blocks will in general contain negligible elements. As a result, an optimal block size that minimizes the CPU time by balancing these two effects is recovered. In calculations on linear alkanes, polyglycines, estane polymers, and water clusters the optimal block size is found to be between 40 and 100 basis functions, where about 55-75% of the machine peak performance was achieved on an IBM RS6000 workstation. In these calculations, the blocked sparse matrix multiplications can be 10 times faster than a standard element-by-element sparse matrix package. Copyright 2003 Wiley Periodicals, Inc. J Comput Chem 24: 618-622, 2003

Massively parallel sparse matrix function calculations with NTPoly

NASA Astrophysics Data System (ADS)

Dawson, William; Nakajima, Takahito

2018-04-01

We present NTPoly, a massively parallel library for computing the functions of sparse, symmetric matrices. The theory of matrix functions is a well developed framework with a wide range of applications including differential equations, graph theory, and electronic structure calculations. One particularly important application area is diagonalization free methods in quantum chemistry. When the input and output of the matrix function are sparse, methods based on polynomial expansions can be used to compute matrix functions in linear time. We present a library based on these methods that can compute a variety of matrix functions. Distributed memory parallelization is based on a communication avoiding sparse matrix multiplication algorithm. OpenMP task parallellization is utilized to implement hybrid parallelization. We describe NTPoly's interface and show how it can be integrated with programs written in many different programming languages. We demonstrate the merits of NTPoly by performing large scale calculations on the K computer.

Exploratory graphical models of functional and structural connectivity patterns for Alzheimer's Disease diagnosis.

PubMed

Ortiz, Andrés; Munilla, Jorge; Álvarez-Illán, Ignacio; Górriz, Juan M; Ramírez, Javier

2015-01-01

Alzheimer's Disease (AD) is the most common neurodegenerative disease in elderly people. Its development has been shown to be closely related to changes in the brain connectivity network and in the brain activation patterns along with structural changes caused by the neurodegenerative process. Methods to infer dependence between brain regions are usually derived from the analysis of covariance between activation levels in the different areas. However, these covariance-based methods are not able to estimate conditional independence between variables to factor out the influence of other regions. Conversely, models based on the inverse covariance, or precision matrix, such as Sparse Gaussian Graphical Models allow revealing conditional independence between regions by estimating the covariance between two variables given the rest as constant. This paper uses Sparse Inverse Covariance Estimation (SICE) methods to learn undirected graphs in order to derive functional and structural connectivity patterns from Fludeoxyglucose (18F-FDG) Position Emission Tomography (PET) data and segmented Magnetic Resonance images (MRI), drawn from the ADNI database, for Control, MCI (Mild Cognitive Impairment Subjects), and AD subjects. Sparse computation fits perfectly here as brain regions usually only interact with a few other areas. The models clearly show different metabolic covariation patters between subject groups, revealing the loss of strong connections in AD and MCI subjects when compared to Controls. Similarly, the variance between GM (Gray Matter) densities of different regions reveals different structural covariation patterns between the different groups. Thus, the different connectivity patterns for controls and AD are used in this paper to select regions of interest in PET and GM images with discriminative power for early AD diagnosis. Finally, functional an structural models are combined to leverage the classification accuracy. The results obtained in this work show the usefulness of the Sparse Gaussian Graphical models to reveal functional and structural connectivity patterns. This information provided by the sparse inverse covariance matrices is not only used in an exploratory way but we also propose a method to use it in a discriminative way. Regression coefficients are used to compute reconstruction errors for the different classes that are then introduced in a SVM for classification. Classification experiments performed using 68 Controls, 70 AD, and 111 MCI images and assessed by cross-validation show the effectiveness of the proposed method.

Novel Fourier-based iterative reconstruction for sparse fan projection using alternating direction total variation minimization

NASA Astrophysics Data System (ADS)

Zhao, Jin; Han-Ming, Zhang; Bin, Yan; Lei, Li; Lin-Yuan, Wang; Ai-Long, Cai

2016-03-01

Sparse-view x-ray computed tomography (CT) imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform (NUFFT) is presented in this work along with advanced total variation (TV) regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively. Projected supported by the National High Technology Research and Development Program of China (Grant No. 2012AA011603) and the National Natural Science Foundation of China (Grant No. 61372172).

Research on Synthesis of Concurrent Computing Systems.

DTIC Science & Technology

1982-09-01

20 1.5.1 An Informal Description of the Techniques ....... ..................... 20 1.5 2 Formal Definitions of Aggregation and Virtualisation ...sparsely interconnected networks . We have also developed techniques to create Kung’s systolic array parallel structure from a specification of matrix...resufts of the computation of that element. For example, if A,j is computed using a single enumeration, then virtualisation would produce a three

Disentangling giant component and finite cluster contributions in sparse random matrix spectra.

PubMed

Kühn, Reimer

2016-04-01

We describe a method for disentangling giant component and finite cluster contributions to sparse random matrix spectra, using sparse symmetric random matrices defined on Erdős-Rényi graphs as an example and test bed. Our methods apply to sparse matrices defined in terms of arbitrary graphs in the configuration model class, as long as they have finite mean degree.

A compressive sensing-based computational method for the inversion of wide-band ground penetrating radar data

NASA Astrophysics Data System (ADS)

Gelmini, A.; Gottardi, G.; Moriyama, T.

2017-10-01

This work presents an innovative computational approach for the inversion of wideband ground penetrating radar (GPR) data. The retrieval of the dielectric characteristics of sparse scatterers buried in a lossy soil is performed by combining a multi-task Bayesian compressive sensing (MT-BCS) solver and a frequency hopping (FH) strategy. The developed methodology is able to benefit from the regularization capabilities of the MT-BCS as well as to exploit the multi-chromatic informative content of GPR measurements. A set of numerical results is reported in order to assess the effectiveness of the proposed GPR inverse scattering technique, as well as to compare it to a simpler single-task implementation.

Compressive sensing using optimized sensing matrix for face verification

NASA Astrophysics Data System (ADS)

Oey, Endra; Jeffry; Wongso, Kelvin; Tommy

2017-12-01

Biometric appears as one of the solutions which is capable in solving problems that occurred in the usage of password in terms of data access, for example there is possibility in forgetting password and hard to recall various different passwords. With biometrics, physical characteristics of a person can be captured and used in the identification process. In this research, facial biometric is used in the verification process to determine whether the user has the authority to access the data or not. Facial biometric is chosen as its low cost implementation and generate quite accurate result for user identification. Face verification system which is adopted in this research is Compressive Sensing (CS) technique, in which aims to reduce dimension size as well as encrypt data in form of facial test image where the image is represented in sparse signals. Encrypted data can be reconstructed using Sparse Coding algorithm. Two types of Sparse Coding namely Orthogonal Matching Pursuit (OMP) and Iteratively Reweighted Least Squares -ℓp (IRLS-ℓp) will be used for comparison face verification system research. Reconstruction results of sparse signals are then used to find Euclidean norm with the sparse signal of user that has been previously saved in system to determine the validity of the facial test image. Results of system accuracy obtained in this research are 99% in IRLS with time response of face verification for 4.917 seconds and 96.33% in OMP with time response of face verification for 0.4046 seconds with non-optimized sensing matrix, while 99% in IRLS with time response of face verification for 13.4791 seconds and 98.33% for OMP with time response of face verification for 3.1571 seconds with optimized sensing matrix.

Hybrid Weighted Minimum Norm Method A new method based LORETA to solve EEG inverse problem.

PubMed

Song, C; Zhuang, T; Wu, Q

2005-01-01

This Paper brings forward a new method to solve EEG inverse problem. Based on following physiological characteristic of neural electrical activity source: first, the neighboring neurons are prone to active synchronously; second, the distribution of source space is sparse; third, the active intensity of the sources are high centralized, we take these prior knowledge as prerequisite condition to develop the inverse solution of EEG, and not assume other characteristic of inverse solution to realize the most commonly 3D EEG reconstruction map. The proposed algorithm takes advantage of LORETA's low resolution method which emphasizes particularly on 'localization' and FOCUSS's high resolution method which emphasizes particularly on 'separability'. The method is still under the frame of the weighted minimum norm method. The keystone is to construct a weighted matrix which takes reference from the existing smoothness operator, competition mechanism and study algorithm. The basic processing is to obtain an initial solution's estimation firstly, then construct a new estimation using the initial solution's information, repeat this process until the solutions under last two estimate processing is keeping unchanged.

Improved microseismic event locations through large-N arrays and wave-equation imaging and inversion

NASA Astrophysics Data System (ADS)

Witten, B.; Shragge, J. C.

2016-12-01

The recent increased focus on small-scale seismicity, Mw < 4 has come about primarily for two reasons. First, there is an increase in induced seismicity related to injection operations primarily for wastewater disposal and hydraulic fracturing for oil and gas recovery and for geothermal energy production. While the seismicity associated with injection is sometimes felt, it is more often weak. Some weak events are detected on current sparse arrays; however, accurate location of the events often requires a larger number of (multi-component) sensors. This leads to the second reason for an increased focus on small magnitude seismicity: a greater number of seismometers are being deployed in large N-arrays. The greater number of sensors decreases the detection threshold and therefore significantly increases the number of weak events found. Overall, these two factors bring new challenges and opportunities. Many standard seismological location and inversion techniques are geared toward large, easily identifiable events recorded on a sparse number of stations. However, with large-N arrays we can detect small events by utilizing multi-trace processing techniques, and increased processing power equips us with tools that employ more complete physics for simultaneously locating events and inverting for P- and S-wave velocity structure. We present a method that uses large-N arrays and wave-equation-based imaging and inversion to jointly locate earthquakes and estimate the elastic velocities of the earth. The technique requires no picking and is thus suitable for weak events. We validate the methodology through synthetic and field data examples.

Structural performance analysis and redesign

NASA Technical Reports Server (NTRS)

Whetstone, W. D.

1978-01-01

Program performs stress buckling and vibrational analysis of large, linear, finite-element systems in excess of 50,000 degrees of freedom. Cost, execution time, and storage requirements are kept reasonable through use of sparse matrix solution techniques, and other computational and data management procedures designed for problems of very large size.

Adaptive Inverse Control for Rotorcraft Vibration Reduction

NASA Technical Reports Server (NTRS)

Jacklin, Stephen A.

1985-01-01

This thesis extends the Least Mean Square (LMS) algorithm to solve the mult!ple-input, multiple-output problem of alleviating N/Rev (revolutions per minute by number of blades) helicopter fuselage vibration by means of adaptive inverse control. A frequency domain locally linear model is used to represent the transfer matrix relating the higher harmonic pitch control inputs to the harmonic vibration outputs to be controlled. By using the inverse matrix as the controller gain matrix, an adaptive inverse regulator is formed to alleviate the N/Rev vibration. The stability and rate of convergence properties of the extended LMS algorithm are discussed. It is shown that the stability ranges for the elements of the stability gain matrix are directly related to the eigenvalues of the vibration signal information matrix for the learning phase, but not for the control phase. The overall conclusion is that the LMS adaptive inverse control method can form a robust vibration control system, but will require some tuning of the input sensor gains, the stability gain matrix, and the amount of control relaxation to be used. The learning curve of the controller during the learning phase is shown to be quantitatively close to that predicted by averaging the learning curves of the normal modes. For higher order transfer matrices, a rough estimate of the inverse is needed to start the algorithm efficiently. The simulation results indicate that the factor which most influences LMS adaptive inverse control is the product of the control relaxation and the the stability gain matrix. A small stability gain matrix makes the controller less sensitive to relaxation selection, and permits faster and more stable vibration reduction, than by choosing the stability gain matrix large and the control relaxation term small. It is shown that the best selections of the stability gain matrix elements and the amount of control relaxation is basically a compromise between slow, stable convergence and fast convergence with increased possibility of unstable identification. In the simulation studies, the LMS adaptive inverse control algorithm is shown to be capable of adapting the inverse (controller) matrix to track changes in the flight conditions. The algorithm converges quickly for moderate disturbances, while taking longer for larger disturbances. Perfect knowledge of the inverse matrix is not required for good control of the N/Rev vibration. However it is shown that measurement noise will prevent the LMS adaptive inverse control technique from controlling the vibration, unless the signal averaging method presented is incorporated into the algorithm.

Track monitoring from the dynamic response of a passing train: A sparse approach

NASA Astrophysics Data System (ADS)

Lederman, George; Chen, Siheng; Garrett, James H.; Kovačević, Jelena; Noh, Hae Young; Bielak, Jacobo

2017-06-01

Collecting vibration data from revenue service trains could be a low-cost way to more frequently monitor railroad tracks, yet operational variability makes robust analysis a challenge. We propose a novel analysis technique for track monitoring that exploits the sparsity inherent in train-vibration data. This sparsity is based on the observation that large vertical train vibrations typically involve the excitation of the train's fundamental mode due to track joints, switchgear, or other discrete hardware. Rather than try to model the entire rail profile, in this study we examine a sparse approach to solving an inverse problem where (1) the roughness is constrained to a discrete and limited set of "bumps"; and (2) the train system is idealized as a simple damped oscillator that models the train's vibration in the fundamental mode. We use an expectation maximization (EM) approach to iteratively solve for the track profile and the train system properties, using orthogonal matching pursuit (OMP) to find the sparse approximation within each step. By enforcing sparsity, the inverse problem is well posed and the train's position can be found relative to the sparse bumps, thus reducing the uncertainty in the GPS data. We validate the sparse approach on two sections of track monitored from an operational train over a 16 month period of time, one where track changes did not occur during this period and another where changes did occur. We show that this approach can not only detect when track changes occur, but also offers insight into the type of such changes.

Crystallization of bFGF-DNA Aptamer Complexes Using a Sparse Matrix Designed for Protein-Nucleic Acid Complexes

NASA Technical Reports Server (NTRS)

Cannone, Jaime J.; Barnes, Cindy L.; Achari, Aniruddha; Kundrot, Craig E.; Whitaker, Ann F. (Technical Monitor)

2001-01-01

The Sparse Matrix approach for obtaining lead crystallization conditions has proven to be very fruitful for the crystallization of proteins and nucleic acids. Here we report a Sparse Matrix developed specifically for the crystallization of protein-DNA complexes. This method is rapid and economical, typically requiring 2.5 mg of complex to test 48 conditions. The method was originally developed to crystallize basic fibroblast growth factor (bFGF) complexed with DNA sequences identified through in vitro selection, or SELEX, methods. Two DNA aptamers that bind with approximately nanomolar affinity and inhibit the angiogenic properties of bFGF were selected for co-crystallization. The Sparse Matrix produced lead crystallization conditions for both bFGF-DNA complexes.

High-SNR spectrum measurement based on Hadamard encoding and sparse reconstruction

NASA Astrophysics Data System (ADS)

Wang, Zhaoxin; Yue, Jiang; Han, Jing; Li, Long; Jin, Yong; Gao, Yuan; Li, Baoming

2017-12-01

The denoising capabilities of the H-matrix and cyclic S-matrix based on the sparse reconstruction, employed in the Pixel of Focal Plane Coded Visible Spectrometer for spectrum measurement are investigated, where the spectrum is sparse in a known basis. In the measurement process, the digital micromirror device plays an important role, which implements the Hadamard coding. In contrast with Hadamard transform spectrometry, based on the shift invariability, this spectrometer may have the advantage of a high efficiency. Simulations and experiments show that the nonlinear solution with a sparse reconstruction has a better signal-to-noise ratio than the linear solution and the H-matrix outperforms the cyclic S-matrix whether the reconstruction method is nonlinear or linear.

Thermodynamic characterization of synchronization-optimized oscillator networks

NASA Astrophysics Data System (ADS)

Yanagita, Tatsuo; Ichinomiya, Takashi

2014-12-01

We consider a canonical ensemble of synchronization-optimized networks of identical oscillators under external noise. By performing a Markov chain Monte Carlo simulation using the Kirchhoff index, i.e., the sum of the inverse eigenvalues of the Laplacian matrix (as a graph Hamiltonian of the network), we construct more than 1 000 different synchronization-optimized networks. We then show that the transition from star to core-periphery structure depends on the connectivity of the network, and is characterized by the node degree variance of the synchronization-optimized ensemble. We find that thermodynamic properties such as heat capacity show anomalies for sparse networks.

Label consistent K-SVD: learning a discriminative dictionary for recognition.

PubMed

Jiang, Zhuolin; Lin, Zhe; Davis, Larry S

2013-11-01

A label consistent K-SVD (LC-KSVD) algorithm to learn a discriminative dictionary for sparse coding is presented. In addition to using class labels of training data, we also associate label information with each dictionary item (columns of the dictionary matrix) to enforce discriminability in sparse codes during the dictionary learning process. More specifically, we introduce a new label consistency constraint called "discriminative sparse-code error" and combine it with the reconstruction error and the classification error to form a unified objective function. The optimal solution is efficiently obtained using the K-SVD algorithm. Our algorithm learns a single overcomplete dictionary and an optimal linear classifier jointly. The incremental dictionary learning algorithm is presented for the situation of limited memory resources. It yields dictionaries so that feature points with the same class labels have similar sparse codes. Experimental results demonstrate that our algorithm outperforms many recently proposed sparse-coding techniques for face, action, scene, and object category recognition under the same learning conditions.

Algorithms and software for solving finite element equations on serial and parallel architectures

NASA Technical Reports Server (NTRS)

Chu, Eleanor; George, Alan

1988-01-01

The primary objective was to compare the performance of state-of-the-art techniques for solving sparse systems with those that are currently available in the Computational Structural Mechanics (MSC) testbed. One of the first tasks was to become familiar with the structure of the testbed, and to install some or all of the SPARSPAK package in the testbed. A brief overview of the CSM Testbed software and its usage is presented. An overview of the sparse matrix research for the Testbed currently employed in the CSM Testbed is given. An interface which was designed and implemented as a research tool for installing and appraising new matrix processors in the CSM Testbed is described. The results of numerical experiments performed in solving a set of testbed demonstration problems using the processor SPK and other experimental processors are contained.

Computing row and column counts for sparse QR and LU factorization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gilbert, John R.; Li, Xiaoye S.; Ng, Esmond G.

2001-01-01

We present algorithms to determine the number of nonzeros in each row and column of the factors of a sparse matrix, for both the QR factorization and the LU factorization with partial pivoting. The algorithms use only the nonzero structure of the input matrix, and run in time nearly linear in the number of nonzeros in that matrix. They may be used to set up data structures or schedule parallel operations in advance of the numerical factorization. The row and column counts we compute are upper bounds on the actual counts. If the input matrix is strong Hall and theremore » is no coincidental numerical cancellation, the counts are exact for QR factorization and are the tightest bounds possible for LU factorization. These algorithms are based on our earlier work on computing row and column counts for sparse Cholesky factorization, plus an efficient method to compute the column elimination tree of a sparse matrix without explicitly forming the product of the matrix and its transpose.« less

Performance comparisons on spatial lattice algorithm and direct matrix inverse method with application to adaptive arrays processing

NASA Technical Reports Server (NTRS)

An, S. H.; Yao, K.

1986-01-01

Lattice algorithm has been employed in numerous adaptive filtering applications such as speech analysis/synthesis, noise canceling, spectral analysis, and channel equalization. In this paper the application to adaptive-array processing is discussed. The advantages are fast convergence rate as well as computational accuracy independent of the noise and interference conditions. The results produced by this technique are compared to those obtained by the direct matrix inverse method.

Sample-Starved Large Scale Network Analysis

DTIC Science & Technology

2016-05-05

As reported in our journal publication (G. Marjanovic and A. O. Hero, ”l0 Sparse Inverse Covariance Estimation,” IEEE Trans on Signal Processing, vol... Marjanovic and A. O. Hero, ”l0 Sparse Inverse Covariance Estimation,” in IEEE Trans on Signal Processing, vol. 63, no. 12, pp. 3218-3231, May 2015. 6. G

Single-Sided Noinvasive Inspection of Multielement Sample Using Fan-Beam Multiplexed Compton Scatter Tomography

DTIC Science & Technology

2000-05-01

a vector , ρ "# represents the set of voxel densities sorted into a vector , and ( )A ρ $# "# represents a 8 mapping of the voxel densities to...density vector in equation (4) suggests that solving for ρ "# by direct inversion is not possible, calling for an iterative technique beginning with...the vector of measured spectra, and D is the diagonal matrix of the inverse of the variances. The diagonal matrix provides weighting terms, which

Disconnected Diagrams in Lattice QCD

NASA Astrophysics Data System (ADS)

Gambhir, Arjun Singh

In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called "disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagrams is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements of the nucleon at two different values of the lattice spacing. Finally, we employ these algorithms to do a high-precision study of strange sigma terms in light nuclei; to our knowledge this is the first calculation of its kind from Lattice QCD.

Disconnected Diagrams in Lattice QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gambhir, Arjun

In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called \\disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagramsmore » is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements of the nucleon at two different values of the lattice spacing. Finally, we employ these algorithms to do a high-precision study of strange sigma terms in light nuclei; to our knowledge this is the first calculation of its kind from Lattice QCD.« less

Filling gaps in large ecological databases: consequences for the study of global-scale plant functional trait patterns

NASA Astrophysics Data System (ADS)

Schrodt, Franziska; Shan, Hanhuai; Fazayeli, Farideh; Karpatne, Anuj; Kattge, Jens; Banerjee, Arindam; Reichstein, Markus; Reich, Peter

2013-04-01

With the advent of remotely sensed data and coordinated efforts to create global databases, the ecological community has progressively become more data-intensive. However, in contrast to other disciplines, statistical ways of handling these large data sets, especially the gaps which are inherent to them, are lacking. Widely used theoretical approaches, for example model averaging based on Akaike's information criterion (AIC), are sensitive to missing values. Yet, the most common way of handling sparse matrices - the deletion of cases with missing data (complete case analysis) - is known to severely reduce statistical power as well as inducing biased parameter estimates. In order to address these issues, we present novel approaches to gap filling in large ecological data sets using matrix factorization techniques. Factorization based matrix completion was developed in a recommender system context and has since been widely used to impute missing data in fields outside the ecological community. Here, we evaluate the effectiveness of probabilistic matrix factorization techniques for imputing missing data in ecological matrices using two imputation techniques. Hierarchical Probabilistic Matrix Factorization (HPMF) effectively incorporates hierarchical phylogenetic information (phylogenetic group, family, genus, species and individual plant) into the trait imputation. Advanced Hierarchical Probabilistic Matrix Factorization (aHPMF) on the other hand includes climate and soil information into the matrix factorization by regressing the environmental variables against residuals of the HPMF. One unique opportunity opened up by aHPMF is out-of-sample prediction, where traits can be predicted for specific species at locations different to those sampled in the past. This has potentially far-reaching consequences for the study of global-scale plant functional trait patterns. We test the accuracy and effectiveness of HPMF and aHPMF in filling sparse matrices, using the TRY database of plant functional traits (http://www.try-db.org). TRY is one of the largest global compilations of plant trait databases (750 traits of 1 million plants), encompassing data on morphological, anatomical, biochemical, phenological and physiological features of plants. However, despite of unprecedented coverage, the TRY database is still very sparse, severely limiting joint trait analyses. Plant traits are the key to understanding how plants as primary producers adjust to changes in environmental conditions and in turn influence them. Forming the basis for Dynamic Global Vegetation Models (DGVMs), plant traits are also fundamental in global change studies for predicting future ecosystem changes. It is thus imperative that missing data is imputed in as accurate and precise a way as possible. In this study, we show the advantages and disadvantages of applying probabilistic matrix factorization techniques in incorporating hierarchical and environmental information for the prediction of missing plant traits as compared to conventional imputation techniques such as the complete case and mean approaches. We will discuss the implications of using gap-filled data for global-scale studies of plant functional trait - environment relationship as opposed to the above-mentioned conventional techniques, using examples of out-of-sample predictions of foliar Nitrogen across several species' ranges and biomes.

Systematic sparse matrix error control for linear scaling electronic structure calculations.

PubMed

Rubensson, Emanuel H; Sałek, Paweł

2005-11-30

Efficient truncation criteria used in multiatom blocked sparse matrix operations for ab initio calculations are proposed. As system size increases, so does the need to stay on top of errors and still achieve high performance. A variant of a blocked sparse matrix algebra to achieve strict error control with good performance is proposed. The presented idea is that the condition to drop a certain submatrix should depend not only on the magnitude of that particular submatrix, but also on which other submatrices that are dropped. The decision to remove a certain submatrix is based on the contribution the removal would cause to the error in the chosen norm. We study the effect of an accumulated truncation error in iterative algorithms like trace correcting density matrix purification. One way to reduce the initial exponential growth of this error is presented. The presented error control for a sparse blocked matrix toolbox allows for achieving optimal performance by performing only necessary operations needed to maintain the requested level of accuracy. Copyright 2005 Wiley Periodicals, Inc.

Parallel Preconditioning for CFD Problems on the CM-5

NASA Technical Reports Server (NTRS)

Simon, Horst D.; Kremenetsky, Mark D.; Richardson, John; Lasinski, T. A. (Technical Monitor)

1994-01-01

Up to today, preconditioning methods on massively parallel systems have faced a major difficulty. The most successful preconditioning methods in terms of accelerating the convergence of the iterative solver such as incomplete LU factorizations are notoriously difficult to implement on parallel machines for two reasons: (1) the actual computation of the preconditioner is not very floating-point intensive, but requires a large amount of unstructured communication, and (2) the application of the preconditioning matrix in the iteration phase (i.e. triangular solves) are difficult to parallelize because of the recursive nature of the computation. Here we present a new approach to preconditioning for very large, sparse, unsymmetric, linear systems, which avoids both difficulties. We explicitly compute an approximate inverse to our original matrix. This new preconditioning matrix can be applied most efficiently for iterative methods on massively parallel machines, since the preconditioning phase involves only a matrix-vector multiplication, with possibly a dense matrix. Furthermore the actual computation of the preconditioning matrix has natural parallelism. For a problem of size n, the preconditioning matrix can be computed by solving n independent small least squares problems. The algorithm and its implementation on the Connection Machine CM-5 are discussed in detail and supported by extensive timings obtained from real problem data.

Method and apparatus for optimized processing of sparse matrices

DOEpatents

Taylor, Valerie E.

1993-01-01

A computer architecture for processing a sparse matrix is disclosed. The apparatus stores a value-row vector corresponding to nonzero values of a sparse matrix. Each of the nonzero values is located at a defined row and column position in the matrix. The value-row vector includes a first vector including nonzero values and delimiting characters indicating a transition from one column to another. The value-row vector also includes a second vector which defines row position values in the matrix corresponding to the nonzero values in the first vector and column position values in the matrix corresponding to the column position of the nonzero values in the first vector. The architecture also includes a circuit for detecting a special character within the value-row vector. Matrix-vector multiplication is executed on the value-row vector. This multiplication is performed by multiplying an index value of the first vector value by a column value from a second matrix to form a matrix-vector product which is added to a previous matrix-vector product.

Fast image decompression for telebrowsing of images

NASA Technical Reports Server (NTRS)

Miaou, Shaou-Gang; Tou, Julius T.

1993-01-01

Progressive image transmission (PIT) is often used to reduce the transmission time of an image telebrowsing system. A side effect of the PIT is the increase of computational complexity at the viewer's site. This effect is more serious in transform domain techniques than in other techniques. Recent attempts to reduce the side effect are futile as they create another side effect, namely, the discontinuous and unpleasant image build-up. Based on a practical assumption that image blocks to be inverse transformed are generally sparse, this paper presents a method to minimize both side effects simultaneously.

A sparse matrix-vector multiplication based algorithm for accurate density matrix computations on systems of millions of atoms

NASA Astrophysics Data System (ADS)

Ghale, Purnima; Johnson, Harley T.

2018-06-01

We present an efficient sparse matrix-vector (SpMV) based method to compute the density matrix P from a given Hamiltonian in electronic structure computations. Our method is a hybrid approach based on Chebyshev-Jackson approximation theory and matrix purification methods like the second order spectral projection purification (SP2). Recent methods to compute the density matrix scale as O(N) in the number of floating point operations but are accompanied by large memory and communication overhead, and they are based on iterative use of the sparse matrix-matrix multiplication kernel (SpGEMM), which is known to be computationally irregular. In addition to irregularity in the sparse Hamiltonian H, the nonzero structure of intermediate estimates of P depends on products of H and evolves over the course of computation. On the other hand, an expansion of the density matrix P in terms of Chebyshev polynomials is straightforward and SpMV based; however, the resulting density matrix may not satisfy the required constraints exactly. In this paper, we analyze the strengths and weaknesses of the Chebyshev-Jackson polynomials and the second order spectral projection purification (SP2) method, and propose to combine them so that the accurate density matrix can be computed using the SpMV computational kernel only, and without having to store the density matrix P. Our method accomplishes these objectives by using the Chebyshev polynomial estimate as the initial guess for SP2, which is followed by using sparse matrix-vector multiplications (SpMVs) to replicate the behavior of the SP2 algorithm for purification. We demonstrate the method on a tight-binding model system of an oxide material containing more than 3 million atoms. In addition, we also present the predicted behavior of our method when applied to near-metallic Hamiltonians with a wide energy spectrum.

Comparative interpretations of renormalization inversion technique for reconstructing unknown emissions from measured atmospheric concentrations

NASA Astrophysics Data System (ADS)

Singh, Sarvesh Kumar; Kumar, Pramod; Rani, Raj; Turbelin, Grégory

2017-04-01

The study highlights a theoretical comparison and various interpretations of a recent inversion technique, called renormalization, developed for the reconstruction of unknown tracer emissions from their measured concentrations. The comparative interpretations are presented in relation to the other inversion techniques based on principle of regularization, Bayesian, minimum norm, maximum entropy on mean, and model resolution optimization. It is shown that the renormalization technique can be interpreted in a similar manner to other techniques, with a practical choice of a priori information and error statistics, while eliminating the need of additional constraints. The study shows that the proposed weight matrix and weighted Gram matrix offer a suitable deterministic choice to the background error and measurement covariance matrices, respectively, in the absence of statistical knowledge about background and measurement errors. The technique is advantageous since it (i) utilizes weights representing a priori information apparent to the monitoring network, (ii) avoids dependence on background source estimates, (iii) improves on alternative choices for the error statistics, (iv) overcomes the colocalization problem in a natural manner, and (v) provides an optimally resolved source reconstruction. A comparative illustration of source retrieval is made by using the real measurements from a continuous point release conducted in Fusion Field Trials, Dugway Proving Ground, Utah.

Incomplete Sparse Approximate Inverses for Parallel Preconditioning

DOE PAGES

Anzt, Hartwig; Huckle, Thomas K.; Bräckle, Jürgen; ...

2017-10-28

In this study, we propose a new preconditioning method that can be seen as a generalization of block-Jacobi methods, or as a simplification of the sparse approximate inverse (SAI) preconditioners. The “Incomplete Sparse Approximate Inverses” (ISAI) is in particular efficient in the solution of sparse triangular linear systems of equations. Those arise, for example, in the context of incomplete factorization preconditioning. ISAI preconditioners can be generated via an algorithm providing fine-grained parallelism, which makes them attractive for hardware with a high concurrency level. Finally, in a study covering a large number of matrices, we identify the ISAI preconditioner as anmore » attractive alternative to exact triangular solves in the context of incomplete factorization preconditioning.« less

A sparse reconstruction method for the estimation of multi-resolution emission fields via atmospheric inversion

DOE PAGES

Ray, J.; Lee, J.; Yadav, V.; ...

2015-04-29

Atmospheric inversions are frequently used to estimate fluxes of atmospheric greenhouse gases (e.g., biospheric CO 2 flux fields) at Earth's surface. These inversions typically assume that flux departures from a prior model are spatially smoothly varying, which are then modeled using a multi-variate Gaussian. When the field being estimated is spatially rough, multi-variate Gaussian models are difficult to construct and a wavelet-based field model may be more suitable. Unfortunately, such models are very high dimensional and are most conveniently used when the estimation method can simultaneously perform data-driven model simplification (removal of model parameters that cannot be reliably estimated) andmore » fitting. Such sparse reconstruction methods are typically not used in atmospheric inversions. In this work, we devise a sparse reconstruction method, and illustrate it in an idealized atmospheric inversion problem for the estimation of fossil fuel CO 2 (ffCO 2) emissions in the lower 48 states of the USA. Our new method is based on stagewise orthogonal matching pursuit (StOMP), a method used to reconstruct compressively sensed images. Our adaptations bestow three properties to the sparse reconstruction procedure which are useful in atmospheric inversions. We have modified StOMP to incorporate prior information on the emission field being estimated and to enforce non-negativity on the estimated field. Finally, though based on wavelets, our method allows for the estimation of fields in non-rectangular geometries, e.g., emission fields inside geographical and political boundaries. Our idealized inversions use a recently developed multi-resolution (i.e., wavelet-based) random field model developed for ffCO 2 emissions and synthetic observations of ffCO 2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of 2. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.« less

A sparse reconstruction method for the estimation of multi-resolution emission fields via atmospheric inversion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ray, J.; Lee, J.; Yadav, V.

Atmospheric inversions are frequently used to estimate fluxes of atmospheric greenhouse gases (e.g., biospheric CO 2 flux fields) at Earth's surface. These inversions typically assume that flux departures from a prior model are spatially smoothly varying, which are then modeled using a multi-variate Gaussian. When the field being estimated is spatially rough, multi-variate Gaussian models are difficult to construct and a wavelet-based field model may be more suitable. Unfortunately, such models are very high dimensional and are most conveniently used when the estimation method can simultaneously perform data-driven model simplification (removal of model parameters that cannot be reliably estimated) andmore » fitting. Such sparse reconstruction methods are typically not used in atmospheric inversions. In this work, we devise a sparse reconstruction method, and illustrate it in an idealized atmospheric inversion problem for the estimation of fossil fuel CO 2 (ffCO 2) emissions in the lower 48 states of the USA. Our new method is based on stagewise orthogonal matching pursuit (StOMP), a method used to reconstruct compressively sensed images. Our adaptations bestow three properties to the sparse reconstruction procedure which are useful in atmospheric inversions. We have modified StOMP to incorporate prior information on the emission field being estimated and to enforce non-negativity on the estimated field. Finally, though based on wavelets, our method allows for the estimation of fields in non-rectangular geometries, e.g., emission fields inside geographical and political boundaries. Our idealized inversions use a recently developed multi-resolution (i.e., wavelet-based) random field model developed for ffCO 2 emissions and synthetic observations of ffCO 2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of 2. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.« less

Compressed sensing for energy-efficient wireless telemonitoring of noninvasive fetal ECG via block sparse Bayesian learning.

PubMed

Zhang, Zhilin; Jung, Tzyy-Ping; Makeig, Scott; Rao, Bhaskar D

2013-02-01

Fetal ECG (FECG) telemonitoring is an important branch in telemedicine. The design of a telemonitoring system via a wireless body area network with low energy consumption for ambulatory use is highly desirable. As an emerging technique, compressed sensing (CS) shows great promise in compressing/reconstructing data with low energy consumption. However, due to some specific characteristics of raw FECG recordings such as nonsparsity and strong noise contamination, current CS algorithms generally fail in this application. This paper proposes to use the block sparse Bayesian learning framework to compress/reconstruct nonsparse raw FECG recordings. Experimental results show that the framework can reconstruct the raw recordings with high quality. Especially, the reconstruction does not destroy the interdependence relation among the multichannel recordings. This ensures that the independent component analysis decomposition of the reconstructed recordings has high fidelity. Furthermore, the framework allows the use of a sparse binary sensing matrix with much fewer nonzero entries to compress recordings. Particularly, each column of the matrix can contain only two nonzero entries. This shows that the framework, compared to other algorithms such as current CS algorithms and wavelet algorithms, can greatly reduce code execution in CPU in the data compression stage.

Sparse subspace clustering for data with missing entries and high-rank matrix completion.

PubMed

Fan, Jicong; Chow, Tommy W S

2017-09-01

Many methods have recently been proposed for subspace clustering, but they are often unable to handle incomplete data because of missing entries. Using matrix completion methods to recover missing entries is a common way to solve the problem. Conventional matrix completion methods require that the matrix should be of low-rank intrinsically, but most matrices are of high-rank or even full-rank in practice, especially when the number of subspaces is large. In this paper, a new method called Sparse Representation with Missing Entries and Matrix Completion is proposed to solve the problems of incomplete-data subspace clustering and high-rank matrix completion. The proposed algorithm alternately computes the matrix of sparse representation coefficients and recovers the missing entries of a data matrix. The proposed algorithm recovers missing entries through minimizing the representation coefficients, representation errors, and matrix rank. Thorough experimental study and comparative analysis based on synthetic data and natural images were conducted. The presented results demonstrate that the proposed algorithm is more effective in subspace clustering and matrix completion compared with other existing methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

NoGOA: predicting noisy GO annotations using evidences and sparse representation.

PubMed

Yu, Guoxian; Lu, Chang; Wang, Jun

2017-07-21

Gene Ontology (GO) is a community effort to represent functional features of gene products. GO annotations (GOA) provide functional associations between GO terms and gene products. Due to resources limitation, only a small portion of annotations are manually checked by curators, and the others are electronically inferred. Although quality control techniques have been applied to ensure the quality of annotations, the community consistently report that there are still considerable noisy (or incorrect) annotations. Given the wide application of annotations, however, how to identify noisy annotations is an important but yet seldom studied open problem. We introduce a novel approach called NoGOA to predict noisy annotations. NoGOA applies sparse representation on the gene-term association matrix to reduce the impact of noisy annotations, and takes advantage of sparse representation coefficients to measure the semantic similarity between genes. Secondly, it preliminarily predicts noisy annotations of a gene based on aggregated votes from semantic neighborhood genes of that gene. Next, NoGOA estimates the ratio of noisy annotations for each evidence code based on direct annotations in GOA files archived on different periods, and then weights entries of the association matrix via estimated ratios and propagates weights to ancestors of direct annotations using GO hierarchy. Finally, it integrates evidence-weighted association matrix and aggregated votes to predict noisy annotations. Experiments on archived GOA files of six model species (H. sapiens, A. thaliana, S. cerevisiae, G. gallus, B. Taurus and M. musculus) demonstrate that NoGOA achieves significantly better results than other related methods and removing noisy annotations improves the performance of gene function prediction. The comparative study justifies the effectiveness of integrating evidence codes with sparse representation for predicting noisy GO annotations. Codes and datasets are available at http://mlda.swu.edu.cn/codes.php?name=NoGOA .

Symmetrized density matrix renormalization group algorithm for low-lying excited states of conjugated carbon systems: Application to 1,12-benzoperylene and polychrysene

NASA Astrophysics Data System (ADS)

Prodhan, Suryoday; Ramasesha, S.

2018-05-01

The symmetry adapted density matrix renormalization group (SDMRG) technique has been an efficient method for studying low-lying eigenstates in one- and quasi-one-dimensional electronic systems. However, the SDMRG method had bottlenecks involving the construction of linearly independent symmetry adapted basis states as the symmetry matrices in the DMRG basis were not sparse. We have developed a modified algorithm to overcome this bottleneck. The new method incorporates end-to-end interchange symmetry (C2) , electron-hole symmetry (J ) , and parity or spin-flip symmetry (P ) in these calculations. The one-to-one correspondence between direct-product basis states in the DMRG Hilbert space for these symmetry operations renders the symmetry matrices in the new basis with maximum sparseness, just one nonzero matrix element per row. Using methods similar to those employed in the exact diagonalization technique for Pariser-Parr-Pople (PPP) models, developed in the 1980s, it is possible to construct orthogonal SDMRG basis states while bypassing the slow step of the Gram-Schmidt orthonormalization procedure. The method together with the PPP model which incorporates long-range electronic correlations is employed to study the correlated excited-state spectra of 1,12-benzoperylene and a narrow mixed graphene nanoribbon with a chrysene molecule as the building unit, comprising both zigzag and cove-edge structures.

Efficient 3D inversions using the Richards equation

NASA Astrophysics Data System (ADS)

Cockett, Rowan; Heagy, Lindsey J.; Haber, Eldad

2018-07-01

Fluid flow in the vadose zone is governed by the Richards equation; it is parameterized by hydraulic conductivity, which is a nonlinear function of pressure head. Investigations in the vadose zone typically require characterizing distributed hydraulic properties. Water content or pressure head data may include direct measurements made from boreholes. Increasingly, proxy measurements from hydrogeophysics are being used to supply more spatially and temporally dense data sets. Inferring hydraulic parameters from such datasets requires the ability to efficiently solve and optimize the nonlinear time domain Richards equation. This is particularly important as the number of parameters to be estimated in a vadose zone inversion continues to grow. In this paper, we describe an efficient technique to invert for distributed hydraulic properties in 1D, 2D, and 3D. Our technique does not store the Jacobian matrix, but rather computes its product with a vector. Existing literature for the Richards equation inversion explicitly calculates the sensitivity matrix using finite difference or automatic differentiation, however, for large scale problems these methods are constrained by computation and/or memory. Using an implicit sensitivity algorithm enables large scale inversion problems for any distributed hydraulic parameters in the Richards equation to become tractable on modest computational resources. We provide an open source implementation of our technique based on the SimPEG framework, and show it in practice for a 3D inversion of saturated hydraulic conductivity using water content data through time.

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pinski, Peter; Riplinger, Christoph; Neese, Frank, E-mail: evaleev@vt.edu, E-mail: frank.neese@cec.mpg.de

2015-07-21

In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data. By combining few elementary operations on sparse maps (inversion, chaining, intersection, etc.), complex algorithms can be developed, illustrated here by a linear-scaling transformation of three-center Coulomb integrals based on our compact code library that implementsmore » sparse maps and operations on them. The sparsity of the three-center integrals arises from spatial locality of the basis functions and domain density fitting approximation. A novel feature of our approach is the use of differential overlap integrals computed in linear-scaling fashion for screening products of basis functions. Finally, a robust linear scaling domain based local pair natural orbital second-order Möller-Plesset (DLPNO-MP2) method is described based on the sparse map infrastructure that only depends on a minimal number of cutoff parameters that can be systematically tightened to approach 100% of the canonical MP2 correlation energy. With default truncation thresholds, DLPNO-MP2 recovers more than 99.9% of the canonical resolution of the identity MP2 (RI-MP2) energy while still showing a very early crossover with respect to the computational effort. Based on extensive benchmark calculations, relative energies are reproduced with an error of typically <0.2 kcal/mol. The efficiency of the local MP2 (LMP2) method can be drastically improved by carrying out the LMP2 iterations in a basis of pair natural orbitals. While the present work focuses on local electron correlation, it is of much broader applicability to computation with sparse tensors in quantum chemistry and beyond.« less

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals.

PubMed

Pinski, Peter; Riplinger, Christoph; Valeev, Edward F; Neese, Frank

2015-07-21

In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data. By combining few elementary operations on sparse maps (inversion, chaining, intersection, etc.), complex algorithms can be developed, illustrated here by a linear-scaling transformation of three-center Coulomb integrals based on our compact code library that implements sparse maps and operations on them. The sparsity of the three-center integrals arises from spatial locality of the basis functions and domain density fitting approximation. A novel feature of our approach is the use of differential overlap integrals computed in linear-scaling fashion for screening products of basis functions. Finally, a robust linear scaling domain based local pair natural orbital second-order Möller-Plesset (DLPNO-MP2) method is described based on the sparse map infrastructure that only depends on a minimal number of cutoff parameters that can be systematically tightened to approach 100% of the canonical MP2 correlation energy. With default truncation thresholds, DLPNO-MP2 recovers more than 99.9% of the canonical resolution of the identity MP2 (RI-MP2) energy while still showing a very early crossover with respect to the computational effort. Based on extensive benchmark calculations, relative energies are reproduced with an error of typically <0.2 kcal/mol. The efficiency of the local MP2 (LMP2) method can be drastically improved by carrying out the LMP2 iterations in a basis of pair natural orbitals. While the present work focuses on local electron correlation, it is of much broader applicability to computation with sparse tensors in quantum chemistry and beyond.

Sparse dictionary learning for resting-state fMRI analysis

NASA Astrophysics Data System (ADS)

Lee, Kangjoo; Han, Paul Kyu; Ye, Jong Chul

2011-09-01

Recently, there has been increased interest in the usage of neuroimaging techniques to investigate what happens in the brain at rest. Functional imaging studies have revealed that the default-mode network activity is disrupted in Alzheimer's disease (AD). However, there is no consensus, as yet, on the choice of analysis method for the application of resting-state analysis for disease classification. This paper proposes a novel compressed sensing based resting-state fMRI analysis tool called Sparse-SPM. As the brain's functional systems has shown to have features of complex networks according to graph theoretical analysis, we apply a graph model to represent a sparse combination of information flows in complex network perspectives. In particular, a new concept of spatially adaptive design matrix has been proposed by implementing sparse dictionary learning based on sparsity. The proposed approach shows better performance compared to other conventional methods, such as independent component analysis (ICA) and seed-based approach, in classifying the AD patients from normal using resting-state analysis.

FPGA implementation of sparse matrix algorithm for information retrieval

NASA Astrophysics Data System (ADS)

Bojanic, Slobodan; Jevtic, Ruzica; Nieto-Taladriz, Octavio

2005-06-01

Information text data retrieval requires a tremendous amount of processing time because of the size of the data and the complexity of information retrieval algorithms. In this paper the solution to this problem is proposed via hardware supported information retrieval algorithms. Reconfigurable computing may adopt frequent hardware modifications through its tailorable hardware and exploits parallelism for a given application through reconfigurable and flexible hardware units. The degree of the parallelism can be tuned for data. In this work we implemented standard BLAS (basic linear algebra subprogram) sparse matrix algorithm named Compressed Sparse Row (CSR) that is showed to be more efficient in terms of storage space requirement and query-processing timing over the other sparse matrix algorithms for information retrieval application. Although inverted index algorithm is treated as the de facto standard for information retrieval for years, an alternative approach to store the index of text collection in a sparse matrix structure gains more attention. This approach performs query processing using sparse matrix-vector multiplication and due to parallelization achieves a substantial efficiency over the sequential inverted index. The parallel implementations of information retrieval kernel are presented in this work targeting the Virtex II Field Programmable Gate Arrays (FPGAs) board from Xilinx. A recent development in scientific applications is the use of FPGA to achieve high performance results. Computational results are compared to implementations on other platforms. The design achieves a high level of parallelism for the overall function while retaining highly optimised hardware within processing unit.

Uniform Recovery Bounds for Structured Random Matrices in Corrupted Compressed Sensing

NASA Astrophysics Data System (ADS)

Zhang, Peng; Gan, Lu; Ling, Cong; Sun, Sumei

2018-04-01

We study the problem of recovering an $s$-sparse signal $\\mathbf{x}^{\\star}\\in\\mathbb{C}^n$ from corrupted measurements $\\mathbf{y} = \\mathbf{A}\\mathbf{x}^{\\star}+\\mathbf{z}^{\\star}+\\mathbf{w}$, where $\\mathbf{z}^{\\star}\\in\\mathbb{C}^m$ is a $k$-sparse corruption vector whose nonzero entries may be arbitrarily large and $\\mathbf{w}\\in\\mathbb{C}^m$ is a dense noise with bounded energy. The aim is to exactly and stably recover the sparse signal with tractable optimization programs. In this paper, we prove the uniform recovery guarantee of this problem for two classes of structured sensing matrices. The first class can be expressed as the product of a unit-norm tight frame (UTF), a random diagonal matrix and a bounded columnwise orthonormal matrix (e.g., partial random circulant matrix). When the UTF is bounded (i.e. $\\mu(\\mathbf{U})\\sim1/\\sqrt{m}$), we prove that with high probability, one can recover an $s$-sparse signal exactly and stably by $l_1$ minimization programs even if the measurements are corrupted by a sparse vector, provided $m = \\mathcal{O}(s \\log^2 s \\log^2 n)$ and the sparsity level $k$ of the corruption is a constant fraction of the total number of measurements. The second class considers randomly sub-sampled orthogonal matrix (e.g., random Fourier matrix). We prove the uniform recovery guarantee provided that the corruption is sparse on certain sparsifying domain. Numerous simulation results are also presented to verify and complement the theoretical results.

Determining biosonar images using sparse representations.

PubMed

Fontaine, Bertrand; Peremans, Herbert

2009-05-01

Echolocating bats are thought to be able to create an image of their environment by emitting pulses and analyzing the reflected echoes. In this paper, the theory of sparse representations and its more recent further development into compressed sensing are applied to this biosonar image formation task. Considering the target image representation as sparse allows formulation of this inverse problem as a convex optimization problem for which well defined and efficient solution methods have been established. The resulting technique, referred to as L1-minimization, is applied to simulated data to analyze its performance relative to delay accuracy and delay resolution experiments. This method performs comparably to the coherent receiver for the delay accuracy experiments, is quite robust to noise, and can reconstruct complex target impulse responses as generated by many closely spaced reflectors with different reflection strengths. This same technique, in addition to reconstructing biosonar target images, can be used to simultaneously localize these complex targets by interpreting location cues induced by the bat's head related transfer function. Finally, a tentative explanation is proposed for specific bat behavioral experiments in terms of the properties of target images as reconstructed by the L1-minimization method.

Matched field localization based on CS-MUSIC algorithm

NASA Astrophysics Data System (ADS)

Guo, Shuangle; Tang, Ruichun; Peng, Linhui; Ji, Xiaopeng

2016-04-01

The problem caused by shortness or excessiveness of snapshots and by coherent sources in underwater acoustic positioning is considered. A matched field localization algorithm based on CS-MUSIC (Compressive Sensing Multiple Signal Classification) is proposed based on the sparse mathematical model of the underwater positioning. The signal matrix is calculated through the SVD (Singular Value Decomposition) of the observation matrix. The observation matrix in the sparse mathematical model is replaced by the signal matrix, and a new concise sparse mathematical model is obtained, which means not only the scale of the localization problem but also the noise level is reduced; then the new sparse mathematical model is solved by the CS-MUSIC algorithm which is a combination of CS (Compressive Sensing) method and MUSIC (Multiple Signal Classification) method. The algorithm proposed in this paper can overcome effectively the difficulties caused by correlated sources and shortness of snapshots, and it can also reduce the time complexity and noise level of the localization problem by using the SVD of the observation matrix when the number of snapshots is large, which will be proved in this paper.

Effect of missing data on multitask prediction methods.

PubMed

de la Vega de León, Antonio; Chen, Beining; Gillet, Valerie J

2018-05-22

There has been a growing interest in multitask prediction in chemoinformatics, helped by the increasing use of deep neural networks in this field. This technique is applied to multitarget data sets, where compounds have been tested against different targets, with the aim of developing models to predict a profile of biological activities for a given compound. However, multitarget data sets tend to be sparse; i.e., not all compound-target combinations have experimental values. There has been little research on the effect of missing data on the performance of multitask methods. We have used two complete data sets to simulate sparseness by removing data from the training set. Different models to remove the data were compared. These sparse sets were used to train two different multitask methods, deep neural networks and Macau, which is a Bayesian probabilistic matrix factorization technique. Results from both methods were remarkably similar and showed that the performance decrease because of missing data is at first small before accelerating after large amounts of data are removed. This work provides a first approximation to assess how much data is required to produce good performance in multitask prediction exercises.

Remote Sensing Image Fusion Method Based on Nonsubsampled Shearlet Transform and Sparse Representation

NASA Astrophysics Data System (ADS)

Moonon, Altan-Ulzii; Hu, Jianwen; Li, Shutao

2015-12-01

The remote sensing image fusion is an important preprocessing technique in remote sensing image processing. In this paper, a remote sensing image fusion method based on the nonsubsampled shearlet transform (NSST) with sparse representation (SR) is proposed. Firstly, the low resolution multispectral (MS) image is upsampled and color space is transformed from Red-Green-Blue (RGB) to Intensity-Hue-Saturation (IHS). Then, the high resolution panchromatic (PAN) image and intensity component of MS image are decomposed by NSST to high and low frequency coefficients. The low frequency coefficients of PAN and the intensity component are fused by the SR with the learned dictionary. The high frequency coefficients of intensity component and PAN image are fused by local energy based fusion rule. Finally, the fused result is obtained by performing inverse NSST and inverse IHS transform. The experimental results on IKONOS and QuickBird satellites demonstrate that the proposed method provides better spectral quality and superior spatial information in the fused image than other remote sensing image fusion methods both in visual effect and object evaluation.

On the inversion of geodetic integrals defined over the sphere using 1-D FFT

NASA Astrophysics Data System (ADS)

García, R. V.; Alejo, C. A.

2005-08-01

An iterative method is presented which performs inversion of integrals defined over the sphere. The method is based on one-dimensional fast Fourier transform (1-D FFT) inversion and is implemented with the projected Landweber technique, which is used to solve constrained least-squares problems reducing the associated 1-D cyclic-convolution error. The results obtained are as precise as the direct matrix inversion approach, but with better computational efficiency. A case study uses the inversion of Hotine’s integral to obtain gravity disturbances from geoid undulations. Numerical convergence is also analyzed and comparisons with respect to the direct matrix inversion method using conjugate gradient (CG) iteration are presented. Like the CG method, the number of iterations needed to get the optimum (i.e., small) error decreases as the measurement noise increases. Nevertheless, for discrete data given over a whole parallel band, the method can be applied directly without implementing the projected Landweber method, since no cyclic convolution error exists.

Tomographic inversion techniques incorporating physical constraints for line integrated spectroscopy in stellarators and tokamaks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pablant, N. A.; Bell, R. E.; Bitter, M.

2014-11-15

Accurate tomographic inversion is important for diagnostic systems on stellarators and tokamaks which rely on measurements of line integrated emission spectra. A tomographic inversion technique based on spline optimization with enforcement of constraints is described that can produce unique and physically relevant inversions even in situations with noisy or incomplete input data. This inversion technique is routinely used in the analysis of data from the x-ray imaging crystal spectrometer (XICS) installed at the Large Helical Device. The XICS diagnostic records a 1D image of line integrated emission spectra from impurities in the plasma. Through the use of Doppler spectroscopy andmore » tomographic inversion, XICS can provide profile measurements of the local emissivity, temperature, and plasma flow. Tomographic inversion requires the assumption that these measured quantities are flux surface functions, and that a known plasma equilibrium reconstruction is available. In the case of low signal levels or partial spatial coverage of the plasma cross-section, standard inversion techniques utilizing matrix inversion and linear-regularization often cannot produce unique and physically relevant solutions. The addition of physical constraints, such as parameter ranges, derivative directions, and boundary conditions, allow for unique solutions to be reliably found. The constrained inversion technique described here utilizes a modified Levenberg-Marquardt optimization scheme, which introduces a condition avoidance mechanism by selective reduction of search directions. The constrained inversion technique also allows for the addition of more complicated parameter dependencies, for example, geometrical dependence of the emissivity due to asymmetries in the plasma density arising from fast rotation. The accuracy of this constrained inversion technique is discussed, with an emphasis on its applicability to systems with limited plasma coverage.« less

Tomographic inversion techniques incorporating physical constraints for line integrated spectroscopy in stellarators and tokamaksa)

DOE PAGES

Pablant, N. A.; Bell, R. E.; Bitter, M.; ...

2014-08-08

Accurate tomographic inversion is important for diagnostic systems on stellarators and tokamaks which rely on measurements of line integrated emission spectra. A tomographic inversion technique based on spline optimization with enforcement of constraints is described that can produce unique and physically relevant inversions even in situations with noisy or incomplete input data. This inversion technique is routinely used in the analysis of data from the x-ray imaging crystal spectrometer (XICS) installed at LHD. The XICS diagnostic records a 1D image of line integrated emission spectra from impurities in the plasma. Through the use of Doppler spectroscopy and tomographic inversion, XICSmore » can provide pro file measurements of the local emissivity, temperature and plasma flow. Tomographic inversion requires the assumption that these measured quantities are flux surface functions, and that a known plasma equilibrium reconstruction is available. In the case of low signal levels or partial spatial coverage of the plasma cross-section, standard inversion techniques utilizing matrix inversion and linear-regularization often cannot produce unique and physically relevant solutions. The addition of physical constraints, such as parameter ranges, derivative directions, and boundary conditions, allow for unique solutions to be reliably found. The constrained inversion technique described here utilizes a modifi ed Levenberg-Marquardt optimization scheme, which introduces a condition avoidance mechanism by selective reduction of search directions. The constrained inversion technique also allows for the addition of more complicated parameter dependencies, for example geometrical dependence of the emissivity due to asymmetries in the plasma density arising from fast rotation. The accuracy of this constrained inversion technique is discussed, with an emphasis on its applicability to systems with limited plasma coverage.« less

Parallel halftoning technique using dot diffusion optimization

NASA Astrophysics Data System (ADS)

Molina-Garcia, Javier; Ponomaryov, Volodymyr I.; Reyes-Reyes, Rogelio; Cruz-Ramos, Clara

2017-05-01

In this paper, a novel approach for halftone images is proposed and implemented for images that are obtained by the Dot Diffusion (DD) method. Designed technique is based on an optimization of the so-called class matrix used in DD algorithm and it consists of generation new versions of class matrix, which has no baron and near-baron in order to minimize inconsistencies during the distribution of the error. Proposed class matrix has different properties and each is designed for two different applications: applications where the inverse-halftoning is necessary, and applications where this method is not required. The proposed method has been implemented in GPU (NVIDIA GeForce GTX 750 Ti), multicore processors (AMD FX(tm)-6300 Six-Core Processor and in Intel core i5-4200U), using CUDA and OpenCV over a PC with linux. Experimental results have shown that novel framework generates a good quality of the halftone images and the inverse halftone images obtained. The simulation results using parallel architectures have demonstrated the efficiency of the novel technique when it is implemented in real-time processing.

Sparse deconvolution for the large-scale ill-posed inverse problem of impact force reconstruction

NASA Astrophysics Data System (ADS)

Qiao, Baijie; Zhang, Xingwu; Gao, Jiawei; Liu, Ruonan; Chen, Xuefeng

2017-01-01

Most previous regularization methods for solving the inverse problem of force reconstruction are to minimize the l2-norm of the desired force. However, these traditional regularization methods such as Tikhonov regularization and truncated singular value decomposition, commonly fail to solve the large-scale ill-posed inverse problem in moderate computational cost. In this paper, taking into account the sparse characteristic of impact force, the idea of sparse deconvolution is first introduced to the field of impact force reconstruction and a general sparse deconvolution model of impact force is constructed. Second, a novel impact force reconstruction method based on the primal-dual interior point method (PDIPM) is proposed to solve such a large-scale sparse deconvolution model, where minimizing the l2-norm is replaced by minimizing the l1-norm. Meanwhile, the preconditioned conjugate gradient algorithm is used to compute the search direction of PDIPM with high computational efficiency. Finally, two experiments including the small-scale or medium-scale single impact force reconstruction and the relatively large-scale consecutive impact force reconstruction are conducted on a composite wind turbine blade and a shell structure to illustrate the advantage of PDIPM. Compared with Tikhonov regularization, PDIPM is more efficient, accurate and robust whether in the single impact force reconstruction or in the consecutive impact force reconstruction.

Communication Optimal Parallel Multiplication of Sparse Random Matrices

DTIC Science & Technology

2013-02-21

Definition 2.1), and (2) the algorithm is sparsity- independent, where the computation is statically partitioned to processors independent of the sparsity...struc- ture of the input matrices (see Definition 2.5). The second assumption applies to nearly all existing al- gorithms for general sparse matrix-matrix...where A and B are n× n ER(d) matrices: Definition 2.1 An ER(d) matrix is an adjacency matrix of an Erdős-Rényi graph with parameters n and d/n. That

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chow, Edmond

Solving sparse problems is at the core of many DOE computational science applications. We focus on the challenge of developing sparse algorithms that can fully exploit the parallelism in extreme-scale computing systems, in particular systems with massive numbers of cores per node. Our approach is to express a sparse matrix factorization as a large number of bilinear constraint equations, and then solving these equations via an asynchronous iterative method. The unknowns in these equations are the matrix entries of the factorization that is desired.

Filtered gradient reconstruction algorithm for compressive spectral imaging

NASA Astrophysics Data System (ADS)

Mejia, Yuri; Arguello, Henry

2017-04-01

Compressive sensing matrices are traditionally based on random Gaussian and Bernoulli entries. Nevertheless, they are subject to physical constraints, and their structure unusually follows a dense matrix distribution, such as the case of the matrix related to compressive spectral imaging (CSI). The CSI matrix represents the integration of coded and shifted versions of the spectral bands. A spectral image can be recovered from CSI measurements by using iterative algorithms for linear inverse problems that minimize an objective function including a quadratic error term combined with a sparsity regularization term. However, current algorithms are slow because they do not exploit the structure and sparse characteristics of the CSI matrices. A gradient-based CSI reconstruction algorithm, which introduces a filtering step in each iteration of a conventional CSI reconstruction algorithm that yields improved image quality, is proposed. Motivated by the structure of the CSI matrix, Φ, this algorithm modifies the iterative solution such that it is forced to converge to a filtered version of the residual ΦTy, where y is the compressive measurement vector. We show that the filtered-based algorithm converges to better quality performance results than the unfiltered version. Simulation results highlight the relative performance gain over the existing iterative algorithms.

Adaptive sparse grid approach for the efficient simulation of pulsed eddy current testing inspections

NASA Astrophysics Data System (ADS)

Miorelli, Roberto; Reboud, Christophe

2018-04-01

Pulsed Eddy Current Testing (PECT) is a popular NonDestructive Testing (NDT) technique for some applications like corrosion monitoring in the oil and gas industry, or rivet inspection in the aeronautic area. Its particularity is to use a transient excitation, which allows to retrieve more information from the piece than conventional harmonic ECT, in a simpler and cheaper way than multi-frequency ECT setups. Efficient modeling tools prove, as usual, very useful to optimize experimental sensors and devices or evaluate their performance, for instance. This paper proposes an efficient simulation of PECT signals based on standard time harmonic solvers and use of an Adaptive Sparse Grid (ASG) algorithm. An adaptive sampling of the ECT signal spectrum is performed with this algorithm, then the complete spectrum is interpolated from this sparse representation and PECT signals are finally synthesized by means of inverse Fourier transform. Simulation results corresponding to existing industrial configurations are presented and the performance of the strategy is discussed by comparison to reference results.

Multi scales based sparse matrix spectral clustering image segmentation

NASA Astrophysics Data System (ADS)

Liu, Zhongmin; Chen, Zhicai; Li, Zhanming; Hu, Wenjin

2018-04-01

In image segmentation, spectral clustering algorithms have to adopt the appropriate scaling parameter to calculate the similarity matrix between the pixels, which may have a great impact on the clustering result. Moreover, when the number of data instance is large, computational complexity and memory use of the algorithm will greatly increase. To solve these two problems, we proposed a new spectral clustering image segmentation algorithm based on multi scales and sparse matrix. We devised a new feature extraction method at first, then extracted the features of image on different scales, at last, using the feature information to construct sparse similarity matrix which can improve the operation efficiency. Compared with traditional spectral clustering algorithm, image segmentation experimental results show our algorithm have better degree of accuracy and robustness.

Recursive partitioned inversion of large (1500 x 1500) symmetric matrices

NASA Technical Reports Server (NTRS)

Putney, B. H.; Brownd, J. E.; Gomez, R. A.

1976-01-01

A recursive algorithm was designed to invert large, dense, symmetric, positive definite matrices using small amounts of computer core, i.e., a small fraction of the core needed to store the complete matrix. The described algorithm is a generalized Gaussian elimination technique. Other algorithms are also discussed for the Cholesky decomposition and step inversion techniques. The purpose of the inversion algorithm is to solve large linear systems of normal equations generated by working geodetic problems. The algorithm was incorporated into a computer program called SOLVE. In the past the SOLVE program has been used in obtaining solutions published as the Goddard earth models.

A path-oriented matrix-based knowledge representation system

NASA Technical Reports Server (NTRS)

Feyock, Stefan; Karamouzis, Stamos T.

1993-01-01

Experience has shown that designing a good representation is often the key to turning hard problems into simple ones. Most AI (Artificial Intelligence) search/representation techniques are oriented toward an infinite domain of objects and arbitrary relations among them. In reality much of what needs to be represented in AI can be expressed using a finite domain and unary or binary predicates. Well-known vector- and matrix-based representations can efficiently represent finite domains and unary/binary predicates, and allow effective extraction of path information by generalized transitive closure/path matrix computations. In order to avoid space limitations a set of abstract sparse matrix data types was developed along with a set of operations on them. This representation forms the basis of an intelligent information system for representing and manipulating relational data.

Multiprocessor sparse L/U decomposition with controlled fill-in

NASA Technical Reports Server (NTRS)

Alaghband, G.; Jordan, H. F.

1985-01-01

Generation of the maximal compatibles of pivot elements for a class of small sparse matrices is studied. The algorithm involves a binary tree search and has a complexity exponential in the order of the matrix. Different strategies for selection of a set of compatible pivots based on the Markowitz criterion are investigated. The competing issues of parallelism and fill-in generation are studied and results are provided. A technque for obtaining an ordered compatible set directly from the ordered incompatible table is given. This technique generates a set of compatible pivots with the property of generating few fills. A new hueristic algorithm is then proposed that combines the idea of an ordered compatible set with a limited binary tree search to generate several sets of compatible pivots in linear time. Finally, an elimination set to reduce the matrix is selected. Parameters are suggested to obtain a balance between parallelism and fill-ins. Results of applying the proposed algorithms on several large application matrices are presented and analyzed.

Three dimensional iterative beam propagation method for optical waveguide devices

NASA Astrophysics Data System (ADS)

Ma, Changbao; Van Keuren, Edward

2006-10-01

The finite difference beam propagation method (FD-BPM) is an effective model for simulating a wide range of optical waveguide structures. The classical FD-BPMs are based on the Crank-Nicholson scheme, and in tridiagonal form can be solved using the Thomas method. We present a different type of algorithm for 3-D structures. In this algorithm, the wave equation is formulated into a large sparse matrix equation which can be solved using iterative methods. The simulation window shifting scheme and threshold technique introduced in our earlier work are utilized to overcome the convergence problem of iterative methods for large sparse matrix equation and wide-angle simulations. This method enables us to develop higher-order 3-D wide-angle (WA-) BPMs based on Pade approximant operators and the multistep method, which are commonly used in WA-BPMs for 2-D structures. Simulations using the new methods will be compared to the analytical results to assure its effectiveness and applicability.

A new wavelet transform to sparsely represent cortical current densities for EEG/MEG inverse problems.

PubMed

Liao, Ke; Zhu, Min; Ding, Lei

2013-08-01

The present study investigated the use of transform sparseness of cortical current density on human brain surface to improve electroencephalography/magnetoencephalography (EEG/MEG) inverse solutions. Transform sparseness was assessed by evaluating compressibility of cortical current densities in transform domains. To do that, a structure compression method from computer graphics was first adopted to compress cortical surface structure, either regular or irregular, into hierarchical multi-resolution meshes. Then, a new face-based wavelet method based on generated multi-resolution meshes was proposed to compress current density functions defined on cortical surfaces. Twelve cortical surface models were built by three EEG/MEG softwares and their structural compressibility was evaluated and compared by the proposed method. Monte Carlo simulations were implemented to evaluate the performance of the proposed wavelet method in compressing various cortical current density distributions as compared to other two available vertex-based wavelet methods. The present results indicate that the face-based wavelet method can achieve higher transform sparseness than vertex-based wavelet methods. Furthermore, basis functions from the face-based wavelet method have lower coherence against typical EEG and MEG measurement systems than vertex-based wavelet methods. Both high transform sparseness and low coherent measurements suggest that the proposed face-based wavelet method can improve the performance of L1-norm regularized EEG/MEG inverse solutions, which was further demonstrated in simulations and experimental setups using MEG data. Thus, this new transform on complicated cortical structure is promising to significantly advance EEG/MEG inverse source imaging technologies. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Distance descending ordering method: An O(n) algorithm for inverting the mass matrix in simulation of macromolecules with long branches

NASA Astrophysics Data System (ADS)

Xu, Xiankun; Li, Peiwen

2017-11-01

Fixman's work in 1974 and the follow-up studies have developed a method that can factorize the inverse of mass matrix into an arithmetic combination of three sparse matrices-one of them is positive definite and needs to be further factorized by using the Cholesky decomposition or similar methods. When the molecule subjected to study is of serial chain structure, this method can achieve O (n) time complexity. However, for molecules with long branches, Cholesky decomposition about the corresponding positive definite matrix will introduce massive fill-in due to its nonzero structure. Although there are several methods can be used to reduce the number of fill-in, none of them could strictly guarantee for zero fill-in for all molecules according to our test, and thus cannot obtain O (n) time complexity by using these traditional methods. In this paper we present a new method that can guarantee for no fill-in in doing the Cholesky decomposition, which was developed based on the correlations between the mass matrix and the geometrical structure of molecules. As a result, the inverting of mass matrix will remain the O (n) time complexity, no matter the molecule structure has long branches or not.

Hybrid-dual-fourier tomographic algorithm for a fast three-dimensionial optical image reconstruction in turbid media

NASA Technical Reports Server (NTRS)

Alfano, Robert R. (Inventor); Cai, Wei (Inventor)

2007-01-01

A reconstruction technique for reducing computation burden in the 3D image processes, wherein the reconstruction procedure comprises an inverse and a forward model. The inverse model uses a hybrid dual Fourier algorithm that combines a 2D Fourier inversion with a 1D matrix inversion to thereby provide high-speed inverse computations. The inverse algorithm uses a hybrid transfer to provide fast Fourier inversion for data of multiple sources and multiple detectors. The forward model is based on an analytical cumulant solution of a radiative transfer equation. The accurate analytical form of the solution to the radiative transfer equation provides an efficient formalism for fast computation of the forward model.

Analysis of protein circular dichroism spectra for secondary structure using a simple matrix multiplication.

PubMed

Compton, L A; Johnson, W C

1986-05-15

Inverse circular dichroism (CD) spectra are presented for each of the five major secondary structures of proteins: alpha-helix, antiparallel and parallel beta-sheet, beta-turn, and other (random) structures. The fraction of the each secondary structure in a protein is predicted by forming the dot product of the corresponding inverse CD spectrum, expressed as a vector, with the CD spectrum of the protein digitized in the same way. We show how this method is based on the construction of the generalized inverse from the singular value decomposition of a set of CD spectra corresponding to proteins whose secondary structures are known from X-ray crystallography. These inverse spectra compute secondary structure directly from protein CD spectra without resorting to least-squares fitting and standard matrix inversion techniques. In addition, spectra corresponding to the individual secondary structures, analogous to the CD spectra of synthetic polypeptides, are generated from the five most significant CD eigenvectors.

Inverse problems with nonnegative and sparse solutions: algorithms and application to the phase retrieval problem

NASA Astrophysics Data System (ADS)

Quy Muoi, Pham; Nho Hào, Dinh; Sahoo, Sujit Kumar; Tang, Dongliang; Cong, Nguyen Huu; Dang, Cuong

2018-05-01

In this paper, we study a gradient-type method and a semismooth Newton method for minimization problems in regularizing inverse problems with nonnegative and sparse solutions. We propose a special penalty functional forcing the minimizers of regularized minimization problems to be nonnegative and sparse, and then we apply the proposed algorithms in a practical the problem. The strong convergence of the gradient-type method and the local superlinear convergence of the semismooth Newton method are proven. Then, we use these algorithms for the phase retrieval problem and illustrate their efficiency in numerical examples, particularly in the practical problem of optical imaging through scattering media where all the noises from experiment are presented.

Limited-memory BFGS based least-squares pre-stack Kirchhoff depth migration

NASA Astrophysics Data System (ADS)

Wu, Shaojiang; Wang, Yibo; Zheng, Yikang; Chang, Xu

2015-08-01

Least-squares migration (LSM) is a linearized inversion technique for subsurface reflectivity estimation. Compared to conventional migration algorithms, it can improve spatial resolution significantly with a few iterative calculations. There are three key steps in LSM, (1) calculate data residuals between observed data and demigrated data using the inverted reflectivity model; (2) migrate data residuals to form reflectivity gradient and (3) update reflectivity model using optimization methods. In order to obtain an accurate and high-resolution inversion result, the good estimation of inverse Hessian matrix plays a crucial role. However, due to the large size of Hessian matrix, the inverse matrix calculation is always a tough task. The limited-memory BFGS (L-BFGS) method can evaluate the Hessian matrix indirectly using a limited amount of computer memory which only maintains a history of the past m gradients (often m < 10). We combine the L-BFGS method with least-squares pre-stack Kirchhoff depth migration. Then, we validate the introduced approach by the 2-D Marmousi synthetic data set and a 2-D marine data set. The results show that the introduced method can effectively obtain reflectivity model and has a faster convergence rate with two comparison gradient methods. It might be significant for general complex subsurface imaging.

On the Duality of Forward and Inverse Light Transport.

PubMed

Chandraker, Manmohan; Bai, Jiamin; Ng, Tian-Tsong; Ramamoorthi, Ravi

2011-10-01

Inverse light transport seeks to undo global illumination effects, such as interreflections, that pervade images of most scenes. This paper presents the theoretical and computational foundations for inverse light transport as a dual of forward rendering. Mathematically, this duality is established through the existence of underlying Neumann series expansions. Physically, it can be shown that each term of our inverse series cancels an interreflection bounce, just as the forward series adds them. While the convergence properties of the forward series are well known, we show that the oscillatory convergence of the inverse series leads to more interesting conditions on material reflectance. Conceptually, the inverse problem requires the inversion of a large light transport matrix, which is impractical for realistic resolutions using standard techniques. A natural consequence of our theoretical framework is a suite of fast computational algorithms for light transport inversion--analogous to finite element radiosity, Monte Carlo and wavelet-based methods in forward rendering--that rely at most on matrix-vector multiplications. We demonstrate two practical applications, namely, separation of individual bounces of the light transport and fast projector radiometric compensation, to display images free of global illumination artifacts in real-world environments.

Sparse matrix methods based on orthogonality and conjugacy

NASA Technical Reports Server (NTRS)

Lawson, C. L.

1973-01-01

A matrix having a high percentage of zero elements is called spares. In the solution of systems of linear equations or linear least squares problems involving large sparse matrices, significant saving of computer cost can be achieved by taking advantage of the sparsity. The conjugate gradient algorithm and a set of related algorithms are described.

Improved Success of Sparse Matrix Protein Crystallization Screening with Heterogeneous Nucleating Agents

PubMed Central

Thakur, Anil S.; Robin, Gautier; Guncar, Gregor; Saunders, Neil F. W.; Newman, Janet; Martin, Jennifer L.; Kobe, Bostjan

2007-01-01

Background Crystallization is a major bottleneck in the process of macromolecular structure determination by X-ray crystallography. Successful crystallization requires the formation of nuclei and their subsequent growth to crystals of suitable size. Crystal growth generally occurs spontaneously in a supersaturated solution as a result of homogenous nucleation. However, in a typical sparse matrix screening experiment, precipitant and protein concentration are not sampled extensively, and supersaturation conditions suitable for nucleation are often missed. Methodology/Principal Findings We tested the effect of nine potential heterogenous nucleating agents on crystallization of ten test proteins in a sparse matrix screen. Several nucleating agents induced crystal formation under conditions where no crystallization occurred in the absence of the nucleating agent. Four nucleating agents: dried seaweed; horse hair; cellulose and hydroxyapatite, had a considerable overall positive effect on crystallization success. This effect was further enhanced when these nucleating agents were used in combination with each other. Conclusions/Significance Our results suggest that the addition of heterogeneous nucleating agents increases the chances of crystal formation when using sparse matrix screens. PMID:17971854

Task-driven dictionary learning.

PubMed

Mairal, Julien; Bach, Francis; Ponce, Jean

2012-04-01

Modeling data with linear combinations of a few elements from a learned dictionary has been the focus of much recent research in machine learning, neuroscience, and signal processing. For signals such as natural images that admit such sparse representations, it is now well established that these models are well suited to restoration tasks. In this context, learning the dictionary amounts to solving a large-scale matrix factorization problem, which can be done efficiently with classical optimization tools. The same approach has also been used for learning features from data for other purposes, e.g., image classification, but tuning the dictionary in a supervised way for these tasks has proven to be more difficult. In this paper, we present a general formulation for supervised dictionary learning adapted to a wide variety of tasks, and present an efficient algorithm for solving the corresponding optimization problem. Experiments on handwritten digit classification, digital art identification, nonlinear inverse image problems, and compressed sensing demonstrate that our approach is effective in large-scale settings, and is well suited to supervised and semi-supervised classification, as well as regression tasks for data that admit sparse representations.

Elongation cutoff technique armed with quantum fast multipole method for linear scaling.

PubMed

Korchowiec, Jacek; Lewandowski, Jakub; Makowski, Marcin; Gu, Feng Long; Aoki, Yuriko

2009-11-30

A linear-scaling implementation of the elongation cutoff technique (ELG/C) that speeds up Hartree-Fock (HF) self-consistent field calculations is presented. The cutoff method avoids the known bottleneck of the conventional HF scheme, that is, diagonalization, because it operates within the low dimension subspace of the whole atomic orbital space. The efficiency of ELG/C is illustrated for two model systems. The obtained results indicate that the ELG/C is a very efficient sparse matrix algebra scheme. Copyright 2009 Wiley Periodicals, Inc.

Preconditioned conjugate residual methods for the solution of spectral equations

NASA Technical Reports Server (NTRS)

Wong, Y. S.; Zang, T. A.; Hussaini, M. Y.

1986-01-01

Conjugate residual methods for the solution of spectral equations are described. An inexact finite-difference operator is introduced as a preconditioner in the iterative procedures. Application of these techniques is limited to problems for which the symmetric part of the coefficient matrix is positive definite. Although the spectral equation is a very ill-conditioned and full matrix problem, the computational effort of the present iterative methods for solving such a system is comparable to that for the sparse matrix equations obtained from the application of either finite-difference or finite-element methods to the same problems. Numerical experiments are shown for a self-adjoint elliptic partial differential equation with Dirichlet boundary conditions, and comparison with other solution procedures for spectral equations is presented.

Intermediate Scale Experimental Design to Validate a Subsurface Inverse Theory Applicable to Date-sparse Conditions

NASA Astrophysics Data System (ADS)

Jiao, J.; Trautz, A.; Zhang, Y.; Illangasekera, T.

2017-12-01

Subsurface flow and transport characterization under data-sparse condition is addressed by a new and computationally efficient inverse theory that simultaneously estimates parameters, state variables, and boundary conditions. Uncertainty in static data can be accounted for while parameter structure can be complex due to process uncertainty. The approach has been successfully extended to inverting transient and unsaturated flows as well as contaminant source identification under unknown initial and boundary conditions. In one example, by sampling numerical experiments simulating two-dimensional steady-state flow in which tracer migrates, a sequential inversion scheme first estimates the flow field and permeability structure before the evolution of tracer plume and dispersivities are jointly estimated. Compared to traditional inversion techniques, the theory does not use forward simulations to assess model-data misfits, thus the knowledge of the difficult-to-determine site boundary condition is not required. To test the general applicability of the theory, data generated during high-precision intermediate-scale experiments (i.e., a scale intermediary to the field and column scales) in large synthetic aquifers can be used. The design of such experiments is not trivial as laboratory conditions have to be selected to mimic natural systems in order to provide useful data, thus requiring a variety of sensors and data collection strategies. This paper presents the design of such an experiment in a synthetic, multi-layered aquifer with dimensions of 242.7 x 119.3 x 7.7 cm3. Different experimental scenarios that will generate data to validate the theory are presented.

Full wave two-dimensional modeling of scattering and inverse scattering for layered rough surfaces with buried objects

NASA Astrophysics Data System (ADS)

Kuo, Chih-Hao

Efficient and accurate modeling of electromagnetic scattering from layered rough surfaces with buried objects finds applications ranging from detection of landmines to remote sensing of subsurface soil moisture. The formulation of a hybrid numerical/analytical solution to electromagnetic scattering from layered rough surfaces is first presented in this dissertation. The solution to scattering from each rough interface is sought independently based on the extended boundary condition method (EBCM), where the scattered fields of each rough interface are expressed as a summation of plane waves and then cast into reflection/transmission matrices. To account for interactions between multiple rough boundaries, the scattering matrix method (SMM) is applied to recursively cascade reflection and transmission matrices of each rough interface and obtain the composite reflection matrix from the overall scattering medium. The validation of this method against the Method of Moments (MoM) and Small Perturbation Method (SPM) is addressed and the numerical results which investigate the potential of low frequency radar systems in estimating deep soil moisture are presented. Computational efficiency of the proposed method is also discussed. In order to demonstrate the capability of this method in modeling coherent multiple scattering phenomena, the proposed method has been employed to analyze backscattering enhancement and satellite peaks due to surface plasmon waves from layered rough surfaces. Numerical results which show the appearance of enhanced backscattered peaks and satellite peaks are presented. Following the development of the EBCM/SMM technique, a technique which incorporates a buried object in layered rough surfaces by employing the T-matrix method and the cylindrical-to-spatial harmonics transformation is proposed. Validation and numerical results are provided. Finally, a multi-frequency polarimetric inversion algorithm for the retrieval of subsurface soil properties using VHF/UHF band radar measurements is devised. The top soil dielectric constant is first determined using an L-band inversion algorithm. For the retrieval of subsurface properties, a time-domain inversion technique is employed together with a parameter optimization for the pulse shape of time delay echoes from VHF/UHF band radar observations. Numerical studies to investigate the accuracy of the proposed inversion technique in presence of errors are addressed.

Real-Time Characterization of Aerospace Structures Using Onboard Strain Measurement Technologies and Inverse Finite Element Method

DTIC Science & Technology

2011-09-01

strain data provided by in-situ strain sensors. The application focus is on the stain data obtained from FBG (Fiber Bragg Grating) sensor arrays...sparsely distributed lines to simulate strain data from FBG (Fiber Bragg Grating) arrays that provide either single-core (axial) or rosette (tri...when the measured strain data are sparse, as it is often the case when FBG sensors are used. For an inverse element without strain-sensor data, the

Numerical methods in Markov chain modeling

NASA Technical Reports Server (NTRS)

Philippe, Bernard; Saad, Youcef; Stewart, William J.

1989-01-01

Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.

A general parallel sparse-blocked matrix multiply for linear scaling SCF theory

NASA Astrophysics Data System (ADS)

Challacombe, Matt

2000-06-01

A general approach to the parallel sparse-blocked matrix-matrix multiply is developed in the context of linear scaling self-consistent-field (SCF) theory. The data-parallel message passing method uses non-blocking communication to overlap computation and communication. The space filling curve heuristic is used to achieve data locality for sparse matrix elements that decay with “separation”. Load balance is achieved by solving the bin packing problem for blocks with variable size.With this new method as the kernel, parallel performance of the simplified density matrix minimization (SDMM) for solution of the SCF equations is investigated for RHF/6-31G ∗∗ water clusters and RHF/3-21G estane globules. Sustained rates above 5.7 GFLOPS for the SDMM have been achieved for (H 2 O) 200 with 95 Origin 2000 processors. Scalability is found to be limited by load imbalance, which increases with decreasing granularity, due primarily to the inhomogeneous distribution of variable block sizes.

Sparse matrix-vector multiplication on network-on-chip

NASA Astrophysics Data System (ADS)

Sun, C.-C.; Götze, J.; Jheng, H.-Y.; Ruan, S.-J.

2010-12-01

In this paper, we present an idea for performing matrix-vector multiplication by using Network-on-Chip (NoC) architecture. In traditional IC design on-chip communications have been designed with dedicated point-to-point interconnections. Therefore, regular local data transfer is the major concept of many parallel implementations. However, when dealing with the parallel implementation of sparse matrix-vector multiplication (SMVM), which is the main step of all iterative algorithms for solving systems of linear equation, the required data transfers depend on the sparsity structure of the matrix and can be extremely irregular. Using the NoC architecture makes it possible to deal with arbitrary structure of the data transfers; i.e. with the irregular structure of the sparse matrices. So far, we have already implemented the proposed SMVM-NoC architecture with the size 4×4 and 5×5 in IEEE 754 single float point precision using FPGA.

Towards seismic waveform inversion of long-offset Ocean-Bottom Seismic data for deep crustal imaging offshore Western Australia

NASA Astrophysics Data System (ADS)

Monnier, S.; Lumley, D. E.; Kamei, R.; Goncharov, A.; Shragge, J. C.

2016-12-01

Ocean Bottom Seismic datasets have become increasingly used in recent years to develop high-resolution, wavelength-scale P-wave velocity models of the lithosphere from waveform inversion, due to their recording of long-offset transmitted phases. New OBS surveys evolve towards novel acquisition geometries involving longer offsets (several hundreds of km), broader frequency content (1-100 Hz), while receiver sampling often remains sparse (several km). Therefore, it is critical to assess the effects of such geometries on the eventual success and resolution of waveform inversion velocity models. In this study, we investigate the feasibility of waveform inversion on the Bart 2D OBS profile acquired offshore Western Australia, to investigate regional crustal and Moho structures. The dataset features 14 broadband seismometers (0.01-100 Hz) from AuScope's national OBS fleet, offsets in excess of 280 km, and a sparse receiver sampling (18 km). We perform our analysis in four stages: (1) field data analysis, (2) 2D P-wave velocity model building, synthetic data (3) modelling, and (4) waveform inversion. Data exploration shows high-quality active-source signal down to 2Hz, and usable first arrivals to offsets greater than 100 km. The background velocity model is constructed by combining crustal and Moho information in continental reference models (e.g., AuSREM, AusMoho). These low-resolution studies suggest a crustal thickness of 20-25 km along our seismic line and constitute a starting point for synthetic modelling and inversion. We perform synthetic 2D time-domain modelling to: (1) evaluate the misfit between synthetic and field data within the usable frequency band (2-10 Hz); (2) validate our velocity model; and (3) observe the effects of sparse OBS interval on data quality. Finally, we apply 2D acoustic frequency-domain waveform inversion to the synthetic data to generate velocity model updates. The inverted model is compared to the reference model to investigate the improved crustal resolution and Moho boundary delineation that could be realized using waveform inversion, and to evaluate the effects of the acquisition parameters. The inversion strategies developed through the synthetic tests will help the subsequent inversion of sparse, long-offset OBS field data.

General Matrix Inversion Technique for the Calibration of Electric Field Sensor Arrays on Aircraft Platforms

NASA Technical Reports Server (NTRS)

Mach, D. M.; Koshak, W. J.

2007-01-01

A matrix calibration procedure has been developed that uniquely relates the electric fields measured at the aircraft with the external vector electric field and net aircraft charge. The calibration method can be generalized to any reasonable combination of electric field measurements and aircraft. A calibration matrix is determined for each aircraft that represents the individual instrument responses to the external electric field. The aircraft geometry and configuration of field mills (FMs) uniquely define the matrix. The matrix can then be inverted to determine the external electric field and net aircraft charge from the FM outputs. A distinct advantage of the method is that if one or more FMs need to be eliminated or deemphasized [e.g., due to a malfunction), it is a simple matter to reinvert the matrix without the malfunctioning FMs. To demonstrate the calibration technique, data are presented from several aircraft programs (ER-2, DC-8, Altus, and Citation).

Visualization of x-ray computer tomography using computer-generated holography

NASA Astrophysics Data System (ADS)

Daibo, Masahiro; Tayama, Norio

1998-09-01

The theory converted from x-ray projection data to the hologram directly by combining the computer tomography (CT) with the computer generated hologram (CGH), is proposed. The purpose of this study is to offer the theory for realizing the all- electronic and high-speed seeing through 3D visualization system, which is for the application to medical diagnosis and non- destructive testing. First, the CT is expressed using the pseudo- inverse matrix which is obtained by the singular value decomposition. CGH is expressed in the matrix style. Next, `projection to hologram conversion' (PTHC) matrix is calculated by the multiplication of phase matrix of CGH with pseudo-inverse matrix of the CT. Finally, the projection vector is converted to the hologram vector directly, by multiplication of the PTHC matrix with the projection vector. Incorporating holographic analog computation into CT reconstruction, it becomes possible that the calculation amount is drastically reduced. We demonstrate the CT cross section which is reconstituted by He-Ne laser in the 3D space from the real x-ray projection data acquired by x-ray television equipment, using our direct conversion technique.

Teaching Tip: When a Matrix and Its Inverse Are Stochastic

ERIC Educational Resources Information Center

Ding, J.; Rhee, N. H.

2013-01-01

A stochastic matrix is a square matrix with nonnegative entries and row sums 1. The simplest example is a permutation matrix, whose rows permute the rows of an identity matrix. A permutation matrix and its inverse are both stochastic. We prove the converse, that is, if a matrix and its inverse are both stochastic, then it is a permutation matrix.

A genetic meta-algorithm-assisted inversion approach: hydrogeological study for the determination of volumetric rock properties and matrix and fluid parameters in unsaturated formations

NASA Astrophysics Data System (ADS)

Szabó, Norbert Péter

2018-03-01

An evolutionary inversion approach is suggested for the interpretation of nuclear and resistivity logs measured by direct-push tools in shallow unsaturated sediments. The efficiency of formation evaluation is improved by estimating simultaneously (1) the petrophysical properties that vary rapidly along a drill hole with depth and (2) the zone parameters that can be treated as constant, in one inversion procedure. In the workflow, the fractional volumes of water, air, matrix and clay are estimated in adjacent depths by linearized inversion, whereas the clay and matrix properties are updated using a float-encoded genetic meta-algorithm. The proposed inversion method provides an objective estimate of the zone parameters that appear in the tool response equations applied to solve the forward problem, which can significantly increase the reliability of the petrophysical model as opposed to setting these parameters arbitrarily. The global optimization meta-algorithm not only assures the best fit between the measured and calculated data but also gives a reliable solution, practically independent of the initial model, as laboratory data are unnecessary in the inversion procedure. The feasibility test uses engineering geophysical sounding logs observed in an unsaturated loessy-sandy formation in Hungary. The multi-borehole extension of the inversion technique is developed to determine the petrophysical properties and their estimation errors along a profile of drill holes. The genetic meta-algorithmic inversion method is recommended for hydrogeophysical logging applications of various kinds to automatically extract the volumetric ratios of rock and fluid constituents as well as the most important zone parameters in a reliable inversion procedure.

A Scalable O(N) Algorithm for Large-Scale Parallel First-Principles Molecular Dynamics Simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Osei-Kuffuor, Daniel; Fattebert, Jean-Luc

2014-01-01

Traditional algorithms for first-principles molecular dynamics (FPMD) simulations only gain a modest capability increase from current petascale computers, due to their O(N 3) complexity and their heavy use of global communications. To address this issue, we are developing a truly scalable O(N) complexity FPMD algorithm, based on density functional theory (DFT), which avoids global communications. The computational model uses a general nonorthogonal orbital formulation for the DFT energy functional, which requires knowledge of selected elements of the inverse of the associated overlap matrix. We present a scalable algorithm for approximately computing selected entries of the inverse of the overlap matrix,more » based on an approximate inverse technique, by inverting local blocks corresponding to principal submatrices of the global overlap matrix. The new FPMD algorithm exploits sparsity and uses nearest neighbor communication to provide a computational scheme capable of extreme scalability. Accuracy is controlled by the mesh spacing of the finite difference discretization, the size of the localization regions in which the electronic orbitals are confined, and a cutoff beyond which the entries of the overlap matrix can be omitted when computing selected entries of its inverse. We demonstrate the algorithm's excellent parallel scaling for up to O(100K) atoms on O(100K) processors, with a wall-clock time of O(1) minute per molecular dynamics time step.« less

Optimal Tikhonov Regularization in Finite-Frequency Tomography

NASA Astrophysics Data System (ADS)

Fang, Y.; Yao, Z.; Zhou, Y.

2017-12-01

The last decade has witnessed a progressive transition in seismic tomography from ray theory to finite-frequency theory which overcomes the resolution limit of the high-frequency approximation in ray theory. In addition to approximations in wave propagation physics, a main difference between ray-theoretical tomography and finite-frequency tomography is the sparseness of the associated sensitivity matrix. It is well known that seismic tomographic problems are ill-posed and regularizations such as damping and smoothing are often applied to analyze the tradeoff between data misfit and model uncertainty. The regularizations depend on the structure of the matrix as well as noise level of the data. Cross-validation has been used to constrain data uncertainties in body-wave finite-frequency inversions when measurements at multiple frequencies are available to invert for a common structure. In this study, we explore an optimal Tikhonov regularization in surface-wave phase-velocity tomography based on minimization of an empirical Bayes risk function using theoretical training datasets. We exploit the structure of the sensitivity matrix in the framework of singular value decomposition (SVD) which also allows for the calculation of complete resolution matrix. We compare the optimal Tikhonov regularization in finite-frequency tomography with traditional tradeo-off analysis using surface wave dispersion measurements from global as well as regional studies.

An adaptive sparse deconvolution method for distinguishing the overlapping echoes of ultrasonic guided waves for pipeline crack inspection

NASA Astrophysics Data System (ADS)

Chang, Yong; Zi, Yanyang; Zhao, Jiyuan; Yang, Zhe; He, Wangpeng; Sun, Hailiang

2017-03-01

In guided wave pipeline inspection, echoes reflected from closely spaced reflectors generally overlap, meaning useful information is lost. To solve the overlapping problem, sparse deconvolution methods have been developed in the past decade. However, conventional sparse deconvolution methods have limitations in handling guided wave signals, because the input signal is directly used as the prototype of the convolution matrix, without considering the waveform change caused by the dispersion properties of the guided wave. In this paper, an adaptive sparse deconvolution (ASD) method is proposed to overcome these limitations. First, the Gaussian echo model is employed to adaptively estimate the column prototype of the convolution matrix instead of directly using the input signal as the prototype. Then, the convolution matrix is constructed upon the estimated results. Third, the split augmented Lagrangian shrinkage (SALSA) algorithm is introduced to solve the deconvolution problem with high computational efficiency. To verify the effectiveness of the proposed method, guided wave signals obtained from pipeline inspection are investigated numerically and experimentally. Compared to conventional sparse deconvolution methods, e.g. the {{l}1} -norm deconvolution method, the proposed method shows better performance in handling the echo overlap problem in the guided wave signal.

Robust extraction of basis functions for simultaneous and proportional myoelectric control via sparse non-negative matrix factorization

NASA Astrophysics Data System (ADS)

Lin, Chuang; Wang, Binghui; Jiang, Ning; Farina, Dario

2018-04-01

Objective. This paper proposes a novel simultaneous and proportional multiple degree of freedom (DOF) myoelectric control method for active prostheses. Approach. The approach is based on non-negative matrix factorization (NMF) of surface EMG signals with the inclusion of sparseness constraints. By applying a sparseness constraint to the control signal matrix, it is possible to extract the basis information from arbitrary movements (quasi-unsupervised approach) for multiple DOFs concurrently. Main Results. In online testing based on target hitting, able-bodied subjects reached a greater throughput (TP) when using sparse NMF (SNMF) than with classic NMF or with linear regression (LR). Accordingly, the completion time (CT) was shorter for SNMF than NMF or LR. The same observations were made in two patients with unilateral limb deficiencies. Significance. The addition of sparseness constraints to NMF allows for a quasi-unsupervised approach to myoelectric control with superior results with respect to previous methods for the simultaneous and proportional control of multi-DOF. The proposed factorization algorithm allows robust simultaneous and proportional control, is superior to previous supervised algorithms, and, because of minimal supervision, paves the way to online adaptation in myoelectric control.

Sparse PCA with Oracle Property.

PubMed

Gu, Quanquan; Wang, Zhaoran; Liu, Han

In this paper, we study the estimation of the k -dimensional sparse principal subspace of covariance matrix Σ in the high-dimensional setting. We aim to recover the oracle principal subspace solution, i.e., the principal subspace estimator obtained assuming the true support is known a priori. To this end, we propose a family of estimators based on the semidefinite relaxation of sparse PCA with novel regularizations. In particular, under a weak assumption on the magnitude of the population projection matrix, one estimator within this family exactly recovers the true support with high probability, has exact rank- k , and attains a [Formula: see text] statistical rate of convergence with s being the subspace sparsity level and n the sample size. Compared to existing support recovery results for sparse PCA, our approach does not hinge on the spiked covariance model or the limited correlation condition. As a complement to the first estimator that enjoys the oracle property, we prove that, another estimator within the family achieves a sharper statistical rate of convergence than the standard semidefinite relaxation of sparse PCA, even when the previous assumption on the magnitude of the projection matrix is violated. We validate the theoretical results by numerical experiments on synthetic datasets.

Sparse PCA with Oracle Property

PubMed Central

Gu, Quanquan; Wang, Zhaoran; Liu, Han

2014-01-01

In this paper, we study the estimation of the k-dimensional sparse principal subspace of covariance matrix Σ in the high-dimensional setting. We aim to recover the oracle principal subspace solution, i.e., the principal subspace estimator obtained assuming the true support is known a priori. To this end, we propose a family of estimators based on the semidefinite relaxation of sparse PCA with novel regularizations. In particular, under a weak assumption on the magnitude of the population projection matrix, one estimator within this family exactly recovers the true support with high probability, has exact rank-k, and attains a s/n statistical rate of convergence with s being the subspace sparsity level and n the sample size. Compared to existing support recovery results for sparse PCA, our approach does not hinge on the spiked covariance model or the limited correlation condition. As a complement to the first estimator that enjoys the oracle property, we prove that, another estimator within the family achieves a sharper statistical rate of convergence than the standard semidefinite relaxation of sparse PCA, even when the previous assumption on the magnitude of the projection matrix is violated. We validate the theoretical results by numerical experiments on synthetic datasets. PMID:25684971

Nonnegative matrix factorization and sparse representation for the automated detection of periodic limb movements in sleep.

PubMed

Shokrollahi, Mehrnaz; Krishnan, Sridhar; Dopsa, Dustin D; Muir, Ryan T; Black, Sandra E; Swartz, Richard H; Murray, Brian J; Boulos, Mark I

2016-11-01

Stroke is a leading cause of death and disability in adults, and incurs a significant economic burden to society. Periodic limb movements (PLMs) in sleep are repetitive movements involving the great toe, ankle, and hip. Evolving evidence suggests that PLMs may be associated with high blood pressure and stroke, but this relationship remains underexplored. Several issues limit the study of PLMs including the need to manually score them, which is time-consuming and costly. For this reason, we developed a novel automated method for nocturnal PLM detection, which was shown to be correlated with (a) the manually scored PLM index on polysomnography, and (b) white matter hyperintensities on brain imaging, which have been demonstrated to be associated with PLMs. Our proposed algorithm consists of three main stages: (1) representing the signal in the time-frequency plane using time-frequency matrices (TFM), (2) applying K-nonnegative matrix factorization technique to decompose the TFM matrix into its significant components, and (3) applying kernel sparse representation for classification (KSRC) to the decomposed signal. Our approach was applied to a dataset that consisted of 65 subjects who underwent polysomnography. An overall classification of 97 % was achieved for discrimination of the aforementioned signals, demonstrating the potential of the presented method.

Social Collaborative Filtering by Trust.

PubMed

Yang, Bo; Lei, Yu; Liu, Jiming; Li, Wenjie

2017-08-01

Recommender systems are used to accurately and actively provide users with potentially interesting information or services. Collaborative filtering is a widely adopted approach to recommendation, but sparse data and cold-start users are often barriers to providing high quality recommendations. To address such issues, we propose a novel method that works to improve the performance of collaborative filtering recommendations by integrating sparse rating data given by users and sparse social trust network among these same users. This is a model-based method that adopts matrix factorization technique that maps users into low-dimensional latent feature spaces in terms of their trust relationship, and aims to more accurately reflect the users reciprocal influence on the formation of their own opinions and to learn better preferential patterns of users for high-quality recommendations. We use four large-scale datasets to show that the proposed method performs much better, especially for cold start users, than state-of-the-art recommendation algorithms for social collaborative filtering based on trust.

Experiments with conjugate gradient algorithms for homotopy curve tracking

NASA Technical Reports Server (NTRS)

Irani, Kashmira M.; Ribbens, Calvin J.; Watson, Layne T.; Kamat, Manohar P.; Walker, Homer F.

1991-01-01

There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Here, variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. The test problems used include actual large scale, sparse structural mechanics problems.

Ordering Unstructured Meshes for Sparse Matrix Computations on Leading Parallel Systems

NASA Technical Reports Server (NTRS)

Oliker, Leonid; Li, Xiaoye; Heber, Gerd; Biswas, Rupak

2000-01-01

The ability of computers to solve hitherto intractable problems and simulate complex processes using mathematical models makes them an indispensable part of modern science and engineering. Computer simulations of large-scale realistic applications usually require solving a set of non-linear partial differential equations (PDES) over a finite region. For example, one thrust area in the DOE Grand Challenge projects is to design future accelerators such as the SpaHation Neutron Source (SNS). Our colleagues at SLAC need to model complex RFQ cavities with large aspect ratios. Unstructured grids are currently used to resolve the small features in a large computational domain; dynamic mesh adaptation will be added in the future for additional efficiency. The PDEs for electromagnetics are discretized by the FEM method, which leads to a generalized eigenvalue problem Kx = AMx, where K and M are the stiffness and mass matrices, and are very sparse. In a typical cavity model, the number of degrees of freedom is about one million. For such large eigenproblems, direct solution techniques quickly reach the memory limits. Instead, the most widely-used methods are Krylov subspace methods, such as Lanczos or Jacobi-Davidson. In all the Krylov-based algorithms, sparse matrix-vector multiplication (SPMV) must be performed repeatedly. Therefore, the efficiency of SPMV usually determines the eigensolver speed. SPMV is also one of the most heavily used kernels in large-scale numerical simulations.

A fast new algorithm for a robot neurocontroller using inverse QR decomposition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morris, A.S.; Khemaissia, S.

2000-01-01

A new adaptive neural network controller for robots is presented. The controller is based on direct adaptive techniques. Unlike many neural network controllers in the literature, inverse dynamical model evaluation is not required. A numerically robust, computationally efficient processing scheme for neutral network weight estimation is described, namely, the inverse QR decomposition (INVQR). The inverse QR decomposition and a weighted recursive least-squares (WRLS) method for neural network weight estimation is derived using Cholesky factorization of the data matrix. The algorithm that performs the efficient INVQR of the underlying space-time data matrix may be implemented in parallel on a triangular array.more » Furthermore, its systolic architecture is well suited for VLSI implementation. Another important benefit is well suited for VLSI implementation. Another important benefit of the INVQR decomposition is that it solves directly for the time-recursive least-squares filter vector, while avoiding the sequential back-substitution step required by the QR decomposition approaches.« less

An efficient numerical technique for calculating thermal spreading resistance

NASA Technical Reports Server (NTRS)

Gale, E. H., Jr.

1977-01-01

An efficient numerical technique for solving the equations resulting from finite difference analyses of fields governed by Poisson's equation is presented. The method is direct (noniterative)and the computer work required varies with the square of the order of the coefficient matrix. The computational work required varies with the cube of this order for standard inversion techniques, e.g., Gaussian elimination, Jordan, Doolittle, etc.

Sequential time interleaved random equivalent sampling for repetitive signal.

PubMed

Zhao, Yijiu; Liu, Jingjing

2016-12-01

Compressed sensing (CS) based sampling techniques exhibit many advantages over other existing approaches for sparse signal spectrum sensing; they are also incorporated into non-uniform sampling signal reconstruction to improve the efficiency, such as random equivalent sampling (RES). However, in CS based RES, only one sample of each acquisition is considered in the signal reconstruction stage, and it will result in more acquisition runs and longer sampling time. In this paper, a sampling sequence is taken in each RES acquisition run, and the corresponding block measurement matrix is constructed using a Whittaker-Shannon interpolation formula. All the block matrices are combined into an equivalent measurement matrix with respect to all sampling sequences. We implemented the proposed approach with a multi-cores analog-to-digital converter (ADC), whose ADC cores are time interleaved. A prototype realization of this proposed CS based sequential random equivalent sampling method has been developed. It is able to capture an analog waveform at an equivalent sampling rate of 40 GHz while sampled at 1 GHz physically. Experiments indicate that, for a sparse signal, the proposed CS based sequential random equivalent sampling exhibits high efficiency.

Comparison of Compressed Sensing Algorithms for Inversion of 3-D Electrical Resistivity Tomography.

NASA Astrophysics Data System (ADS)

Peddinti, S. R.; Ranjan, S.; Kbvn, D. P.

2016-12-01

Image reconstruction algorithms derived from electrical resistivity tomography (ERT) are highly non-linear, sparse, and ill-posed. The inverse problem is much severe, when dealing with 3-D datasets that result in large sized matrices. Conventional gradient based techniques using L2 norm minimization with some sort of regularization can impose smoothness constraint on the solution. Compressed sensing (CS) is relatively new technique that takes the advantage of inherent sparsity in parameter space in one or the other form. If favorable conditions are met, CS was proven to be an efficient image reconstruction technique that uses limited observations without losing edge sharpness. This paper deals with the development of an open source 3-D resistivity inversion tool using CS framework. The forward model was adopted from RESINVM3D (Pidlisecky et al., 2007) with CS as the inverse code. Discrete cosine transformation (DCT) function was used to induce model sparsity in orthogonal form. Two CS based algorithms viz., interior point method and two-step IST were evaluated on a synthetic layered model with surface electrode observations. The algorithms were tested (in terms of quality and convergence) under varying degrees of parameter heterogeneity, model refinement, and reduced observation data space. In comparison to conventional gradient algorithms, CS was proven to effectively reconstruct the sub-surface image with less computational cost. This was observed by a general increase in NRMSE from 0.5 in 10 iterations using gradient algorithm to 0.8 in 5 iterations using CS algorithms.

Solving large-scale dynamic systems using band Lanczos method in Rockwell NASTRAN on CRAY X-MP

NASA Technical Reports Server (NTRS)

Gupta, V. K.; Zillmer, S. D.; Allison, R. E.

1986-01-01

The improved cost effectiveness using better models, more accurate and faster algorithms and large scale computing offers more representative dynamic analyses. The band Lanczos eigen-solution method was implemented in Rockwell's version of 1984 COSMIC-released NASTRAN finite element structural analysis computer program to effectively solve for structural vibration modes including those of large complex systems exceeding 10,000 degrees of freedom. The Lanczos vectors were re-orthogonalized locally using the Lanczos Method and globally using the modified Gram-Schmidt method for sweeping rigid-body modes and previously generated modes and Lanczos vectors. The truncated band matrix was solved for vibration frequencies and mode shapes using Givens rotations. Numerical examples are included to demonstrate the cost effectiveness and accuracy of the method as implemented in ROCKWELL NASTRAN. The CRAY version is based on RPK's COSMIC/NASTRAN. The band Lanczos method was more reliable and accurate and converged faster than the single vector Lanczos Method. The band Lanczos method was comparable to the subspace iteration method which was a block version of the inverse power method. However, the subspace matrix tended to be fully populated in the case of subspace iteration and not as sparse as a band matrix.

Sparse and redundant representations for inverse problems and recognition

NASA Astrophysics Data System (ADS)

Patel, Vishal M.

Sparse and redundant representation of data enables the description of signals as linear combinations of a few atoms from a dictionary. In this dissertation, we study applications of sparse and redundant representations in inverse problems and object recognition. Furthermore, we propose two novel imaging modalities based on the recently introduced theory of Compressed Sensing (CS). This dissertation consists of four major parts. In the first part of the dissertation, we study a new type of deconvolution algorithm that is based on estimating the image from a shearlet decomposition. Shearlets provide a multi-directional and multi-scale decomposition that has been mathematically shown to represent distributed discontinuities such as edges better than traditional wavelets. We develop a deconvolution algorithm that allows for the approximation inversion operator to be controlled on a multi-scale and multi-directional basis. Furthermore, we develop a method for the automatic determination of the threshold values for the noise shrinkage for each scale and direction without explicit knowledge of the noise variance using a generalized cross validation method. In the second part of the dissertation, we study a reconstruction method that recovers highly undersampled images assumed to have a sparse representation in a gradient domain by using partial measurement samples that are collected in the Fourier domain. Our method makes use of a robust generalized Poisson solver that greatly aids in achieving a significantly improved performance over similar proposed methods. We will demonstrate by experiments that this new technique is more flexible to work with either random or restricted sampling scenarios better than its competitors. In the third part of the dissertation, we introduce a novel Synthetic Aperture Radar (SAR) imaging modality which can provide a high resolution map of the spatial distribution of targets and terrain using a significantly reduced number of needed transmitted and/or received electromagnetic waveforms. We demonstrate that this new imaging scheme, requires no new hardware components and allows the aperture to be compressed. Also, it presents many new applications and advantages which include strong resistance to countermesasures and interception, imaging much wider swaths and reduced on-board storage requirements. The last part of the dissertation deals with object recognition based on learning dictionaries for simultaneous sparse signal approximations and feature extraction. A dictionary is learned for each object class based on given training examples which minimize the representation error with a sparseness constraint. A novel test image is then projected onto the span of the atoms in each learned dictionary. The residual vectors along with the coefficients are then used for recognition. Applications to illumination robust face recognition and automatic target recognition are presented.

Response of selected binomial coefficients to varying degrees of matrix sparseness and to matrices with known data interrelationships

USGS Publications Warehouse

Archer, A.W.; Maples, C.G.

1989-01-01

Numerous departures from ideal relationships are revealed by Monte Carlo simulations of widely accepted binomial coefficients. For example, simulations incorporating varying levels of matrix sparseness (presence of zeros indicating lack of data) and computation of expected values reveal that not only are all common coefficients influenced by zero data, but also that some coefficients do not discriminate between sparse or dense matrices (few zero data). Such coefficients computationally merge mutually shared and mutually absent information and do not exploit all the information incorporated within the standard 2 ?? 2 contingency table; therefore, the commonly used formulae for such coefficients are more complicated than the actual range of values produced. Other coefficients do differentiate between mutual presences and absences; however, a number of these coefficients do not demonstrate a linear relationship to matrix sparseness. Finally, simulations using nonrandom matrices with known degrees of row-by-row similarities signify that several coefficients either do not display a reasonable range of values or are nonlinear with respect to known relationships within the data. Analyses with nonrandom matrices yield clues as to the utility of certain coefficients for specific applications. For example, coefficients such as Jaccard, Dice, and Baroni-Urbani and Buser are useful if correction of sparseness is desired, whereas the Russell-Rao coefficient is useful when sparseness correction is not desired. ?? 1989 International Association for Mathematical Geology.

Sparse representation of whole-brain fMRI signals for identification of functional networks.

PubMed

Lv, Jinglei; Jiang, Xi; Li, Xiang; Zhu, Dajiang; Chen, Hanbo; Zhang, Tuo; Zhang, Shu; Hu, Xintao; Han, Junwei; Huang, Heng; Zhang, Jing; Guo, Lei; Liu, Tianming

2015-02-01

There have been several recent studies that used sparse representation for fMRI signal analysis and activation detection based on the assumption that each voxel's fMRI signal is linearly composed of sparse components. Previous studies have employed sparse coding to model functional networks in various modalities and scales. These prior contributions inspired the exploration of whether/how sparse representation can be used to identify functional networks in a voxel-wise way and on the whole brain scale. This paper presents a novel, alternative methodology of identifying multiple functional networks via sparse representation of whole-brain task-based fMRI signals. Our basic idea is that all fMRI signals within the whole brain of one subject are aggregated into a big data matrix, which is then factorized into an over-complete dictionary basis matrix and a reference weight matrix via an effective online dictionary learning algorithm. Our extensive experimental results have shown that this novel methodology can uncover multiple functional networks that can be well characterized and interpreted in spatial, temporal and frequency domains based on current brain science knowledge. Importantly, these well-characterized functional network components are quite reproducible in different brains. In general, our methods offer a novel, effective and unified solution to multiple fMRI data analysis tasks including activation detection, de-activation detection, and functional network identification. Copyright © 2014 Elsevier B.V. All rights reserved.

Magnetotelluric inversion via reverse time migration algorithm of seismic data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ha, Taeyoung; Shin, Changsoo

2007-07-01

We propose a new algorithm for two-dimensional magnetotelluric (MT) inversion. Our algorithm is an MT inversion based on the steepest descent method, borrowed from the backpropagation technique of seismic inversion or reverse time migration, introduced in the middle 1980s by Lailly and Tarantola. The steepest descent direction can be calculated efficiently by using the symmetry of numerical Green's function derived from a mixed finite element method proposed by Nedelec for Maxwell's equation, without calculating the Jacobian matrix explicitly. We construct three different objective functions by taking the logarithm of the complex apparent resistivity as introduced in the recent waveform inversionmore » algorithm by Shin and Min. These objective functions can be naturally separated into amplitude inversion, phase inversion and simultaneous inversion. We demonstrate our algorithm by showing three inversion results for synthetic data.« less

Large-scale inverse model analyses employing fast randomized data reduction

NASA Astrophysics Data System (ADS)

Lin, Youzuo; Le, Ellen B.; O'Malley, Daniel; Vesselinov, Velimir V.; Bui-Thanh, Tan

2017-08-01

When the number of observations is large, it is computationally challenging to apply classical inverse modeling techniques. We have developed a new computationally efficient technique for solving inverse problems with a large number of observations (e.g., on the order of 107 or greater). Our method, which we call the randomized geostatistical approach (RGA), is built upon the principal component geostatistical approach (PCGA). We employ a data reduction technique combined with the PCGA to improve the computational efficiency and reduce the memory usage. Specifically, we employ a randomized numerical linear algebra technique based on a so-called "sketching" matrix to effectively reduce the dimension of the observations without losing the information content needed for the inverse analysis. In this way, the computational and memory costs for RGA scale with the information content rather than the size of the calibration data. Our algorithm is coded in Julia and implemented in the MADS open-source high-performance computational framework (http://mads.lanl.gov). We apply our new inverse modeling method to invert for a synthetic transmissivity field. Compared to a standard geostatistical approach (GA), our method is more efficient when the number of observations is large. Most importantly, our method is capable of solving larger inverse problems than the standard GA and PCGA approaches. Therefore, our new model inversion method is a powerful tool for solving large-scale inverse problems. The method can be applied in any field and is not limited to hydrogeological applications such as the characterization of aquifer heterogeneity.

FPGA architecture and implementation of sparse matrix vector multiplication for the finite element method

NASA Astrophysics Data System (ADS)

Elkurdi, Yousef; Fernández, David; Souleimanov, Evgueni; Giannacopoulos, Dennis; Gross, Warren J.

2008-04-01

The Finite Element Method (FEM) is a computationally intensive scientific and engineering analysis tool that has diverse applications ranging from structural engineering to electromagnetic simulation. The trends in floating-point performance are moving in favor of Field-Programmable Gate Arrays (FPGAs), hence increasing interest has grown in the scientific community to exploit this technology. We present an architecture and implementation of an FPGA-based sparse matrix-vector multiplier (SMVM) for use in the iterative solution of large, sparse systems of equations arising from FEM applications. FEM matrices display specific sparsity patterns that can be exploited to improve the efficiency of hardware designs. Our architecture exploits FEM matrix sparsity structure to achieve a balance between performance and hardware resource requirements by relying on external SDRAM for data storage while utilizing the FPGAs computational resources in a stream-through systolic approach. The architecture is based on a pipelined linear array of processing elements (PEs) coupled with a hardware-oriented matrix striping algorithm and a partitioning scheme which enables it to process arbitrarily big matrices without changing the number of PEs in the architecture. Therefore, this architecture is only limited by the amount of external RAM available to the FPGA. The implemented SMVM-pipeline prototype contains 8 PEs and is clocked at 110 MHz obtaining a peak performance of 1.76 GFLOPS. For 8 GB/s of memory bandwidth typical of recent FPGA systems, this architecture can achieve 1.5 GFLOPS sustained performance. Using multiple instances of the pipeline, linear scaling of the peak and sustained performance can be achieved. Our stream-through architecture provides the added advantage of enabling an iterative implementation of the SMVM computation required by iterative solution techniques such as the conjugate gradient method, avoiding initialization time due to data loading and setup inside the FPGA internal memory.

Salient Object Detection via Structured Matrix Decomposition.

PubMed

Peng, Houwen; Li, Bing; Ling, Haibin; Hu, Weiming; Xiong, Weihua; Maybank, Stephen J

2016-05-04

Low-rank recovery models have shown potential for salient object detection, where a matrix is decomposed into a low-rank matrix representing image background and a sparse matrix identifying salient objects. Two deficiencies, however, still exist. First, previous work typically assumes the elements in the sparse matrix are mutually independent, ignoring the spatial and pattern relations of image regions. Second, when the low-rank and sparse matrices are relatively coherent, e.g., when there are similarities between the salient objects and background or when the background is complicated, it is difficult for previous models to disentangle them. To address these problems, we propose a novel structured matrix decomposition model with two structural regularizations: (1) a tree-structured sparsity-inducing regularization that captures the image structure and enforces patches from the same object to have similar saliency values, and (2) a Laplacian regularization that enlarges the gaps between salient objects and the background in feature space. Furthermore, high-level priors are integrated to guide the matrix decomposition and boost the detection. We evaluate our model for salient object detection on five challenging datasets including single object, multiple objects and complex scene images, and show competitive results as compared with 24 state-of-the-art methods in terms of seven performance metrics.

An Improved TA-SVM Method Without Matrix Inversion and Its Fast Implementation for Nonstationary Datasets.

PubMed

Shi, Yingzhong; Chung, Fu-Lai; Wang, Shitong

2015-09-01

Recently, a time-adaptive support vector machine (TA-SVM) is proposed for handling nonstationary datasets. While attractive performance has been reported and the new classifier is distinctive in simultaneously solving several SVM subclassifiers locally and globally by using an elegant SVM formulation in an alternative kernel space, the coupling of subclassifiers brings in the computation of matrix inversion, thus resulting to suffer from high computational burden in large nonstationary dataset applications. To overcome this shortcoming, an improved TA-SVM (ITA-SVM) is proposed using a common vector shared by all the SVM subclassifiers involved. ITA-SVM not only keeps an SVM formulation, but also avoids the computation of matrix inversion. Thus, we can realize its fast version, that is, improved time-adaptive core vector machine (ITA-CVM) for large nonstationary datasets by using the CVM technique. ITA-CVM has the merit of asymptotic linear time complexity for large nonstationary datasets as well as inherits the advantage of TA-SVM. The effectiveness of the proposed classifiers ITA-SVM and ITA-CVM is also experimentally confirmed.

Clutter Mitigation in Echocardiography Using Sparse Signal Separation

PubMed Central

Yavneh, Irad

2015-01-01

In ultrasound imaging, clutter artifacts degrade images and may cause inaccurate diagnosis. In this paper, we apply a method called Morphological Component Analysis (MCA) for sparse signal separation with the objective of reducing such clutter artifacts. The MCA approach assumes that the two signals in the additive mix have each a sparse representation under some dictionary of atoms (a matrix), and separation is achieved by finding these sparse representations. In our work, an adaptive approach is used for learning the dictionary from the echo data. MCA is compared to Singular Value Filtering (SVF), a Principal Component Analysis- (PCA-) based filtering technique, and to a high-pass Finite Impulse Response (FIR) filter. Each filter is applied to a simulated hypoechoic lesion sequence, as well as experimental cardiac ultrasound data. MCA is demonstrated in both cases to outperform the FIR filter and obtain results comparable to the SVF method in terms of contrast-to-noise ratio (CNR). Furthermore, MCA shows a lower impact on tissue sections while removing the clutter artifacts. In experimental heart data, MCA obtains in our experiments clutter mitigation with an average CNR improvement of 1.33 dB. PMID:26199622

Guided wave localization of damage via sparse reconstruction

NASA Astrophysics Data System (ADS)

Levine, Ross M.; Michaels, Jennifer E.; Lee, Sang Jun

2012-05-01

Ultrasonic guided waves are frequently applied for structural health monitoring and nondestructive evaluation of plate-like metallic and composite structures. Spatially distributed arrays of fixed piezoelectric transducers can be used to detect damage by recording and analyzing all pairwise signal combinations. By subtracting pre-recorded baseline signals, the effects due to scatterer interactions can be isolated. Given these residual signals, techniques such as delay-and-sum imaging are capable of detecting flaws, but do not exploit the expected sparse nature of damage. It is desired to determine the location of a possible flaw by leveraging the anticipated sparsity of damage; i.e., most of the structure is assumed to be damage-free. Unlike least-squares methods, L1-norm minimization techniques favor sparse solutions to inverse problems such as the one considered here of locating damage. Using this type of method, it is possible to exploit sparsity of damage by formulating the imaging process as an optimization problem. A model-based damage localization method is presented that simultaneously decomposes all scattered signals into location-based signal components. The method is first applied to simulated data to investigate sensitivity to both model mismatch and additive noise, and then to experimental data recorded from an aluminum plate with artificial damage. Compared to delay-and-sum imaging, results exhibit a significant reduction in both spot size and imaging artifacts when the model is reasonably well-matched to the data.

Bayesian inference of the number of factors in gene-expression analysis: application to human virus challenge studies.

PubMed

Chen, Bo; Chen, Minhua; Paisley, John; Zaas, Aimee; Woods, Christopher; Ginsburg, Geoffrey S; Hero, Alfred; Lucas, Joseph; Dunson, David; Carin, Lawrence

2010-11-09

Nonparametric Bayesian techniques have been developed recently to extend the sophistication of factor models, allowing one to infer the number of appropriate factors from the observed data. We consider such techniques for sparse factor analysis, with application to gene-expression data from three virus challenge studies. Particular attention is placed on employing the Beta Process (BP), the Indian Buffet Process (IBP), and related sparseness-promoting techniques to infer a proper number of factors. The posterior density function on the model parameters is computed using Gibbs sampling and variational Bayesian (VB) analysis. Time-evolving gene-expression data are considered for respiratory syncytial virus (RSV), Rhino virus, and influenza, using blood samples from healthy human subjects. These data were acquired in three challenge studies, each executed after receiving institutional review board (IRB) approval from Duke University. Comparisons are made between several alternative means of per-forming nonparametric factor analysis on these data, with comparisons as well to sparse-PCA and Penalized Matrix Decomposition (PMD), closely related non-Bayesian approaches. Applying the Beta Process to the factor scores, or to the singular values of a pseudo-SVD construction, the proposed algorithms infer the number of factors in gene-expression data. For real data the "true" number of factors is unknown; in our simulations we consider a range of noise variances, and the proposed Bayesian models inferred the number of factors accurately relative to other methods in the literature, such as sparse-PCA and PMD. We have also identified a "pan-viral" factor of importance for each of the three viruses considered in this study. We have identified a set of genes associated with this pan-viral factor, of interest for early detection of such viruses based upon the host response, as quantified via gene-expression data.

Shape models of asteroids reconstructed from WISE data and sparse photometry

NASA Astrophysics Data System (ADS)

Durech, Josef; Hanus, Josef; Ali-Lagoa, Victor

2017-10-01

By combining sparse-in-time photometry from the Lowell Observatory photometry database with WISE observations, we reconstructed convex shape models for about 700 new asteroids and for other ~850 we derived 'partial' models with unconstrained ecliptic longitude of the spin axis direction. In our approach, the WISE data were treated as reflected light, which enabled us to directly join them with sparse photometry into one dataset that was processed by the lightcurve inversion method. This simplified treatment of thermal infrared data turned out to provide correct results, because in most cases the phase offset between optical and thermal lightcurves was small and the correct sidereal rotation period was determined. The spin and shape parameters derived from only optical data and from a combination of optical and WISE data were very similar. The new models together with those already available in the Database of Asteroid Models from Inversion Techniques (DAMIT) represent a sample of ~1650 asteroids. When including also partial models, the total sample is about 2500 asteroids, which significantly increases the number of models with respect to those that have been available so far. We will show the distribution of spin axes for different size groups and also for several collisional families. These observed distributions in general agree with theoretical expectations proving that smaller asteroids are more affected by YORP/Yarkovsky evolution. In asteroid families, we see a clear bimodal distribution of prograde/retrograde rotation that correlates with the position to the right/left from the center of the family measured by the semimajor axis.

Blind source separation by sparse decomposition

NASA Astrophysics Data System (ADS)

Zibulevsky, Michael; Pearlmutter, Barak A.

2000-04-01

The blind source separation problem is to extract the underlying source signals from a set of their linear mixtures, where the mixing matrix is unknown. This situation is common, eg in acoustics, radio, and medical signal processing. We exploit the property of the sources to have a sparse representation in a corresponding signal dictionary. Such a dictionary may consist of wavelets, wavelet packets, etc., or be obtained by learning from a given family of signals. Starting from the maximum a posteriori framework, which is applicable to the case of more sources than mixtures, we derive a few other categories of objective functions, which provide faster and more robust computations, when there are an equal number of sources and mixtures. Our experiments with artificial signals and with musical sounds demonstrate significantly better separation than other known techniques.

Improving IMRT delivery efficiency with reweighted L1-minimization for inverse planning

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Hojin; Becker, Stephen; Lee, Rena

2013-07-15

Purpose: This study presents an improved technique to further simplify the fluence-map in intensity modulated radiation therapy (IMRT) inverse planning, thereby reducing plan complexity and improving delivery efficiency, while maintaining the plan quality.Methods: First-order total-variation (TV) minimization (min.) based on L1-norm has been proposed to reduce the complexity of fluence-map in IMRT by generating sparse fluence-map variations. However, with stronger dose sparing to the critical structures, the inevitable increase in the fluence-map complexity can lead to inefficient dose delivery. Theoretically, L0-min. is the ideal solution for the sparse signal recovery problem, yet practically intractable due to its nonconvexity of themore » objective function. As an alternative, the authors use the iteratively reweighted L1-min. technique to incorporate the benefits of the L0-norm into the tractability of L1-min. The weight multiplied to each element is inversely related to the magnitude of the corresponding element, which is iteratively updated by the reweighting process. The proposed penalizing process combined with TV min. further improves sparsity in the fluence-map variations, hence ultimately enhancing the delivery efficiency. To validate the proposed method, this work compares three treatment plans obtained from quadratic min. (generally used in clinic IMRT), conventional TV min., and our proposed reweighted TV min. techniques, implemented by a large-scale L1-solver (template for first-order conic solver), for five patient clinical data. Criteria such as conformation number (CN), modulation index (MI), and estimated treatment time are employed to assess the relationship between the plan quality and delivery efficiency.Results: The proposed method yields simpler fluence-maps than the quadratic and conventional TV based techniques. To attain a given CN and dose sparing to the critical organs for 5 clinical cases, the proposed method reduces the number of segments by 10-15 and 30-35, relative to TV min. and quadratic min. based plans, while MIs decreases by about 20%-30% and 40%-60% over the plans by two existing techniques, respectively. With such conditions, the total treatment time of the plans obtained from our proposed method can be reduced by 12-30 s and 30-80 s mainly due to greatly shorter multileaf collimator (MLC) traveling time in IMRT step-and-shoot delivery.Conclusions: The reweighted L1-minimization technique provides a promising solution to simplify the fluence-map variations in IMRT inverse planning. It improves the delivery efficiency by reducing the entire segments and treatment time, while maintaining the plan quality in terms of target conformity and critical structure sparing.« less

A sparse reconstruction method for the estimation of multiresolution emission fields via atmospheric inversion

DOE PAGES

Ray, J.; Lee, J.; Yadav, V.; ...

2014-08-20

We present a sparse reconstruction scheme that can also be used to ensure non-negativity when fitting wavelet-based random field models to limited observations in non-rectangular geometries. The method is relevant when multiresolution fields are estimated using linear inverse problems. Examples include the estimation of emission fields for many anthropogenic pollutants using atmospheric inversion or hydraulic conductivity in aquifers from flow measurements. The scheme is based on three new developments. Firstly, we extend an existing sparse reconstruction method, Stagewise Orthogonal Matching Pursuit (StOMP), to incorporate prior information on the target field. Secondly, we develop an iterative method that uses StOMP tomore » impose non-negativity on the estimated field. Finally, we devise a method, based on compressive sensing, to limit the estimated field within an irregularly shaped domain. We demonstrate the method on the estimation of fossil-fuel CO 2 (ffCO 2) emissions in the lower 48 states of the US. The application uses a recently developed multiresolution random field model and synthetic observations of ffCO 2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of two. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.« less

Using a multifrontal sparse solver in a high performance, finite element code

NASA Technical Reports Server (NTRS)

King, Scott D.; Lucas, Robert; Raefsky, Arthur

1990-01-01

We consider the performance of the finite element method on a vector supercomputer. The computationally intensive parts of the finite element method are typically the individual element forms and the solution of the global stiffness matrix both of which are vectorized in high performance codes. To further increase throughput, new algorithms are needed. We compare a multifrontal sparse solver to a traditional skyline solver in a finite element code on a vector supercomputer. The multifrontal solver uses the Multiple-Minimum Degree reordering heuristic to reduce the number of operations required to factor a sparse matrix and full matrix computational kernels (e.g., BLAS3) to enhance vector performance. The net result in an order-of-magnitude reduction in run time for a finite element application on one processor of a Cray X-MP.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carpentier, J.L.; Di Bono, P.J.; Tournebise, P.J.

The efficient bounding method for DC contingency analysis is improved using reciprocity properties. Knowing the consequences of the outage of a branch, these properties provide the consequences on that branch of various kinds of outages. This is used in order to reduce computation times and to get rid of some difficulties, such as those occurring when a branch flow is close to its limit before outage. Compensation, sparse vector, sparse inverse and bounding techniques are also used. A program has been implemented for single branch outages and tested on actual French EHV 650 bus network. Computation times are 60% ofmore » the Efficient Bounding method. The relevant algorithm is described in detail in the first part of this paper. In the second part, reciprocity properties and bounding formulas are extended for multiple branch outages and for multiple generator or load outages. An algorithm is proposed in order to handle all these cases simultaneously.« less

Characterizing the inverses of block tridiagonal, block Toeplitz matrices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boffi, Nicholas M.; Hill, Judith C.; Reuter, Matthew G.

2014-12-04

We consider the inversion of block tridiagonal, block Toeplitz matrices and comment on the behaviour of these inverses as one moves away from the diagonal. Using matrix M bius transformations, we first present an O(1) representation (with respect to the number of block rows and block columns) for the inverse matrix and subsequently use this representation to characterize the inverse matrix. There are four symmetry-distinct cases where the blocks of the inverse matrix (i) decay to zero on both sides of the diagonal, (ii) oscillate on both sides, (iii) decay on one side and oscillate on the other and (iv)more » decay on one side and grow on the other. This characterization exposes the necessary conditions for the inverse matrix to be numerically banded and may also aid in the design of preconditioners and fast algorithms. Finally, we present numerical examples of these matrix types.« less

Algorithms and Application of Sparse Matrix Assembly and Equation Solvers for Aeroacoustics

NASA Technical Reports Server (NTRS)

Watson, W. R.; Nguyen, D. T.; Reddy, C. J.; Vatsa, V. N.; Tang, W. H.

2001-01-01

An algorithm for symmetric sparse equation solutions on an unstructured grid is described. Efficient, sequential sparse algorithms for degree-of-freedom reordering, supernodes, symbolic/numerical factorization, and forward backward solution phases are reviewed. Three sparse algorithms for the generation and assembly of symmetric systems of matrix equations are presented. The accuracy and numerical performance of the sequential version of the sparse algorithms are evaluated over the frequency range of interest in a three-dimensional aeroacoustics application. Results show that the solver solutions are accurate using a discretization of 12 points per wavelength. Results also show that the first assembly algorithm is impractical for high-frequency noise calculations. The second and third assembly algorithms have nearly equal performance at low values of source frequencies, but at higher values of source frequencies the third algorithm saves CPU time and RAM. The CPU time and the RAM required by the second and third assembly algorithms are two orders of magnitude smaller than that required by the sparse equation solver. A sequential version of these sparse algorithms can, therefore, be conveniently incorporated into a substructuring for domain decomposition formulation to achieve parallel computation, where different substructures are handles by different parallel processors.

Automatic segmentation of right ventricle on ultrasound images using sparse matrix transform and level set

NASA Astrophysics Data System (ADS)

Qin, Xulei; Cong, Zhibin; Halig, Luma V.; Fei, Baowei

2013-03-01

An automatic framework is proposed to segment right ventricle on ultrasound images. This method can automatically segment both epicardial and endocardial boundaries from a continuous echocardiography series by combining sparse matrix transform (SMT), a training model, and a localized region based level set. First, the sparse matrix transform extracts main motion regions of myocardium as eigenimages by analyzing statistical information of these images. Second, a training model of right ventricle is registered to the extracted eigenimages in order to automatically detect the main location of the right ventricle and the corresponding transform relationship between the training model and the SMT-extracted results in the series. Third, the training model is then adjusted as an adapted initialization for the segmentation of each image in the series. Finally, based on the adapted initializations, a localized region based level set algorithm is applied to segment both epicardial and endocardial boundaries of the right ventricle from the whole series. Experimental results from real subject data validated the performance of the proposed framework in segmenting right ventricle from echocardiography. The mean Dice scores for both epicardial and endocardial boundaries are 89.1%+/-2.3% and 83.6+/-7.3%, respectively. The automatic segmentation method based on sparse matrix transform and level set can provide a useful tool for quantitative cardiac imaging.

Robust Principal Component Analysis Regularized by Truncated Nuclear Norm for Identifying Differentially Expressed Genes.

PubMed

Wang, Ya-Xuan; Gao, Ying-Lian; Liu, Jin-Xing; Kong, Xiang-Zhen; Li, Hai-Jun

2017-09-01

Identifying differentially expressed genes from the thousands of genes is a challenging task. Robust principal component analysis (RPCA) is an efficient method in the identification of differentially expressed genes. RPCA method uses nuclear norm to approximate the rank function. However, theoretical studies showed that the nuclear norm minimizes all singular values, so it may not be the best solution to approximate the rank function. The truncated nuclear norm is defined as the sum of some smaller singular values, which may achieve a better approximation of the rank function than nuclear norm. In this paper, a novel method is proposed by replacing nuclear norm of RPCA with the truncated nuclear norm, which is named robust principal component analysis regularized by truncated nuclear norm (TRPCA). The method decomposes the observation matrix of genomic data into a low-rank matrix and a sparse matrix. Because the significant genes can be considered as sparse signals, the differentially expressed genes are viewed as the sparse perturbation signals. Thus, the differentially expressed genes can be identified according to the sparse matrix. The experimental results on The Cancer Genome Atlas data illustrate that the TRPCA method outperforms other state-of-the-art methods in the identification of differentially expressed genes.

HYPOTHESIS TESTING FOR HIGH-DIMENSIONAL SPARSE BINARY REGRESSION

PubMed Central

Mukherjee, Rajarshi; Pillai, Natesh S.; Lin, Xihong

2015-01-01

In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate the complexity of the hypothesis testing problem when the design matrix is sparse. We observe a new phenomenon in the behavior of detection boundary which does not occur in the case of Gaussian linear regression. We derive the detection boundary as a function of two components: a design matrix sparsity index and signal strength, each of which is a function of the sparsity of the alternative. For any alternative, if the design matrix sparsity index is too high, any test is asymptotically powerless irrespective of the magnitude of signal strength. For binary design matrices with the sparsity index that is not too high, our results are parallel to those in the Gaussian case. In this context, we derive detection boundaries for both dense and sparse regimes. For the dense regime, we show that the generalized likelihood ratio is rate optimal; for the sparse regime, we propose an extended Higher Criticism Test and show it is rate optimal and sharp. We illustrate the finite sample properties of the theoretical results using simulation studies. PMID:26246645

Bilinear Inverse Problems: Theory, Algorithms, and Applications

NASA Astrophysics Data System (ADS)

Ling, Shuyang

We will discuss how several important real-world signal processing problems, such as self-calibration and blind deconvolution, can be modeled as bilinear inverse problems and solved by convex and nonconvex optimization approaches. In Chapter 2, we bring together three seemingly unrelated concepts, self-calibration, compressive sensing and biconvex optimization. We show how several self-calibration problems can be treated efficiently within the framework of biconvex compressive sensing via a new method called SparseLift. More specifically, we consider a linear system of equations y = DAx, where the diagonal matrix D (which models the calibration error) is unknown and x is an unknown sparse signal. By "lifting" this biconvex inverse problem and exploiting sparsity in this model, we derive explicit theoretical guarantees under which both x and D can be recovered exactly, robustly, and numerically efficiently. In Chapter 3, we study the question of the joint blind deconvolution and blind demixing, i.e., extracting a sequence of functions [special characters omitted] from observing only the sum of their convolutions [special characters omitted]. In particular, for the special case s = 1, it becomes the well-known blind deconvolution problem. We present a non-convex algorithm which guarantees exact recovery under conditions that are competitive with convex optimization methods, with the additional advantage of being computationally much more efficient. We discuss several applications of the proposed framework in image processing and wireless communications in connection with the Internet-of-Things. In Chapter 4, we consider three different self-calibration models of practical relevance. We show how their corresponding bilinear inverse problems can be solved by both the simple linear least squares approach and the SVD-based approach. As a consequence, the proposed algorithms are numerically extremely efficient, thus allowing for real-time deployment. Explicit theoretical guarantees and stability theory are derived and the number of sampling complexity is nearly optimal (up to a poly-log factor). Applications in imaging sciences and signal processing are discussed and numerical simulations are presented to demonstrate the effectiveness and efficiency of our approach.

Source term identification in atmospheric modelling via sparse optimization

NASA Astrophysics Data System (ADS)

Adam, Lukas; Branda, Martin; Hamburger, Thomas

2015-04-01

Inverse modelling plays an important role in identifying the amount of harmful substances released into atmosphere during major incidents such as power plant accidents or volcano eruptions. Another possible application of inverse modelling lies in the monitoring the CO2 emission limits where only observations at certain places are available and the task is to estimate the total releases at given locations. This gives rise to minimizing the discrepancy between the observations and the model predictions. There are two standard ways of solving such problems. In the first one, this discrepancy is regularized by adding additional terms. Such terms may include Tikhonov regularization, distance from a priori information or a smoothing term. The resulting, usually quadratic, problem is then solved via standard optimization solvers. The second approach assumes that the error term has a (normal) distribution and makes use of Bayesian modelling to identify the source term. Instead of following the above-mentioned approaches, we utilize techniques from the field of compressive sensing. Such techniques look for a sparsest solution (solution with the smallest number of nonzeros) of a linear system, where a maximal allowed error term may be added to this system. Even though this field is a developed one with many possible solution techniques, most of them do not consider even the simplest constraints which are naturally present in atmospheric modelling. One of such examples is the nonnegativity of release amounts. We believe that the concept of a sparse solution is natural in both problems of identification of the source location and of the time process of the source release. In the first case, it is usually assumed that there are only few release points and the task is to find them. In the second case, the time window is usually much longer than the duration of the actual release. In both cases, the optimal solution should contain a large amount of zeros, giving rise to the concept of sparsity. In the paper, we summarize several optimization techniques which are used for finding sparse solutions and propose their modifications to handle selected constraints such as nonnegativity constraints and simple linear constraints, for example the minimal or maximal amount of total release. These techniques range from successive convex approximations to solution of one nonconvex problem. On simple examples, we explain these techniques and compare them from the point of implementation simplicity, approximation capability and convergence properties. Finally, these methods will be applied on the European Tracer Experiment (ETEX) data and the results will be compared with the current state of arts techniques such as regularized least squares or Bayesian approach. The obtained results show the surprisingly good results of these techniques. This research is supported by EEA/Norwegian Financial Mechanism under project 7F14287 STRADI.

A cut-&-paste strategy for the 3-D inversion of helicopter-borne electromagnetic data - I. 3-D inversion using the explicit Jacobian and a tensor-based formulation

NASA Astrophysics Data System (ADS)

Scheunert, M.; Ullmann, A.; Afanasjew, M.; Börner, R.-U.; Siemon, B.; Spitzer, K.

2016-06-01

We present an inversion concept for helicopter-borne frequency-domain electromagnetic (HEM) data capable of reconstructing 3-D conductivity structures in the subsurface. Standard interpretation procedures often involve laterally constrained stitched 1-D inversion techniques to create pseudo-3-D models that are largely representative for smoothly varying conductivity distributions in the subsurface. Pronounced lateral conductivity changes may, however, produce significant artifacts that can lead to serious misinterpretation. Still, 3-D inversions of entire survey data sets are numerically very expensive. Our approach is therefore based on a cut-&-paste strategy whereupon the full 3-D inversion needs to be applied only to those parts of the survey where the 1-D inversion actually fails. The introduced 3-D Gauss-Newton inversion scheme exploits information given by a state-of-the-art (laterally constrained) 1-D inversion. For a typical HEM measurement, an explicit representation of the Jacobian matrix is inevitable which is caused by the unique transmitter-receiver relation. We introduce tensor quantities which facilitate the matrix assembly of the forward operator as well as the efficient calculation of the Jacobian. The finite difference forward operator incorporates the displacement currents because they may seriously affect the electromagnetic response at frequencies above 100. Finally, we deliver the proof of concept for the inversion using a synthetic data set with a noise level of up to 5%.

DAMIT: a database of asteroid models

NASA Astrophysics Data System (ADS)

Durech, J.; Sidorin, V.; Kaasalainen, M.

2010-04-01

Context. Apart from a few targets that were directly imaged by spacecraft, remote sensing techniques are the main source of information about the basic physical properties of asteroids, such as the size, the spin state, or the spectral type. The most widely used observing technique - time-resolved photometry - provides us with data that can be used for deriving asteroid shapes and spin states. In the past decade, inversion of asteroid lightcurves has led to more than a hundred asteroid models. In the next decade, when data from all-sky surveys are available, the number of asteroid models will increase. Combining photometry with, e.g., adaptive optics data produces more detailed models. Aims: We created the Database of Asteroid Models from Inversion Techniques (DAMIT) with the aim of providing the astronomical community access to reliable and up-to-date physical models of asteroids - i.e., their shapes, rotation periods, and spin axis directions. Models from DAMIT can be used for further detailed studies of individual objects, as well as for statistical studies of the whole set. Methods: Most DAMIT models were derived from photometric data by the lightcurve inversion method. Some of them have been further refined or scaled using adaptive optics images, infrared observations, or occultation data. A substantial number of the models were derived also using sparse photometric data from astrometric databases. Results: At present, the database contains models of more than one hundred asteroids. For each asteroid, DAMIT provides the polyhedral shape model, the sidereal rotation period, the spin axis direction, and the photometric data used for the inversion. The database is updated when new models are available or when already published models are updated or refined. We have also released the C source code for the lightcurve inversion and for the direct problem (updates and extensions will follow).

Quantum Support Vector Machine for Big Data Classification

NASA Astrophysics Data System (ADS)

Rebentrost, Patrick; Mohseni, Masoud; Lloyd, Seth

2014-09-01

Supervised machine learning is the classification of new data based on already classified training examples. In this work, we show that the support vector machine, an optimized binary classifier, can be implemented on a quantum computer, with complexity logarithmic in the size of the vectors and the number of training examples. In cases where classical sampling algorithms require polynomial time, an exponential speedup is obtained. At the core of this quantum big data algorithm is a nonsparse matrix exponentiation technique for efficiently performing a matrix inversion of the training data inner-product (kernel) matrix.

Strategies for vectorizing the sparse matrix vector product on the CRAY XMP, CRAY 2, and CYBER 205

NASA Technical Reports Server (NTRS)

Bauschlicher, Charles W., Jr.; Partridge, Harry

1987-01-01

Large, randomly sparse matrix vector products are important in a number of applications in computational chemistry, such as matrix diagonalization and the solution of simultaneous equations. Vectorization of this process is considered for the CRAY XMP, CRAY 2, and CYBER 205, using a matrix of dimension of 20,000 with from 1 percent to 6 percent nonzeros. Efficient scatter/gather capabilities add coding flexibility and yield significant improvements in performance. For the CYBER 205, it is shown that minor changes in the IO can reduce the CPU time by a factor of 50. Similar changes in the CRAY codes make a far smaller improvement.

Efficient electromagnetic source imaging with adaptive standardized LORETA/FOCUSS.

PubMed

Schimpf, Paul H; Liu, Hesheng; Ramon, Ceon; Haueisen, Jens

2005-05-01

Functional brain imaging and source localization based on the scalp's potential field require a solution to an ill-posed inverse problem with many solutions. This makes it necessary to incorporate a priori knowledge in order to select a particular solution. A computational challenge for some subject-specific head models is that many inverse algorithms require a comprehensive sampling of the candidate source space at the desired resolution. In this study, we present an algorithm that can accurately reconstruct details of localized source activity from a sparse sampling of the candidate source space. Forward computations are minimized through an adaptive procedure that increases source resolution as the spatial extent is reduced. With this algorithm, we were able to compute inverses using only 6% to 11% of the full resolution lead-field, with a localization accuracy that was not significantly different than an exhaustive search through a fully-sampled source space. The technique is, therefore, applicable for use with anatomically-realistic, subject-specific forward models for applications with spatially concentrated source activity.

Coded excitation with spectrum inversion (CEXSI) for ultrasound array imaging.

PubMed

Wang, Yao; Metzger, Kurt; Stephens, Douglas N; Williams, Gregory; Brownlie, Scott; O'Donnell, Matthew

2003-07-01

In this paper, a scheme called coded excitation with spectrum inversion (CEXSI) is presented. An established optimal binary code whose spectrum has no nulls and possesses the least variation is encoded as a burst for transmission. Using this optimal code, the decoding filter can be derived directly from its inverse spectrum. Various transmission techniques can be used to improve energy coupling within the system pass-band. We demonstrate its potential to achieve excellent decoding with very low (< 80 dB) side-lobes. For a 2.6 micros code, an array element with a center frequency of 10 MHz and fractional bandwidth of 38%, range side-lobes of about 40 dB have been achieved experimentally with little compromise in range resolution. The signal-to-noise ratio (SNR) improvement also has been characterized at about 14 dB. Along with simulations and experimental data, we present a formulation of the scheme, according to which CEXSI can be extended to improve SNR in sparse array imaging in general.

Linear-scaling density-functional simulations of charged point defects in Al2O3 using hierarchical sparse matrix algebra.

PubMed

Hine, N D M; Haynes, P D; Mostofi, A A; Payne, M C

2010-09-21

We present calculations of formation energies of defects in an ionic solid (Al(2)O(3)) extrapolated to the dilute limit, corresponding to a simulation cell of infinite size. The large-scale calculations required for this extrapolation are enabled by developments in the approach to parallel sparse matrix algebra operations, which are central to linear-scaling density-functional theory calculations. The computational cost of manipulating sparse matrices, whose sizes are determined by the large number of basis functions present, is greatly improved with this new approach. We present details of the sparse algebra scheme implemented in the ONETEP code using hierarchical sparsity patterns, and demonstrate its use in calculations on a wide range of systems, involving thousands of atoms on hundreds to thousands of parallel processes.

Characterizing and differentiating task-based and resting state fMRI signals via two-stage sparse representations.

PubMed

Zhang, Shu; Li, Xiang; Lv, Jinglei; Jiang, Xi; Guo, Lei; Liu, Tianming

2016-03-01

A relatively underexplored question in fMRI is whether there are intrinsic differences in terms of signal composition patterns that can effectively characterize and differentiate task-based or resting state fMRI (tfMRI or rsfMRI) signals. In this paper, we propose a novel two-stage sparse representation framework to examine the fundamental difference between tfMRI and rsfMRI signals. Specifically, in the first stage, the whole-brain tfMRI or rsfMRI signals of each subject were composed into a big data matrix, which was then factorized into a subject-specific dictionary matrix and a weight coefficient matrix for sparse representation. In the second stage, all of the dictionary matrices from both tfMRI/rsfMRI data across multiple subjects were composed into another big data-matrix, which was further sparsely represented by a cross-subjects common dictionary and a weight matrix. This framework has been applied on the recently publicly released Human Connectome Project (HCP) fMRI data and experimental results revealed that there are distinctive and descriptive atoms in the cross-subjects common dictionary that can effectively characterize and differentiate tfMRI and rsfMRI signals, achieving 100% classification accuracy. Moreover, our methods and results can be meaningfully interpreted, e.g., the well-known default mode network (DMN) activities can be recovered from the very noisy and heterogeneous aggregated big-data of tfMRI and rsfMRI signals across all subjects in HCP Q1 release.

Background recovery via motion-based robust principal component analysis with matrix factorization

NASA Astrophysics Data System (ADS)

Pan, Peng; Wang, Yongli; Zhou, Mingyuan; Sun, Zhipeng; He, Guoping

2018-03-01

Background recovery is a key technique in video analysis, but it still suffers from many challenges, such as camouflage, lighting changes, and diverse types of image noise. Robust principal component analysis (RPCA), which aims to recover a low-rank matrix and a sparse matrix, is a general framework for background recovery. The nuclear norm is widely used as a convex surrogate for the rank function in RPCA, which requires computing the singular value decomposition (SVD), a task that is increasingly costly as matrix sizes and ranks increase. However, matrix factorization greatly reduces the dimension of the matrix for which the SVD must be computed. Motion information has been shown to improve low-rank matrix recovery in RPCA, but this method still finds it difficult to handle original video data sets because of its batch-mode formulation and implementation. Hence, in this paper, we propose a motion-assisted RPCA model with matrix factorization (FM-RPCA) for background recovery. Moreover, an efficient linear alternating direction method of multipliers with a matrix factorization (FL-ADM) algorithm is designed for solving the proposed FM-RPCA model. Experimental results illustrate that the method provides stable results and is more efficient than the current state-of-the-art algorithms.

Computing sparse derivatives and consecutive zeros problem

NASA Astrophysics Data System (ADS)

Chandra, B. V. Ravi; Hossain, Shahadat

2013-02-01

We describe a substitution based sparse Jacobian matrix determination method using algorithmic differentiation. Utilizing the a priori known sparsity pattern, a compression scheme is determined using graph coloring. The "compressed pattern" of the Jacobian matrix is then reordered into a form suitable for computation by substitution. We show that the column reordering of the compressed pattern matrix (so as to align the zero entries into consecutive locations in each row) can be viewed as a variant of traveling salesman problem. Preliminary computational results show that on the test problems the performance of nearest-neighbor type heuristic algorithms is highly encouraging.

From the Rendering Equation to Stratified Light Transport Inversion

DTIC Science & Technology

2010-12-09

iteratively. These approaches relate closely to the radiosity method for diffuse global illumination in forward rendering (Hanrahan et al, 1991; Gortler et...currently simply use sparse matrices to represent T, we are also interested in exploring connections with hierar- chical and wavelet radiosity as in...Seidel iterative methods used in radiosity . 2.4 Inverse Light Transport Previous work on inverse rendering has considered inversion of the direct

Partitioning Rectangular and Structurally Nonsymmetric Sparse Matrices for Parallel Processing

DOE Office of Scientific and Technical Information (OSTI.GOV)

B. Hendrickson; T.G. Kolda

1998-09-01

A common operation in scientific computing is the multiplication of a sparse, rectangular or structurally nonsymmetric matrix and a vector. In many applications the matrix- transpose-vector product is also required. This paper addresses the efficient parallelization of these operations. We show that the problem can be expressed in terms of partitioning bipartite graphs. We then introduce several algorithms for this partitioning problem and compare their performance on a set of test matrices.

A tight and explicit representation of Q in sparse QR factorization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ng, E.G.; Peyton, B.W.

1992-05-01

In QR factorization of a sparse m{times}n matrix A (m {ge} n) the orthogonal factor Q is often stored implicitly as a lower trapezoidal matrix H known as the Householder matrix. This paper presents a simple characterization of the row structure of Q, which could be used as the basis for a sparse data structure that can store Q explicitly. The new characterization is a simple extension of a well known row-oriented characterization of the structure of H. Hare, Johnson, Olesky, and van den Driessche have recently provided a complete sparsity analysis of the QR factorization. Let U be themore » matrix consisting of the first n columns of Q. Using results from, we show that the data structures for H and U resulting from our characterizations are tight when A is a strong Hall matrix. We also show that H and the lower trapezoidal part of U have the same sparsity characterization when A is strong Hall. We then show that this characterization can be extended to any weak Hall matrix that has been permuted into block upper triangular form. Finally, we show that permuting to block triangular form never increases the fill incurred during the factorization.« less

Doubly Nonparametric Sparse Nonnegative Matrix Factorization Based on Dependent Indian Buffet Processes.

PubMed

Xuan, Junyu; Lu, Jie; Zhang, Guangquan; Xu, Richard Yi Da; Luo, Xiangfeng

2018-05-01

Sparse nonnegative matrix factorization (SNMF) aims to factorize a data matrix into two optimized nonnegative sparse factor matrices, which could benefit many tasks, such as document-word co-clustering. However, the traditional SNMF typically assumes the number of latent factors (i.e., dimensionality of the factor matrices) to be fixed. This assumption makes it inflexible in practice. In this paper, we propose a doubly sparse nonparametric NMF framework to mitigate this issue by using dependent Indian buffet processes (dIBP). We apply a correlation function for the generation of two stick weights associated with each column pair of factor matrices while still maintaining their respective marginal distribution specified by IBP. As a consequence, the generation of two factor matrices will be columnwise correlated. Under this framework, two classes of correlation function are proposed: 1) using bivariate Beta distribution and 2) using Copula function. Compared with the single IBP-based NMF, this paper jointly makes two factor matrices nonparametric and sparse, which could be applied to broader scenarios, such as co-clustering. This paper is seen to be much more flexible than Gaussian process-based and hierarchial Beta process-based dIBPs in terms of allowing the two corresponding binary matrix columns to have greater variations in their nonzero entries. Our experiments on synthetic data show the merits of this paper compared with the state-of-the-art models in respect of factorization efficiency, sparsity, and flexibility. Experiments on real-world data sets demonstrate the efficiency of this paper in document-word co-clustering tasks.

Large Covariance Estimation by Thresholding Principal Orthogonal Complements

PubMed Central

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2012-01-01

This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the Principal Orthogonal complEment Thresholding (POET) method to explore such an approximate factor structure with sparsity. The POET estimator includes the sample covariance matrix, the factor-based covariance matrix (Fan, Fan, and Lv, 2008), the thresholding estimator (Bickel and Levina, 2008) and the adaptive thresholding estimator (Cai and Liu, 2011) as specific examples. We provide mathematical insights when the factor analysis is approximately the same as the principal component analysis for high-dimensional data. The rates of convergence of the sparse residual covariance matrix and the conditional sparse covariance matrix are studied under various norms. It is shown that the impact of estimating the unknown factors vanishes as the dimensionality increases. The uniform rates of convergence for the unobserved factors and their factor loadings are derived. The asymptotic results are also verified by extensive simulation studies. Finally, a real data application on portfolio allocation is presented. PMID:24348088

Large Covariance Estimation by Thresholding Principal Orthogonal Complements.

PubMed

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2013-09-01

This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the Principal Orthogonal complEment Thresholding (POET) method to explore such an approximate factor structure with sparsity. The POET estimator includes the sample covariance matrix, the factor-based covariance matrix (Fan, Fan, and Lv, 2008), the thresholding estimator (Bickel and Levina, 2008) and the adaptive thresholding estimator (Cai and Liu, 2011) as specific examples. We provide mathematical insights when the factor analysis is approximately the same as the principal component analysis for high-dimensional data. The rates of convergence of the sparse residual covariance matrix and the conditional sparse covariance matrix are studied under various norms. It is shown that the impact of estimating the unknown factors vanishes as the dimensionality increases. The uniform rates of convergence for the unobserved factors and their factor loadings are derived. The asymptotic results are also verified by extensive simulation studies. Finally, a real data application on portfolio allocation is presented.

Fast Low-Rank Bayesian Matrix Completion With Hierarchical Gaussian Prior Models

NASA Astrophysics Data System (ADS)

Yang, Linxiao; Fang, Jun; Duan, Huiping; Li, Hongbin; Zeng, Bing

2018-06-01

The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to follow a Gaussian distribution with zero mean and a common precision matrix, and a Wishart distribution is specified as a hyperprior over the precision matrix. We show that such a hierarchical Gaussian prior has the potential to encourage a low-rank solution. Based on the proposed hierarchical prior model, a variational Bayesian method is developed for matrix completion, where the generalized approximate massage passing (GAMP) technique is embedded into the variational Bayesian inference in order to circumvent cumbersome matrix inverse operations. Simulation results show that our proposed method demonstrates superiority over existing state-of-the-art matrix completion methods.

Sparseness- and continuity-constrained seismic imaging

NASA Astrophysics Data System (ADS)

Herrmann, Felix J.

2005-04-01

Non-linear solution strategies to the least-squares seismic inverse-scattering problem with sparseness and continuity constraints are proposed. Our approach is designed to (i) deal with substantial amounts of additive noise (SNR < 0 dB); (ii) use the sparseness and locality (both in position and angle) of directional basis functions (such as curvelets and contourlets) on the model: the reflectivity; and (iii) exploit the near invariance of these basis functions under the normal operator, i.e., the scattering-followed-by-imaging operator. Signal-to-noise ratio and the continuity along the imaged reflectors are significantly enhanced by formulating the solution of the seismic inverse problem in terms of an optimization problem. During the optimization, sparseness on the basis and continuity along the reflectors are imposed by jointly minimizing the l1- and anisotropic diffusion/total-variation norms on the coefficients and reflectivity, respectively. [Joint work with Peyman P. Moghaddam was carried out as part of the SINBAD project, with financial support secured through ITF (the Industry Technology Facilitator) from the following organizations: BG Group, BP, ExxonMobil, and SHELL. Additional funding came from the NSERC Discovery Grants 22R81254.

3D Airborne Electromagnetic Inversion: A case study from the Musgrave Region, South Australia

NASA Astrophysics Data System (ADS)

Cox, L. H.; Wilson, G. A.; Zhdanov, M. S.; Sunwall, D. A.

2012-12-01

Geophysicists know and accept that geology is inherently 3D, and is resultant from complex, overlapping processes related to genesis, metamorphism, deformation, alteration, weathering, and/or hydrogeology. Yet, the geophysics community has long relied on qualitative analysis, conductivity depth imaging (CDIs), 1D inversion, and/or plate modeling. There are many reasons for this deficiency, not the least of which has been the lack of capacity for historic 3D AEM inversion algorithms to invert entire surveys so as to practically affect exploration decisions. Our recent introduction of a moving sensitivity domain (footprint) methodology has been a paradigm shift in AEM interpretation. The basis of this method is that one needs only to calculate the responses and sensitivities for that part of the 3D earth model that is within the AEM system's sensitivity domain (footprint), and then superimpose all sensitivity domains into a single, sparse sensitivity matrix for the entire 3D earth model which is then updated in a regularized inversion scheme. This has made it practical to rigorously invert entire surveys with thousands of line kilometers of AEM data to mega-cell 3D models in hours using multi-processor workstations. Since 2010, over eighty individual projects have been completed for Aerodat, AEROTEM, DIGHEM, GEOTEM, HELITEM, HoisTEM, MEGATEM, RepTEM, RESOLVE, SkyTEM, SPECTREM, TEMPEST, and VTEM data from Australia, Brazil, Canada, Finland, Ghana, Peru, Tanzania, the US, and Zambia. Examples of 3D AEM inversion have been published for a variety of applications, including mineral exploration, oil sands exploration, salinity, permafrost, and bathymetry mapping. In this paper, we present a comparison of 3D inversions for SkyTEM, SPECTREM, TEMPET and VTEM data acquired over the same area in the Musgrave region of South Australia for exploration under cover.

Sparse Reconstruction Techniques in MRI: Methods, Applications, and Challenges to Clinical Adoption

PubMed Central

Yang, Alice Chieh-Yu; Kretzler, Madison; Sudarski, Sonja; Gulani, Vikas; Seiberlich, Nicole

2016-01-01

The family of sparse reconstruction techniques, including the recently introduced compressed sensing framework, has been extensively explored to reduce scan times in Magnetic Resonance Imaging (MRI). While there are many different methods that fall under the general umbrella of sparse reconstructions, they all rely on the idea that a priori information about the sparsity of MR images can be employed to reconstruct full images from undersampled data. This review describes the basic ideas behind sparse reconstruction techniques, how they could be applied to improve MR imaging, and the open challenges to their general adoption in a clinical setting. The fundamental principles underlying different classes of sparse reconstructions techniques are examined, and the requirements that each make on the undersampled data outlined. Applications that could potentially benefit from the accelerations that sparse reconstructions could provide are described, and clinical studies using sparse reconstructions reviewed. Lastly, technical and clinical challenges to widespread implementation of sparse reconstruction techniques, including optimization, reconstruction times, artifact appearance, and comparison with current gold-standards, are discussed. PMID:27003227

Parallel Conjugate Gradient: Effects of Ordering Strategies, Programming Paradigms, and Architectural Platforms

NASA Technical Reports Server (NTRS)

Oliker, Leonid; Heber, Gerd; Biswas, Rupak

2000-01-01

The Conjugate Gradient (CG) algorithm is perhaps the best-known iterative technique to solve sparse linear systems that are symmetric and positive definite. A sparse matrix-vector multiply (SPMV) usually accounts for most of the floating-point operations within a CG iteration. In this paper, we investigate the effects of various ordering and partitioning strategies on the performance of parallel CG and SPMV using different programming paradigms and architectures. Results show that for this class of applications, ordering significantly improves overall performance, that cache reuse may be more important than reducing communication, and that it is possible to achieve message passing performance using shared memory constructs through careful data ordering and distribution. However, a multi-threaded implementation of CG on the Tera MTA does not require special ordering or partitioning to obtain high efficiency and scalability.

A trade-off solution between model resolution and covariance in surface-wave inversion

USGS Publications Warehouse

Xia, J.; Xu, Y.; Miller, R.D.; Zeng, C.

2010-01-01

Regularization is necessary for inversion of ill-posed geophysical problems. Appraisal of inverse models is essential for meaningful interpretation of these models. Because uncertainties are associated with regularization parameters, extra conditions are usually required to determine proper parameters for assessing inverse models. Commonly used techniques for assessment of a geophysical inverse model derived (generally iteratively) from a linear system are based on calculating the model resolution and the model covariance matrices. Because the model resolution and the model covariance matrices of the regularized solutions are controlled by the regularization parameter, direct assessment of inverse models using only the covariance matrix may provide incorrect results. To assess an inverted model, we use the concept of a trade-off between model resolution and covariance to find a proper regularization parameter with singular values calculated in the last iteration. We plot the singular values from large to small to form a singular value plot. A proper regularization parameter is normally the first singular value that approaches zero in the plot. With this regularization parameter, we obtain a trade-off solution between model resolution and model covariance in the vicinity of a regularized solution. The unit covariance matrix can then be used to calculate error bars of the inverse model at a resolution level determined by the regularization parameter. We demonstrate this approach with both synthetic and real surface-wave data. ?? 2010 Birkh??user / Springer Basel AG.

Collaborative sparse priors for multi-view ATR

NASA Astrophysics Data System (ADS)

Li, Xuelu; Monga, Vishal

2018-04-01

Recent work has seen a surge of sparse representation based classification (SRC) methods applied to automatic target recognition problems. While traditional SRC approaches used l0 or l1 norm to quantify sparsity, spike and slab priors have established themselves as the gold standard for providing general tunable sparse structures on vectors. In this work, we employ collaborative spike and slab priors that can be applied to matrices to encourage sparsity for the problem of multi-view ATR. That is, target images captured from multiple views are expanded in terms of a training dictionary multiplied with a coefficient matrix. Ideally, for a test image set comprising of multiple views of a target, coefficients corresponding to its identifying class are expected to be active, while others should be zero, i.e. the coefficient matrix is naturally sparse. We develop a new approach to solve the optimization problem that estimates the sparse coefficient matrix jointly with the sparsity inducing parameters in the collaborative prior. ATR problems are investigated on the mid-wave infrared (MWIR) database made available by the US Army Night Vision and Electronic Sensors Directorate, which has a rich collection of views. Experimental results show that the proposed joint prior and coefficient estimation method (JPCEM) can: 1.) enable improved accuracy when multiple views vs. a single one are invoked, and 2.) outperform state of the art alternatives particularly when training imagery is limited.

New shape models of asteroids reconstructed from sparse-in-time photometry

NASA Astrophysics Data System (ADS)

Durech, Josef; Hanus, Josef; Vanco, Radim; Oszkiewicz, Dagmara Anna

2015-08-01

Asteroid physical parameters - the shape, the sidereal rotation period, and the spin axis orientation - can be reconstructed from the disk-integrated photometry either dense (classical lightcurves) or sparse in time by the lightcurve inversion method. We will review our recent progress in asteroid shape reconstruction from sparse photometry. The problem of finding a unique solution of the inverse problem is time consuming because the sidereal rotation period has to be found by scanning a wide interval of possible periods. This can be efficiently solved by splitting the period parameter space into small parts that are sent to computers of volunteers and processed in parallel. We will show how this approach of distributed computing works with currently available sparse photometry processed in the framework of project Asteroids@home. In particular, we will show the results based on the Lowell Photometric Database. The method produce reliable asteroid models with very low rate of false solutions and the pipelines and codes can be directly used also to other sources of sparse photometry - Gaia data, for example. We will present the distribution of spin axis of hundreds of asteroids, discuss the dependence of the spin obliquity on the size of an asteroid,and show examples of spin-axis distribution in asteroid families that confirm the Yarkovsky/YORP evolution scenario.

Toward in situ x-ray diffraction imaging at the nanometer scale

NASA Astrophysics Data System (ADS)

Zatsepin, Nadia A.; Dilanian, Ruben A.; Nikulin, Andrei Y.; Gable, Brian M.; Muddle, Barry C.; Sakata, Osami

2008-08-01

We present the results of preliminary investigations determining the sensitivity and applicability of a novel x-ray diffraction based nanoscale imaging technique, including simulations and experiments. The ultimate aim of this nascent technique is non-destructive, bulk-material characterization on the nanometer scale, involving three dimensional image reconstructions of embedded nanoparticles and in situ sample characterization. The approach is insensitive to x-ray coherence, making it applicable to synchrotron and laboratory hard x-ray sources, opening the possibility of unprecedented nanometer resolution with the latter. The technique is being developed with a focus on analyzing a technologically important light metal alloy, Al-xCu (where x is 2.0-5.0 %wt). The mono- and polycrystalline samples contain crystallographically oriented, weakly diffracting Al2Cu nanoprecipitates in a sparse, spatially random dispersion within the Al matrix. By employing a triple-axis diffractometer in the non-dispersive setup we collected two-dimensional reciprocal space maps of synchrotron x-rays diffracted from the Al2Cu nanoparticles. The intensity profiles of the diffraction peaks confirmed the sensitivity of the technique to the presence and orientation of the nanoparticles. This is a fundamental step towards in situ observation of such extremely sparse, weakly diffracting nanoprecipitates embedded in light metal alloys at early stages of their growth.

Spatial operator approach to flexible multibody system dynamics and control

NASA Technical Reports Server (NTRS)

Rodriguez, G.

1991-01-01

The inverse and forward dynamics problems for flexible multibody systems were solved using the techniques of spatially recursive Kalman filtering and smoothing. These algorithms are easily developed using a set of identities associated with mass matrix factorization and inversion. These identities are easily derived using the spatial operator algebra developed by the author. Current work is aimed at computational experiments with the described algorithms and at modelling for control design of limber manipulator systems. It is also aimed at handling and manipulation of flexible objects.

Load cell having strain gauges of arbitrary location

DOEpatents

Spletzer, Barry [Albuquerque, NM

2007-03-13

A load cell utilizes a plurality of strain gauges mounted upon the load cell body such that there are six independent load-strain relations. Load is determined by applying the inverse of a load-strain sensitivity matrix to a measured strain vector. The sensitivity matrix is determined by performing a multivariate regression technique on a set of known loads correlated to the resulting strains. Temperature compensation is achieved by configuring the strain gauges as co-located orthogonal pairs.

Computing Generalized Matrix Inverse on Spiking Neural Substrate.

PubMed

Shukla, Rohit; Khoram, Soroosh; Jorgensen, Erik; Li, Jing; Lipasti, Mikko; Wright, Stephen

2018-01-01

Emerging neural hardware substrates, such as IBM's TrueNorth Neurosynaptic System, can provide an appealing platform for deploying numerical algorithms. For example, a recurrent Hopfield neural network can be used to find the Moore-Penrose generalized inverse of a matrix, thus enabling a broad class of linear optimizations to be solved efficiently, at low energy cost. However, deploying numerical algorithms on hardware platforms that severely limit the range and precision of representation for numeric quantities can be quite challenging. This paper discusses these challenges and proposes a rigorous mathematical framework for reasoning about range and precision on such substrates. The paper derives techniques for normalizing inputs and properly quantizing synaptic weights originating from arbitrary systems of linear equations, so that solvers for those systems can be implemented in a provably correct manner on hardware-constrained neural substrates. The analytical model is empirically validated on the IBM TrueNorth platform, and results show that the guarantees provided by the framework for range and precision hold under experimental conditions. Experiments with optical flow demonstrate the energy benefits of deploying a reduced-precision and energy-efficient generalized matrix inverse engine on the IBM TrueNorth platform, reflecting 10× to 100× improvement over FPGA and ARM core baselines.

Immunohistochemical evidence of rapid extracellular matrix remodeling after iron-particle irradiation of mouse mammary gland

NASA Technical Reports Server (NTRS)

Ehrhart, E. J.; Gillette, E. L.; Barcellos-Hoff, M. H.; Chaterjee, A. (Principal Investigator)

1996-01-01

High-LET radiation has unique physical and biological properties compared to sparsely ionizing radiation. Recent studies demonstrate that sparsely ionizing radiation rapidly alters the pattern of extracellular matrix expression in several tissues, but little is known about the effect of heavy-ion radiation. This study investigates densely ionizing radiation-induced changes in extracellular matrix localization in the mammary glands of adult female BALB/c mice after whole-body irradiation with 0.8 Gy 600 MeV iron particles. The basement membrane and interstitial extracellular matrix proteins of the mammary gland stroma were mapped with respect to time postirradiation using immunofluorescence. Collagen III was induced in the adipose stroma within 1 day, continued to increase through day 9 and was resolved by day 14. Immunoreactive tenascin was induced in the epithelium by day 1, was evident at the epithelial-stromal interface by day 5-9 and persisted as a condensed layer beneath the basement membrane through day 14. These findings parallel similar changes induced by gamma irradiation but demonstrate different onset and chronicity. In contrast, the integrity of epithelial basement membrane, which was unaffected by sparsely ionizing radiation, was disrupted by iron-particle irradiation. Laminin immunoreactivity was mildly irregular at 1 h postirradiation and showed discontinuities and thickening from days 1 to 9. Continuity was restored by day 14. Thus high-LET radiation, like sparsely ionizing radiation, induces rapid-remodeling of the stromal extracellular matrix but also appears to alter the integrity of the epithelial basement membrane, which is an important regulator of epithelial cell proliferation and differentiation.

A space efficient flexible pivot selection approach to evaluate determinant and inverse of a matrix.

PubMed

Jafree, Hafsa Athar; Imtiaz, Muhammad; Inayatullah, Syed; Khan, Fozia Hanif; Nizami, Tajuddin

2014-01-01

This paper presents new simple approaches for evaluating determinant and inverse of a matrix. The choice of pivot selection has been kept arbitrary thus they reduce the error while solving an ill conditioned system. Computation of determinant of a matrix has been made more efficient by saving unnecessary data storage and also by reducing the order of the matrix at each iteration, while dictionary notation [1] has been incorporated for computing the matrix inverse thereby saving unnecessary calculations. These algorithms are highly class room oriented, easy to use and implemented by students. By taking the advantage of flexibility in pivot selection, one may easily avoid development of the fractions by most. Unlike the matrix inversion method [2] and [3], the presented algorithms obviate the use of permutations and inverse permutations.

Denoised Wigner distribution deconvolution via low-rank matrix completion

DOE PAGES

Lee, Justin; Barbastathis, George

2016-08-23

Wigner distribution deconvolution (WDD) is a decades-old method for recovering phase from intensity measurements. Although the technique offers an elegant linear solution to the quadratic phase retrieval problem, it has seen limited adoption due to its high computational/memory requirements and the fact that the technique often exhibits high noise sensitivity. Here, we propose a method for noise suppression in WDD via low-rank noisy matrix completion. Our technique exploits the redundancy of an object’s phase space to denoise its WDD reconstruction. We show in model calculations that our technique outperforms other WDD algorithms as well as modern iterative methods for phasemore » retrieval such as ptychography. Here, our results suggest that a class of phase retrieval techniques relying on regularized direct inversion of ptychographic datasets (instead of iterative reconstruction techniques) can provide accurate quantitative phase information in the presence of high levels of noise.« less

Denoised Wigner distribution deconvolution via low-rank matrix completion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Justin; Barbastathis, George

Wigner distribution deconvolution (WDD) is a decades-old method for recovering phase from intensity measurements. Although the technique offers an elegant linear solution to the quadratic phase retrieval problem, it has seen limited adoption due to its high computational/memory requirements and the fact that the technique often exhibits high noise sensitivity. Here, we propose a method for noise suppression in WDD via low-rank noisy matrix completion. Our technique exploits the redundancy of an object’s phase space to denoise its WDD reconstruction. We show in model calculations that our technique outperforms other WDD algorithms as well as modern iterative methods for phasemore » retrieval such as ptychography. Here, our results suggest that a class of phase retrieval techniques relying on regularized direct inversion of ptychographic datasets (instead of iterative reconstruction techniques) can provide accurate quantitative phase information in the presence of high levels of noise.« less

Discriminative Transfer Subspace Learning via Low-Rank and Sparse Representation.

PubMed

Xu, Yong; Fang, Xiaozhao; Wu, Jian; Li, Xuelong; Zhang, David

2016-02-01

In this paper, we address the problem of unsupervised domain transfer learning in which no labels are available in the target domain. We use a transformation matrix to transfer both the source and target data to a common subspace, where each target sample can be represented by a combination of source samples such that the samples from different domains can be well interlaced. In this way, the discrepancy of the source and target domains is reduced. By imposing joint low-rank and sparse constraints on the reconstruction coefficient matrix, the global and local structures of data can be preserved. To enlarge the margins between different classes as much as possible and provide more freedom to diminish the discrepancy, a flexible linear classifier (projection) is obtained by learning a non-negative label relaxation matrix that allows the strict binary label matrix to relax into a slack variable matrix. Our method can avoid a potentially negative transfer by using a sparse matrix to model the noise and, thus, is more robust to different types of noise. We formulate our problem as a constrained low-rankness and sparsity minimization problem and solve it by the inexact augmented Lagrange multiplier method. Extensive experiments on various visual domain adaptation tasks show the superiority of the proposed method over the state-of-the art methods. The MATLAB code of our method will be publicly available at http://www.yongxu.org/lunwen.html.

Effects of Ordering Strategies and Programming Paradigms on Sparse Matrix Computations

NASA Technical Reports Server (NTRS)

Oliker, Leonid; Li, Xiaoye; Husbands, Parry; Biswas, Rupak; Biegel, Bryan (Technical Monitor)

2002-01-01

The Conjugate Gradient (CG) algorithm is perhaps the best-known iterative technique to solve sparse linear systems that are symmetric and positive definite. For systems that are ill-conditioned, it is often necessary to use a preconditioning technique. In this paper, we investigate the effects of various ordering and partitioning strategies on the performance of parallel CG and ILU(O) preconditioned CG (PCG) using different programming paradigms and architectures. Results show that for this class of applications: ordering significantly improves overall performance on both distributed and distributed shared-memory systems, that cache reuse may be more important than reducing communication, that it is possible to achieve message-passing performance using shared-memory constructs through careful data ordering and distribution, and that a hybrid MPI+OpenMP paradigm increases programming complexity with little performance gains. A implementation of CG on the Cray MTA does not require special ordering or partitioning to obtain high efficiency and scalability, giving it a distinct advantage for adaptive applications; however, it shows limited scalability for PCG due to a lack of thread level parallelism.

Solving an inverse eigenvalue problem with triple constraints on eigenvalues, singular values, and diagonal elements

NASA Astrophysics Data System (ADS)

Wu, Sheng-Jhih; Chu, Moody T.

2017-08-01

An inverse eigenvalue problem usually entails two constraints, one conditioned upon the spectrum and the other on the structure. This paper investigates the problem where triple constraints of eigenvalues, singular values, and diagonal entries are imposed simultaneously. An approach combining an eclectic mix of skills from differential geometry, optimization theory, and analytic gradient flow is employed to prove the solvability of such a problem. The result generalizes the classical Mirsky, Sing-Thompson, and Weyl-Horn theorems concerning the respective majorization relationships between any two of the arrays of main diagonal entries, eigenvalues, and singular values. The existence theory fills a gap in the classical matrix theory. The problem might find applications in wireless communication and quantum information science. The technique employed can be implemented as a first-step numerical method for constructing the matrix. With slight modification, the approach might be used to explore similar types of inverse problems where the prescribed entries are at general locations.

Improved analysis of SP and CoSaMP under total perturbations

NASA Astrophysics Data System (ADS)

Li, Haifeng

2016-12-01

Practically, in the underdetermined model y= A x, where x is a K sparse vector (i.e., it has no more than K nonzero entries), both y and A could be totally perturbed. A more relaxed condition means less number of measurements are needed to ensure the sparse recovery from theoretical aspect. In this paper, based on restricted isometry property (RIP), for subspace pursuit (SP) and compressed sampling matching pursuit (CoSaMP), two relaxed sufficient conditions are presented under total perturbations to guarantee that the sparse vector x is recovered. Taking random matrix as measurement matrix, we also discuss the advantage of our condition. Numerical experiments validate that SP and CoSaMP can provide oracle-order recovery performance.

Multi-energy CT based on a prior rank, intensity and sparsity model (PRISM).

PubMed

Gao, Hao; Yu, Hengyong; Osher, Stanley; Wang, Ge

2011-11-01

We propose a compressive sensing approach for multi-energy computed tomography (CT), namely the prior rank, intensity and sparsity model (PRISM). To further compress the multi-energy image for allowing the reconstruction with fewer CT data and less radiation dose, the PRISM models a multi-energy image as the superposition of a low-rank matrix and a sparse matrix (with row dimension in space and column dimension in energy), where the low-rank matrix corresponds to the stationary background over energy that has a low matrix rank, and the sparse matrix represents the rest of distinct spectral features that are often sparse. Distinct from previous methods, the PRISM utilizes the generalized rank, e.g., the matrix rank of tight-frame transform of a multi-energy image, which offers a way to characterize the multi-level and multi-filtered image coherence across the energy spectrum. Besides, the energy-dependent intensity information can be incorporated into the PRISM in terms of the spectral curves for base materials, with which the restoration of the multi-energy image becomes the reconstruction of the energy-independent material composition matrix. In other words, the PRISM utilizes prior knowledge on the generalized rank and sparsity of a multi-energy image, and intensity/spectral characteristics of base materials. Furthermore, we develop an accurate and fast split Bregman method for the PRISM and demonstrate the superior performance of the PRISM relative to several competing methods in simulations.

Atmospheric particulate analysis using angular light scattering

NASA Technical Reports Server (NTRS)

Hansen, M. Z.

1980-01-01

Using the light scattering matrix elements measured by a polar nephelometer, a procedure for estimating the characteristics of atmospheric particulates was developed. A theoretical library data set of scattering matrices derived from Mie theory was tabulated for a range of values of the size parameter and refractive index typical of atmospheric particles. Integration over the size parameter yielded the scattering matrix elements for a variety of hypothesized particulate size distributions. A least squares curve fitting technique was used to find a best fit from the library data for the experimental measurements. This was used as a first guess for a nonlinear iterative inversion of the size distributions. A real index of 1.50 and an imaginary index of -0.005 are representative of the smoothed inversion results for the near ground level atmospheric aerosol in Tucson.

Detection of Protein Complexes Based on Penalized Matrix Decomposition in a Sparse Protein⁻Protein Interaction Network.

PubMed

Cao, Buwen; Deng, Shuguang; Qin, Hua; Ding, Pingjian; Chen, Shaopeng; Li, Guanghui

2018-06-15

High-throughput technology has generated large-scale protein interaction data, which is crucial in our understanding of biological organisms. Many complex identification algorithms have been developed to determine protein complexes. However, these methods are only suitable for dense protein interaction networks, because their capabilities decrease rapidly when applied to sparse protein⁻protein interaction (PPI) networks. In this study, based on penalized matrix decomposition ( PMD ), a novel method of penalized matrix decomposition for the identification of protein complexes (i.e., PMD pc ) was developed to detect protein complexes in the human protein interaction network. This method mainly consists of three steps. First, the adjacent matrix of the protein interaction network is normalized. Second, the normalized matrix is decomposed into three factor matrices. The PMD pc method can detect protein complexes in sparse PPI networks by imposing appropriate constraints on factor matrices. Finally, the results of our method are compared with those of other methods in human PPI network. Experimental results show that our method can not only outperform classical algorithms, such as CFinder, ClusterONE, RRW, HC-PIN, and PCE-FR, but can also achieve an ideal overall performance in terms of a composite score consisting of F-measure, accuracy (ACC), and the maximum matching ratio (MMR).

Target detection in GPR data using joint low-rank and sparsity constraints

NASA Astrophysics Data System (ADS)

Bouzerdoum, Abdesselam; Tivive, Fok Hing Chi; Abeynayake, Canicious

2016-05-01

In ground penetrating radars, background clutter, which comprises the signals backscattered from the rough, uneven ground surface and the background noise, impairs the visualization of buried objects and subsurface inspections. In this paper, a clutter mitigation method is proposed for target detection. The removal of background clutter is formulated as a constrained optimization problem to obtain a low-rank matrix and a sparse matrix. The low-rank matrix captures the ground surface reflections and the background noise, whereas the sparse matrix contains the target reflections. An optimization method based on split-Bregman algorithm is developed to estimate these two matrices from the input GPR data. Evaluated on real radar data, the proposed method achieves promising results in removing the background clutter and enhancing the target signature.

Refractive index inversion based on Mueller matrix method

NASA Astrophysics Data System (ADS)

Fan, Huaxi; Wu, Wenyuan; Huang, Yanhua; Li, Zhaozhao

2016-03-01

Based on Stokes vector and Jones vector, the correlation between Mueller matrix elements and refractive index was studied with the result simplified, and through Mueller matrix way, the expression of refractive index inversion was deduced. The Mueller matrix elements, under different incident angle, are simulated through the expression of specular reflection so as to analyze the influence of the angle of incidence and refractive index on it, which is verified through the measure of the Mueller matrix elements of polished metal surface. Research shows that, under the condition of specular reflection, the result of Mueller matrix inversion is consistent with the experiment and can be used as an index of refraction of inversion method, and it provides a new way for target detection and recognition technology.

Seismic data restoration with a fast L1 norm trust region method

NASA Astrophysics Data System (ADS)

Cao, Jingjie; Wang, Yanfei

2014-08-01

Seismic data restoration is a major strategy to provide reliable wavefield when field data dissatisfy the Shannon sampling theorem. Recovery by sparsity-promoting inversion often get sparse solutions of seismic data in a transformed domains, however, most methods for sparsity-promoting inversion are line-searching methods which are efficient but are inclined to obtain local solutions. Using trust region method which can provide globally convergent solutions is a good choice to overcome this shortcoming. A trust region method for sparse inversion has been proposed, however, the efficiency should be improved to suitable for large-scale computation. In this paper, a new L1 norm trust region model is proposed for seismic data restoration and a robust gradient projection method for solving the sub-problem is utilized. Numerical results of synthetic and field data demonstrate that the proposed trust region method can get excellent computation speed and is a viable alternative for large-scale computation.

Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions

NASA Technical Reports Server (NTRS)

Hodge, Steve L.; Zorumski, William E.; Watson, Willie R.

1995-01-01

The Helmholtz equation is solved within a three-dimensional rectangular duct with a nonlocal radiation boundary condition at the duct exit plane. This condition accurately models the acoustic admittance at an arbitrarily-located computational boundary plane. A linear system of equations is constructed with second-order central differences for the Helmholtz operator and second-order backward differences for both local admittance conditions and the gradient term in the nonlocal radiation boundary condition. The resulting matrix equation is large, sparse, and non-Hermitian. The size and structure of the matrix makes direct solution techniques impractical; as a result, a nonstationary iterative technique is used for its solution. The theory behind the nonstationary technique is reviewed, and numerical results are presented for radiation from both a point source and a planar acoustic source. The solutions with the nonlocal boundary conditions are invariant to the location of the computational boundary, and the same nonlocal conditions are valid for all solutions. The nonlocal conditions thus provide a means of minimizing the size of three-dimensional computational domains.

Sparse image reconstruction for molecular imaging.

PubMed

Ting, Michael; Raich, Raviv; Hero, Alfred O

2009-06-01

The application that motivates this paper is molecular imaging at the atomic level. When discretized at subatomic distances, the volume is inherently sparse. Noiseless measurements from an imaging technology can be modeled by convolution of the image with the system point spread function (psf). Such is the case with magnetic resonance force microscopy (MRFM), an emerging technology where imaging of an individual tobacco mosaic virus was recently demonstrated with nanometer resolution. We also consider additive white Gaussian noise (AWGN) in the measurements. Many prior works of sparse estimators have focused on the case when H has low coherence; however, the system matrix H in our application is the convolution matrix for the system psf. A typical convolution matrix has high coherence. This paper, therefore, does not assume a low coherence H. A discrete-continuous form of the Laplacian and atom at zero (LAZE) p.d.f. used by Johnstone and Silverman is formulated, and two sparse estimators derived by maximizing the joint p.d.f. of the observation and image conditioned on the hyperparameters. A thresholding rule that generalizes the hard and soft thresholding rule appears in the course of the derivation. This so-called hybrid thresholding rule, when used in the iterative thresholding framework, gives rise to the hybrid estimator, a generalization of the lasso. Estimates of the hyperparameters for the lasso and hybrid estimator are obtained via Stein's unbiased risk estimate (SURE). A numerical study with a Gaussian psf and two sparse images shows that the hybrid estimator outperforms the lasso.

Sparse spikes super-resolution on thin grids II: the continuous basis pursuit

NASA Astrophysics Data System (ADS)

Duval, Vincent; Peyré, Gabriel

2017-09-01

This article analyzes the performance of the continuous basis pursuit (C-BP) method for sparse super-resolution. The C-BP has been recently proposed by Ekanadham, Tranchina and Simoncelli as a refined discretization scheme for the recovery of spikes in inverse problems regularization. One of the most well known discretization scheme, the basis pursuit (BP, also known as \

Bayesian inference of the number of factors in gene-expression analysis: application to human virus challenge studies

PubMed Central

2010-01-01

Background Nonparametric Bayesian techniques have been developed recently to extend the sophistication of factor models, allowing one to infer the number of appropriate factors from the observed data. We consider such techniques for sparse factor analysis, with application to gene-expression data from three virus challenge studies. Particular attention is placed on employing the Beta Process (BP), the Indian Buffet Process (IBP), and related sparseness-promoting techniques to infer a proper number of factors. The posterior density function on the model parameters is computed using Gibbs sampling and variational Bayesian (VB) analysis. Results Time-evolving gene-expression data are considered for respiratory syncytial virus (RSV), Rhino virus, and influenza, using blood samples from healthy human subjects. These data were acquired in three challenge studies, each executed after receiving institutional review board (IRB) approval from Duke University. Comparisons are made between several alternative means of per-forming nonparametric factor analysis on these data, with comparisons as well to sparse-PCA and Penalized Matrix Decomposition (PMD), closely related non-Bayesian approaches. Conclusions Applying the Beta Process to the factor scores, or to the singular values of a pseudo-SVD construction, the proposed algorithms infer the number of factors in gene-expression data. For real data the "true" number of factors is unknown; in our simulations we consider a range of noise variances, and the proposed Bayesian models inferred the number of factors accurately relative to other methods in the literature, such as sparse-PCA and PMD. We have also identified a "pan-viral" factor of importance for each of the three viruses considered in this study. We have identified a set of genes associated with this pan-viral factor, of interest for early detection of such viruses based upon the host response, as quantified via gene-expression data. PMID:21062443

Randomized subspace-based robust principal component analysis for hyperspectral anomaly detection

NASA Astrophysics Data System (ADS)

Sun, Weiwei; Yang, Gang; Li, Jialin; Zhang, Dianfa

2018-01-01

A randomized subspace-based robust principal component analysis (RSRPCA) method for anomaly detection in hyperspectral imagery (HSI) is proposed. The RSRPCA combines advantages of randomized column subspace and robust principal component analysis (RPCA). It assumes that the background has low-rank properties, and the anomalies are sparse and do not lie in the column subspace of the background. First, RSRPCA implements random sampling to sketch the original HSI dataset from columns and to construct a randomized column subspace of the background. Structured random projections are also adopted to sketch the HSI dataset from rows. Sketching from columns and rows could greatly reduce the computational requirements of RSRPCA. Second, the RSRPCA adopts the columnwise RPCA (CWRPCA) to eliminate negative effects of sampled anomaly pixels and that purifies the previous randomized column subspace by removing sampled anomaly columns. The CWRPCA decomposes the submatrix of the HSI data into a low-rank matrix (i.e., background component), a noisy matrix (i.e., noise component), and a sparse anomaly matrix (i.e., anomaly component) with only a small proportion of nonzero columns. The algorithm of inexact augmented Lagrange multiplier is utilized to optimize the CWRPCA problem and estimate the sparse matrix. Nonzero columns of the sparse anomaly matrix point to sampled anomaly columns in the submatrix. Third, all the pixels are projected onto the complemental subspace of the purified randomized column subspace of the background and the anomaly pixels in the original HSI data are finally exactly located. Several experiments on three real hyperspectral images are carefully designed to investigate the detection performance of RSRPCA, and the results are compared with four state-of-the-art methods. Experimental results show that the proposed RSRPCA outperforms four comparison methods both in detection performance and in computational time.

Inverse lithography using sparse mask representations

NASA Astrophysics Data System (ADS)

Ionescu, Radu C.; Hurley, Paul; Apostol, Stefan

2015-03-01

We present a novel optimisation algorithm for inverse lithography, based on optimization of the mask derivative, a domain inherently sparse, and for rectilinear polygons, invertible. The method is first developed assuming a point light source, and then extended to general incoherent sources. What results is a fast algorithm, producing manufacturable masks (the search space is constrained to rectilinear polygons), and flexible (specific constraints such as minimal line widths can be imposed). One inherent trick is to treat polygons as continuous entities, thus making aerial image calculation extremely fast and accurate. Requirements for mask manufacturability can be integrated in the optimization without too much added complexity. We also explain how to extend the scheme for phase-changing mask optimization.

Quantum algorithms for Gibbs sampling and hitting-time estimation

DOE PAGES

Chowdhury, Anirban Narayan; Somma, Rolando D.

2017-02-01

In this paper, we present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in √Nβ/Ζ and polynomial in log(1/ϵ), where N is the Hilbert space dimension, β is the inverse temperature, Ζ is the partition function, and ϵ is the desired precision of the output state. Our quantum algorithm exponentially improves the dependence on 1/ϵ and quadratically improves the dependence on β of known quantum algorithms for this problem. The second algorithm estimates the hitting time of a Markov chain. Formore » a sparse stochastic matrix Ρ, it runs in time almost linear in 1/(ϵΔ 3/2), where ϵ is the absolute precision in the estimation and Δ is a parameter determined by Ρ, and whose inverse is an upper bound of the hitting time. Our quantum algorithm quadratically improves the dependence on 1/ϵ and 1/Δ of the analog classical algorithm for hitting-time estimation. Finally, both algorithms use tools recently developed in the context of Hamiltonian simulation, spectral gap amplification, and solving linear systems of equations.« less

Bayesian statistical ionospheric tomography improved by incorporating ionosonde measurements

NASA Astrophysics Data System (ADS)

Norberg, Johannes; Virtanen, Ilkka I.; Roininen, Lassi; Vierinen, Juha; Orispää, Mikko; Kauristie, Kirsti; Lehtinen, Markku S.

2016-04-01

We validate two-dimensional ionospheric tomography reconstructions against EISCAT incoherent scatter radar measurements. Our tomography method is based on Bayesian statistical inversion with prior distribution given by its mean and covariance. We employ ionosonde measurements for the choice of the prior mean and covariance parameters and use the Gaussian Markov random fields as a sparse matrix approximation for the numerical computations. This results in a computationally efficient tomographic inversion algorithm with clear probabilistic interpretation. We demonstrate how this method works with simultaneous beacon satellite and ionosonde measurements obtained in northern Scandinavia. The performance is compared with results obtained with a zero-mean prior and with the prior mean taken from the International Reference Ionosphere 2007 model. In validating the results, we use EISCAT ultra-high-frequency incoherent scatter radar measurements as the ground truth for the ionization profile shape. We find that in comparison to the alternative prior information sources, ionosonde measurements improve the reconstruction by adding accurate information about the absolute value and the altitude distribution of electron density. With an ionosonde at continuous disposal, the presented method enhances stand-alone near-real-time ionospheric tomography for the given conditions significantly.

Spherical space Bessel-Legendre-Fourier localized modes solver for electromagnetic waves.

PubMed

Alzahrani, Mohammed A; Gauthier, Robert C

2015-10-05

Maxwell's vector wave equations are solved for dielectric configurations that match the symmetry of a spherical computational domain. The electric or magnetic field components and the inverse of the dielectric profile are series expansion defined using basis functions composed of the lowest order spherical Bessel function, polar angle single index dependant Legendre polynomials and azimuthal complex exponential (BLF). The series expressions and non-traditional form of the basis functions result in an eigenvalue matrix formulation of Maxwell's equations that are relatively compact and accurately solvable on a desktop PC. The BLF matrix returns the frequencies and field profiles for steady states modes. The key steps leading to the matrix populating expressions are provided. The validity of the numerical technique is confirmed by comparing the results of computations to those published using complementary techniques.

Solving large-scale PDE-constrained Bayesian inverse problems with Riemann manifold Hamiltonian Monte Carlo

NASA Astrophysics Data System (ADS)

Bui-Thanh, T.; Girolami, M.

2014-11-01

We consider the Riemann manifold Hamiltonian Monte Carlo (RMHMC) method for solving statistical inverse problems governed by partial differential equations (PDEs). The Bayesian framework is employed to cast the inverse problem into the task of statistical inference whose solution is the posterior distribution in infinite dimensional parameter space conditional upon observation data and Gaussian prior measure. We discretize both the likelihood and the prior using the H1-conforming finite element method together with a matrix transfer technique. The power of the RMHMC method is that it exploits the geometric structure induced by the PDE constraints of the underlying inverse problem. Consequently, each RMHMC posterior sample is almost uncorrelated/independent from the others providing statistically efficient Markov chain simulation. However this statistical efficiency comes at a computational cost. This motivates us to consider computationally more efficient strategies for RMHMC. At the heart of our construction is the fact that for Gaussian error structures the Fisher information matrix coincides with the Gauss-Newton Hessian. We exploit this fact in considering a computationally simplified RMHMC method combining state-of-the-art adjoint techniques and the superiority of the RMHMC method. Specifically, we first form the Gauss-Newton Hessian at the maximum a posteriori point and then use it as a fixed constant metric tensor throughout RMHMC simulation. This eliminates the need for the computationally costly differential geometric Christoffel symbols, which in turn greatly reduces computational effort at a corresponding loss of sampling efficiency. We further reduce the cost of forming the Fisher information matrix by using a low rank approximation via a randomized singular value decomposition technique. This is efficient since a small number of Hessian-vector products are required. The Hessian-vector product in turn requires only two extra PDE solves using the adjoint technique. Various numerical results up to 1025 parameters are presented to demonstrate the ability of the RMHMC method in exploring the geometric structure of the problem to propose (almost) uncorrelated/independent samples that are far away from each other, and yet the acceptance rate is almost unity. The results also suggest that for the PDE models considered the proposed fixed metric RMHMC can attain almost as high a quality performance as the original RMHMC, i.e. generating (almost) uncorrelated/independent samples, while being two orders of magnitude less computationally expensive.

Sparse matrix beamforming and image reconstruction for real-time 2D HIFU monitoring using Harmonic Motion Imaging for Focused Ultrasound (HMIFU) with in vitro validation

PubMed Central

Hou, Gary Y.; Provost, Jean; Grondin, Julien; Wang, Shutao; Marquet, Fabrice; Bunting, Ethan; Konofagou, Elisa E.

2015-01-01

Harmonic Motion Imaging for Focused Ultrasound (HMIFU) is a recently developed High-Intensity Focused Ultrasound (HIFU) treatment monitoring method. HMIFU utilizes an Amplitude-Modulated (fAM = 25 Hz) HIFU beam to induce a localized focal oscillatory motion, which is simultaneously estimated and imaged by confocally-aligned imaging transducer. HMIFU feasibilities have been previously shown in silico, in vitro, and in vivo in 1-D or 2-D monitoring of HIFU treatment. The objective of this study is to develop and show the feasibility of a novel fast beamforming algorithm for image reconstruction using GPU-based sparse-matrix operation with real-time feedback. In this study, the algorithm was implemented onto a fully integrated, clinically relevant HMIFU system composed of a 93-element HIFU transducer (fcenter = 4.5MHz) and coaxially-aligned 64-element phased array (fcenter = 2.5MHz) for displacement excitation and motion estimation, respectively. A single transmit beam with divergent beam transmit was used while fast beamforming was implemented using a GPU-based delay-and-sum method and a sparse-matrix operation. Axial HMI displacements were then estimated from the RF signals using a 1-D normalized cross-correlation method and streamed to a graphic user interface. The present work developed and implemented a sparse matrix beamforming onto a fully-integrated, clinically relevant system, which can stream displacement images up to 15 Hz using a GPU-based processing, an increase of 100 fold in rate of streaming displacement images compared to conventional CPU-based conventional beamforming and reconstruction processing. The achieved feedback rate is also currently the fastest and only approach that does not require interrupting the HIFU treatment amongst the acoustic radiation force based HIFU imaging techniques. Results in phantom experiments showed reproducible displacement imaging, and monitoring of twenty two in vitro HIFU treatments using the new 2D system showed a consistent average focal displacement decrease of 46.7±14.6% during lesion formation. Complementary focal temperature monitoring also indicated an average rate of displacement increase and decrease with focal temperature at 0.84±1.15 %/ °C, and 2.03± 0.93%/ °C, respectively. These results reinforce the HMIFU capability of estimating and monitoring stiffness related changes in real time. Current ongoing studies include clinical translation of the presented system for monitoring of HIFU treatment for breast and pancreatic tumor applications. PMID:24960528

Analysing 21cm signal with artificial neural network

NASA Astrophysics Data System (ADS)

Shimabukuro, Hayato; a Semelin, Benoit

2018-05-01

The 21cm signal at epoch of reionization (EoR) should be observed within next decade. We expect that cosmic 21cm signal at the EoR provides us both cosmological and astrophysical information. In order to extract fruitful information from observation data, we need to develop inversion method. For such a method, we introduce artificial neural network (ANN) which is one of the machine learning techniques. We apply the ANN to inversion problem to constrain astrophysical parameters from 21cm power spectrum. We train the architecture of the neural network with 70 training datasets and apply it to 54 test datasets with different value of parameters. We find that the quality of the parameter reconstruction depends on the sensitivity of the power spectrum to the different parameter sets at a given redshift and also find that the accuracy of reconstruction is improved by increasing the number of given redshifts. We conclude that the ANN is viable inversion method whose main strength is that they require a sparse extrapolation of the parameter space and thus should be usable with full simulation.

3-D minimum-structure inversion of magnetotelluric data using the finite-element method and tetrahedral grids

NASA Astrophysics Data System (ADS)

Jahandari, H.; Farquharson, C. G.

2017-11-01

Unstructured grids enable representing arbitrary structures more accurately and with fewer cells compared to regular structured grids. These grids also allow more efficient refinements compared to rectilinear meshes. In this study, tetrahedral grids are used for the inversion of magnetotelluric (MT) data, which allows for the direct inclusion of topography in the model, for constraining an inversion using a wireframe-based geological model and for local refinement at the observation stations. A minimum-structure method with an iterative model-space Gauss-Newton algorithm for optimization is used. An iterative solver is employed for solving the normal system of equations at each Gauss-Newton step and the sensitivity matrix-vector products that are required by this solver are calculated using pseudo-forward problems. This method alleviates the need to explicitly form the Hessian or Jacobian matrices which significantly reduces the required computation memory. Forward problems are formulated using an edge-based finite-element approach and a sparse direct solver is used for the solutions. This solver allows saving and re-using the factorization of matrices for similar pseudo-forward problems within a Gauss-Newton iteration which greatly minimizes the computation time. Two examples are presented to show the capability of the algorithm: the first example uses a benchmark model while the second example represents a realistic geological setting with topography and a sulphide deposit. The data that are inverted are the full-tensor impedance and the magnetic transfer function vector. The inversions sufficiently recovered the models and reproduced the data, which shows the effectiveness of unstructured grids for complex and realistic MT inversion scenarios. The first example is also used to demonstrate the computational efficiency of the presented model-space method by comparison with its data-space counterpart.

Distorted Born iterative T-matrix method for inversion of CSEM data in anisotropic media

NASA Astrophysics Data System (ADS)

Jakobsen, Morten; Tveit, Svenn

2018-05-01

We present a direct iterative solutions to the nonlinear controlled-source electromagnetic (CSEM) inversion problem in the frequency domain, which is based on a volume integral equation formulation of the forward modelling problem in anisotropic conductive media. Our vectorial nonlinear inverse scattering approach effectively replaces an ill-posed nonlinear inverse problem with a series of linear ill-posed inverse problems, for which there already exist efficient (regularized) solution methods. The solution update the dyadic Green's function's from the source to the scattering-volume and from the scattering-volume to the receivers, after each iteration. The T-matrix approach of multiple scattering theory is used for efficient updating of all dyadic Green's functions after each linearized inversion step. This means that we have developed a T-matrix variant of the Distorted Born Iterative (DBI) method, which is often used in the acoustic and electromagnetic (medical) imaging communities as an alternative to contrast-source inversion. The main advantage of using the T-matrix approach in this context, is that it eliminates the need to perform a full forward simulation at each iteration of the DBI method, which is known to be consistent with the Gauss-Newton method. The T-matrix allows for a natural domain decomposition, since in the sense that a large model can be decomposed into an arbitrary number of domains that can be treated independently and in parallel. The T-matrix we use for efficient model updating is also independent of the source-receiver configuration, which could be an advantage when performing fast-repeat modelling and time-lapse inversion. The T-matrix is also compatible with the use of modern renormalization methods that can potentially help us to reduce the sensitivity of the CSEM inversion results on the starting model. To illustrate the performance and potential of our T-matrix variant of the DBI method for CSEM inversion, we performed a numerical experiments based on synthetic CSEM data associated with 2D VTI and 3D orthorombic model inversions. The results of our numerical experiment suggest that the DBIT method for inversion of CSEM data in anisotropic media is both accurate and efficient.

Highly parallel sparse Cholesky factorization

NASA Technical Reports Server (NTRS)

Gilbert, John R.; Schreiber, Robert

1990-01-01

Several fine grained parallel algorithms were developed and compared to compute the Cholesky factorization of a sparse matrix. The experimental implementations are on the Connection Machine, a distributed memory SIMD machine whose programming model conceptually supplies one processor per data element. In contrast to special purpose algorithms in which the matrix structure conforms to the connection structure of the machine, the focus is on matrices with arbitrary sparsity structure. The most promising algorithm is one whose inner loop performs several dense factorizations simultaneously on a 2-D grid of processors. Virtually any massively parallel dense factorization algorithm can be used as the key subroutine. The sparse code attains execution rates comparable to those of the dense subroutine. Although at present architectural limitations prevent the dense factorization from realizing its potential efficiency, it is concluded that a regular data parallel architecture can be used efficiently to solve arbitrarily structured sparse problems. A performance model is also presented and it is used to analyze the algorithms.

Cortical dipole imaging using truncated total least squares considering transfer matrix error.

PubMed

Hori, Junichi; Takeuchi, Kosuke

2013-01-01

Cortical dipole imaging has been proposed as a method to visualize electroencephalogram in high spatial resolution. We investigated the inverse technique of cortical dipole imaging using a truncated total least squares (TTLS). The TTLS is a regularization technique to reduce the influence from both the measurement noise and the transfer matrix error caused by the head model distortion. The estimation of the regularization parameter was also investigated based on L-curve. The computer simulation suggested that the estimation accuracy was improved by the TTLS compared with Tikhonov regularization. The proposed method was applied to human experimental data of visual evoked potentials. We confirmed the TTLS provided the high spatial resolution of cortical dipole imaging.

Fast space-varying convolution using matrix source coding with applications to camera stray light reduction.

PubMed

Wei, Jianing; Bouman, Charles A; Allebach, Jan P

2014-05-01

Many imaging applications require the implementation of space-varying convolution for accurate restoration and reconstruction of images. Here, we use the term space-varying convolution to refer to linear operators whose impulse response has slow spatial variation. In addition, these space-varying convolution operators are often dense, so direct implementation of the convolution operator is typically computationally impractical. One such example is the problem of stray light reduction in digital cameras, which requires the implementation of a dense space-varying deconvolution operator. However, other inverse problems, such as iterative tomographic reconstruction, can also depend on the implementation of dense space-varying convolution. While space-invariant convolution can be efficiently implemented with the fast Fourier transform, this approach does not work for space-varying operators. So direct convolution is often the only option for implementing space-varying convolution. In this paper, we develop a general approach to the efficient implementation of space-varying convolution, and demonstrate its use in the application of stray light reduction. Our approach, which we call matrix source coding, is based on lossy source coding of the dense space-varying convolution matrix. Importantly, by coding the transformation matrix, we not only reduce the memory required to store it; we also dramatically reduce the computation required to implement matrix-vector products. Our algorithm is able to reduce computation by approximately factoring the dense space-varying convolution operator into a product of sparse transforms. Experimental results show that our method can dramatically reduce the computation required for stray light reduction while maintaining high accuracy.

Low-rank and Adaptive Sparse Signal (LASSI) Models for Highly Accelerated Dynamic Imaging

PubMed Central

Ravishankar, Saiprasad; Moore, Brian E.; Nadakuditi, Raj Rao; Fessler, Jeffrey A.

2017-01-01

Sparsity-based approaches have been popular in many applications in image processing and imaging. Compressed sensing exploits the sparsity of images in a transform domain or dictionary to improve image recovery from undersampled measurements. In the context of inverse problems in dynamic imaging, recent research has demonstrated the promise of sparsity and low-rank techniques. For example, the patches of the underlying data are modeled as sparse in an adaptive dictionary domain, and the resulting image and dictionary estimation from undersampled measurements is called dictionary-blind compressed sensing, or the dynamic image sequence is modeled as a sum of low-rank and sparse (in some transform domain) components (L+S model) that are estimated from limited measurements. In this work, we investigate a data-adaptive extension of the L+S model, dubbed LASSI, where the temporal image sequence is decomposed into a low-rank component and a component whose spatiotemporal (3D) patches are sparse in some adaptive dictionary domain. We investigate various formulations and efficient methods for jointly estimating the underlying dynamic signal components and the spatiotemporal dictionary from limited measurements. We also obtain efficient sparsity penalized dictionary-blind compressed sensing methods as special cases of our LASSI approaches. Our numerical experiments demonstrate the promising performance of LASSI schemes for dynamic magnetic resonance image reconstruction from limited k-t space data compared to recent methods such as k-t SLR and L+S, and compared to the proposed dictionary-blind compressed sensing method. PMID:28092528

Low-Rank and Adaptive Sparse Signal (LASSI) Models for Highly Accelerated Dynamic Imaging.

PubMed

Ravishankar, Saiprasad; Moore, Brian E; Nadakuditi, Raj Rao; Fessler, Jeffrey A

2017-05-01

Sparsity-based approaches have been popular in many applications in image processing and imaging. Compressed sensing exploits the sparsity of images in a transform domain or dictionary to improve image recovery fromundersampledmeasurements. In the context of inverse problems in dynamic imaging, recent research has demonstrated the promise of sparsity and low-rank techniques. For example, the patches of the underlying data are modeled as sparse in an adaptive dictionary domain, and the resulting image and dictionary estimation from undersampled measurements is called dictionary-blind compressed sensing, or the dynamic image sequence is modeled as a sum of low-rank and sparse (in some transform domain) components (L+S model) that are estimated from limited measurements. In this work, we investigate a data-adaptive extension of the L+S model, dubbed LASSI, where the temporal image sequence is decomposed into a low-rank component and a component whose spatiotemporal (3D) patches are sparse in some adaptive dictionary domain. We investigate various formulations and efficient methods for jointly estimating the underlying dynamic signal components and the spatiotemporal dictionary from limited measurements. We also obtain efficient sparsity penalized dictionary-blind compressed sensing methods as special cases of our LASSI approaches. Our numerical experiments demonstrate the promising performance of LASSI schemes for dynamicmagnetic resonance image reconstruction from limited k-t space data compared to recent methods such as k-t SLR and L+S, and compared to the proposed dictionary-blind compressed sensing method.

Efficient Transition Probability Computation for Continuous-Time Branching Processes via Compressed Sensing.

PubMed

Xu, Jason; Minin, Vladimir N

2015-07-01

Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the discrete state space is large or uncountable. Classical methods such as matrix exponentiation are infeasible for large or countably infinite state spaces, and sampling-based alternatives are computationally intensive, requiring integration over all possible hidden events. Recent work has successfully applied generating function techniques to computing transition probabilities for linear multi-type branching processes. While these techniques often require significantly fewer computations than matrix exponentiation, they also become prohibitive in applications with large populations. We propose a compressed sensing framework that significantly accelerates the generating function method, decreasing computational cost up to a logarithmic factor by only assuming the probability mass of transitions is sparse. We demonstrate accurate and efficient transition probability computations in branching process models for blood cell formation and evolution of self-replicating transposable elements in bacterial genomes.

Efficient Transition Probability Computation for Continuous-Time Branching Processes via Compressed Sensing

PubMed Central

Xu, Jason; Minin, Vladimir N.

2016-01-01

Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the discrete state space is large or uncountable. Classical methods such as matrix exponentiation are infeasible for large or countably infinite state spaces, and sampling-based alternatives are computationally intensive, requiring integration over all possible hidden events. Recent work has successfully applied generating function techniques to computing transition probabilities for linear multi-type branching processes. While these techniques often require significantly fewer computations than matrix exponentiation, they also become prohibitive in applications with large populations. We propose a compressed sensing framework that significantly accelerates the generating function method, decreasing computational cost up to a logarithmic factor by only assuming the probability mass of transitions is sparse. We demonstrate accurate and efficient transition probability computations in branching process models for blood cell formation and evolution of self-replicating transposable elements in bacterial genomes. PMID:26949377

Solving Large-Scale Inverse Magnetostatic Problems using the Adjoint Method

PubMed Central

Bruckner, Florian; Abert, Claas; Wautischer, Gregor; Huber, Christian; Vogler, Christoph; Hinze, Michael; Suess, Dieter

2017-01-01

An efficient algorithm for the reconstruction of the magnetization state within magnetic components is presented. The occurring inverse magnetostatic problem is solved by means of an adjoint approach, based on the Fredkin-Koehler method for the solution of the forward problem. Due to the use of hybrid FEM-BEM coupling combined with matrix compression techniques the resulting algorithm is well suited for large-scale problems. Furthermore the reconstruction of the magnetization state within a permanent magnet as well as an optimal design application are demonstrated. PMID:28098851

Kinetics of diffusion-controlled annihilation with sparse initial conditions

DOE PAGES

Ben-Naim, Eli; Krapivsky, Paul

2016-12-16

Here, we study diffusion-controlled single-species annihilation with sparse initial conditions. In this random process, particles undergo Brownian motion, and when two particles meet, both disappear. We also focus on sparse initial conditions where particles occupy a subspace of dimension δ that is embedded in a larger space of dimension d. Furthermore, we find that the co-dimension Δ = d - δ governs the behavior. All particles disappear when the co-dimension is sufficiently small, Δ ≤ 2; otherwise, a finite fraction of particles indefinitely survive. We establish the asymptotic behavior of the probability S(t) that a test particle survives until time t. When the subspace is a line, δ = 1, we find inverse logarithmic decay,more » $$S\\sim {(\\mathrm{ln}t)}^{-1}$$, in three dimensions, and a modified power-law decay, $$S\\sim (\\mathrm{ln}t){t}^{-1/2}$$, in two dimensions. In general, the survival probability decays algebraically when Δ < 2, and there is an inverse logarithmic decay at the critical co-dimension Δ = 2.« less

Logarithmic Laplacian Prior Based Bayesian Inverse Synthetic Aperture Radar Imaging.

PubMed

Zhang, Shuanghui; Liu, Yongxiang; Li, Xiang; Bi, Guoan

2016-04-28

This paper presents a novel Inverse Synthetic Aperture Radar Imaging (ISAR) algorithm based on a new sparse prior, known as the logarithmic Laplacian prior. The newly proposed logarithmic Laplacian prior has a narrower main lobe with higher tail values than the Laplacian prior, which helps to achieve performance improvement on sparse representation. The logarithmic Laplacian prior is used for ISAR imaging within the Bayesian framework to achieve better focused radar image. In the proposed method of ISAR imaging, the phase errors are jointly estimated based on the minimum entropy criterion to accomplish autofocusing. The maximum a posterior (MAP) estimation and the maximum likelihood estimation (MLE) are utilized to estimate the model parameters to avoid manually tuning process. Additionally, the fast Fourier Transform (FFT) and Hadamard product are used to minimize the required computational efficiency. Experimental results based on both simulated and measured data validate that the proposed algorithm outperforms the traditional sparse ISAR imaging algorithms in terms of resolution improvement and noise suppression.

A three-dimensional wide-angle BPM for optical waveguide structures.

PubMed

Ma, Changbao; Van Keuren, Edward

2007-01-22

Algorithms for effective modeling of optical propagation in three- dimensional waveguide structures are critical for the design of photonic devices. We present a three-dimensional (3-D) wide-angle beam propagation method (WA-BPM) using Hoekstra's scheme. A sparse matrix algebraic equation is formed and solved using iterative methods. The applicability, accuracy and effectiveness of our method are demonstrated by applying it to simulations of wide-angle beam propagation, along with a technique for shifting the simulation window to reduce the dimension of the numerical equation and a threshold technique to further ensure its convergence. These techniques can ensure the implementation of iterative methods for waveguide structures by relaxing the convergence problem, which will further enable us to develop higher-order 3-D WA-BPMs based on Padé approximant operators.

A three-dimensional wide-angle BPM for optical waveguide structures

NASA Astrophysics Data System (ADS)

Ma, Changbao; van Keuren, Edward

2007-01-01

Algorithms for effective modeling of optical propagation in three- dimensional waveguide structures are critical for the design of photonic devices. We present a three-dimensional (3-D) wide-angle beam propagation method (WA-BPM) using Hoekstra’s scheme. A sparse matrix algebraic equation is formed and solved using iterative methods. The applicability, accuracy and effectiveness of our method are demonstrated by applying it to simulations of wide-angle beam propagation, along with a technique for shifting the simulation window to reduce the dimension of the numerical equation and a threshold technique to further ensure its convergence. These techniques can ensure the implementation of iterative methods for waveguide structures by relaxing the convergence problem, which will further enable us to develop higher-order 3-D WA-BPMs based on Padé approximant operators.

Total recall in distributive associative memories

NASA Technical Reports Server (NTRS)

Danforth, Douglas G.

1991-01-01

Iterative error correction of asymptotically large associative memories is equivalent to a one-step learning rule. This rule is the inverse of the activation function of the memory. Spectral representations of nonlinear activation functions are used to obtain the inverse in closed form for Sparse Distributed Memory, Selected-Coordinate Design, and Radial Basis Functions.

Calibration of remotely sensed proportion or area estimates for misclassification error

Treesearch

Raymond L. Czaplewski; Glenn P. Catts

1992-01-01

Classifications of remotely sensed data contain misclassification errors that bias areal estimates. Monte Carlo techniques were used to compare two statistical methods that correct or calibrate remotely sensed areal estimates for misclassification bias using reference data from an error matrix. The inverse calibration estimator was consistently superior to the...

Computing Generalized Matrix Inverse on Spiking Neural Substrate

PubMed Central

Shukla, Rohit; Khoram, Soroosh; Jorgensen, Erik; Li, Jing; Lipasti, Mikko; Wright, Stephen

2018-01-01

Emerging neural hardware substrates, such as IBM's TrueNorth Neurosynaptic System, can provide an appealing platform for deploying numerical algorithms. For example, a recurrent Hopfield neural network can be used to find the Moore-Penrose generalized inverse of a matrix, thus enabling a broad class of linear optimizations to be solved efficiently, at low energy cost. However, deploying numerical algorithms on hardware platforms that severely limit the range and precision of representation for numeric quantities can be quite challenging. This paper discusses these challenges and proposes a rigorous mathematical framework for reasoning about range and precision on such substrates. The paper derives techniques for normalizing inputs and properly quantizing synaptic weights originating from arbitrary systems of linear equations, so that solvers for those systems can be implemented in a provably correct manner on hardware-constrained neural substrates. The analytical model is empirically validated on the IBM TrueNorth platform, and results show that the guarantees provided by the framework for range and precision hold under experimental conditions. Experiments with optical flow demonstrate the energy benefits of deploying a reduced-precision and energy-efficient generalized matrix inverse engine on the IBM TrueNorth platform, reflecting 10× to 100× improvement over FPGA and ARM core baselines. PMID:29593483

The construction of sparse models of Mars' crustal magnetic field

NASA Astrophysics Data System (ADS)

Moore, Kimberly; Bloxham, Jeremy

2017-04-01

The crustal magnetic field of Mars is a key constraint on Martian geophysical history, especially the timing of the dynamo shutoff. Maps of the crustal magnetic field of Mars show wide variations in the intensity of magnetization, with most of the Northern hemisphere only weakly magnetized. Previous methods of analysis tend to favor smooth solutions for the crustal magnetic field of Mars, making use of techniques such as L2 norms. Here we utilize inversion methods designed for sparse models, to see how much of the surface area of Mars must be magnetized in order to fit available spacecraft magnetic field data. We solve for the crustal magnetic field at 10,000 individual magnetic pixels on the surface of Mars. We employ an L1 regularization, and solve for models where each magnetic pixel is identically zero, unless required otherwise by the data. We find solutions with an adequate fit to the data with over 90% sparsity (90% of magnetic pixels having a field value of exactly 0). We contrast these solutions with L2-based solutions, as well as an elastic net model (combination of L1 and L2). We find our sparse solutions look dramatically different from previous models in the literature, but still give a physically reasonable history of the dynamo (shutting off around 4.1 Ga).

Sparse electrocardiogram signals recovery based on solving a row echelon-like form of system.

PubMed

Cai, Pingmei; Wang, Guinan; Yu, Shiwei; Zhang, Hongjuan; Ding, Shuxue; Wu, Zikai

2016-02-01

The study of biology and medicine in a noise environment is an evolving direction in biological data analysis. Among these studies, analysis of electrocardiogram (ECG) signals in a noise environment is a challenging direction in personalized medicine. Due to its periodic characteristic, ECG signal can be roughly regarded as sparse biomedical signals. This study proposes a two-stage recovery algorithm for sparse biomedical signals in time domain. In the first stage, the concentration subspaces are found in advance. Then by exploiting these subspaces, the mixing matrix is estimated accurately. In the second stage, based on the number of active sources at each time point, the time points are divided into different layers. Next, by constructing some transformation matrices, these time points form a row echelon-like system. After that, the sources at each layer can be solved out explicitly by corresponding matrix operations. It is noting that all these operations are conducted under a weak sparse condition that the number of active sources is less than the number of observations. Experimental results show that the proposed method has a better performance for sparse ECG signal recovery problem.

Deconvolution using a neural network

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lehman, S.K.

1990-11-15

Viewing one dimensional deconvolution as a matrix inversion problem, we compare a neural network backpropagation matrix inverse with LMS, and pseudo-inverse. This is a largely an exercise in understanding how our neural network code works. 1 ref.

Direct-current vertical electrical-resistivity soundings in the Lower Peninsula of Michigan

USGS Publications Warehouse

Westjohn, D.B.; Carter, P.J.

1989-01-01

Ninety-three direct-current vertical electrical-resistivity soundings were conducted in the Lower Peninsula of Michigan from June through October 1987. These soundings were made to assist in mapping the depth to brine in areas where borehole resistivity logs and water-quality data are sparse or lacking. The Schlumberger array for placement of current and potential electrodes was used for each sounding. Vertical electrical-resistivity sounding field data, shifted and smoothed sounding data, and electric layers calculated using inverse modeling techniques are presented. Also included is a summary of the near-surface conditions and depths to conductors and resistors for each sounding location.

Hardware Implementation of a MIMO Decoder Using Matrix Factorization Based Channel Estimation

NASA Astrophysics Data System (ADS)

Islam, Mohammad Tariqul; Numan, Mostafa Wasiuddin; Misran, Norbahiah; Ali, Mohd Alauddin Mohd; Singh, Mandeep

2011-05-01

This paper presents an efficient hardware realization of multiple-input multiple-output (MIMO) wireless communication decoder that utilizes the available resources by adopting the technique of parallelism. The hardware is designed and implemented on Xilinx Virtex™-4 XC4VLX60 field programmable gate arrays (FPGA) device in a modular approach which simplifies and eases hardware update, and facilitates testing of the various modules independently. The decoder involves a proficient channel estimation module that employs matrix factorization on least squares (LS) estimation to reduce a full rank matrix into a simpler form in order to eliminate matrix inversion. This results in performance improvement and complexity reduction of the MIMO system. Performance evaluation of the proposed method is validated through MATLAB simulations which indicate 2 dB improvement in terms of SNR compared to LS estimation. Moreover complexity comparison is performed in terms of mathematical operations, which shows that the proposed approach appreciably outperforms LS estimation at a lower complexity and represents a good solution for channel estimation technique.

Unlocking the spatial inversion of large scanning magnetic microscopy datasets

NASA Astrophysics Data System (ADS)

Myre, J. M.; Lascu, I.; Andrade Lima, E.; Feinberg, J. M.; Saar, M. O.; Weiss, B. P.

2013-12-01

Modern scanning magnetic microscopy provides the ability to perform high-resolution, ultra-high sensitivity moment magnetometry, with spatial resolutions better than 10^-4 m and magnetic moments as weak as 10^-16 Am^2. These microscopy capabilities have enhanced numerous magnetic studies, including investigations of the paleointensity of the Earth's magnetic field, shock magnetization and demagnetization of impacts, magnetostratigraphy, the magnetic record in speleothems, and the records of ancient core dynamos of planetary bodies. A common component among many studies utilizing scanning magnetic microscopy is solving an inverse problem to determine the non-negative magnitude of the magnetic moments that produce the measured component of the magnetic field. The two most frequently used methods to solve this inverse problem are classic fast Fourier techniques in the frequency domain and non-negative least squares (NNLS) methods in the spatial domain. Although Fourier techniques are extremely fast, they typically violate non-negativity and it is difficult to implement constraints associated with the space domain. NNLS methods do not violate non-negativity, but have typically been computation time prohibitive for samples of practical size or resolution. Existing NNLS methods use multiple techniques to attain tractable computation. To reduce computation time in the past, typically sample size or scan resolution would have to be reduced. Similarly, multiple inversions of smaller sample subdivisions can be performed, although this frequently results in undesirable artifacts at subdivision boundaries. Dipole interactions can also be filtered to only compute interactions above a threshold which enables the use of sparse methods through artificial sparsity. To improve upon existing spatial domain techniques, we present the application of the TNT algorithm, named TNT as it is a "dynamite" non-negative least squares algorithm which enhances the performance and accuracy of spatial domain inversions. We show that the TNT algorithm reduces the execution time of spatial domain inversions from months to hours and that inverse solution accuracy is improved as the TNT algorithm naturally produces solutions with small norms. Using sIRM and NRM measures of multiple synthetic and natural samples we show that the capabilities of the TNT algorithm allow very large samples to be inverted without the need for alternative techniques to make the problems tractable. Ultimately, the TNT algorithm enables accurate spatial domain analysis of scanning magnetic microscopy data on an accelerated time scale that renders spatial domain analyses tractable for numerous studies, including searches for the best fit of unidirectional magnetization direction and high-resolution step-wise magnetization and demagnetization.

Using sparse regularization for multi-resolution tomography of the ionosphere

NASA Astrophysics Data System (ADS)

Panicciari, T.; Smith, N. D.; Mitchell, C. N.; Da Dalt, F.; Spencer, P. S. J.

2015-10-01

Computerized ionospheric tomography (CIT) is a technique that allows reconstructing the state of the ionosphere in terms of electron content from a set of slant total electron content (STEC) measurements. It is usually denoted as an inverse problem. In this experiment, the measurements are considered coming from the phase of the GPS signal and, therefore, affected by bias. For this reason the STEC cannot be considered in absolute terms but rather in relative terms. Measurements are collected from receivers not evenly distributed in space and together with limitations such as angle and density of the observations, they are the cause of instability in the operation of inversion. Furthermore, the ionosphere is a dynamic medium whose processes are continuously changing in time and space. This can affect CIT by limiting the accuracy in resolving structures and the processes that describe the ionosphere. Some inversion techniques are based on ℓ2 minimization algorithms (i.e. Tikhonov regularization) and a standard approach is implemented here using spherical harmonics as a reference to compare the new method. A new approach is proposed for CIT that aims to permit sparsity in the reconstruction coefficients by using wavelet basis functions. It is based on the ℓ1 minimization technique and wavelet basis functions due to their properties of compact representation. The ℓ1 minimization is selected because it can optimize the result with an uneven distribution of observations by exploiting the localization property of wavelets. Also illustrated is how the inter-frequency biases on the STEC are calibrated within the operation of inversion, and this is used as a way for evaluating the accuracy of the method. The technique is demonstrated using a simulation, showing the advantage of ℓ1 minimization to estimate the coefficients over the ℓ2 minimization. This is in particular true for an uneven observation geometry and especially for multi-resolution CIT.

Overview of Sparse Graph for Multiple Access in Future Mobile Networks

NASA Astrophysics Data System (ADS)

Lei, Jing; Li, Baoguo; Li, Erbao; Gong, Zhenghui

2017-10-01

Multiple access via sparse graph, such as low density signature (LDS) and sparse code multiple access (SCMA), is a promising technique for future wireless communications. This survey presents an overview of the developments in this burgeoning field, including transmitter structures, extrinsic information transform (EXIT) chart analysis and comparisons with existing multiple access techniques. Such technique enables multiple access under overloaded conditions to achieve a satisfactory performance. Message passing algorithm is utilized for multi-user detection in the receiver, and structures of the sparse graph are illustrated in detail. Outlooks and challenges of this technique are also presented.

An improved pulse sequence and inversion algorithm of T2 spectrum

NASA Astrophysics Data System (ADS)

Ge, Xinmin; Chen, Hua; Fan, Yiren; Liu, Juntao; Cai, Jianchao; Liu, Jianyu

2017-03-01

The nuclear magnetic resonance transversal relaxation time is widely applied in geological prospecting, both in laboratory and downhole environments. However, current methods used for data acquisition and inversion should be reformed to characterize geological samples with complicated relaxation components and pore size distributions, such as samples of tight oil, gas shale, and carbonate. We present an improved pulse sequence to collect transversal relaxation signals based on the CPMG (Carr, Purcell, Meiboom, and Gill) pulse sequence. The echo spacing is not constant but varies in different windows, depending on prior knowledge or customer requirements. We use the entropy based truncated singular value decomposition (TSVD) to compress the ill-posed matrix and discard small singular values which cause the inversion instability. A hybrid algorithm combining the iterative TSVD and a simultaneous iterative reconstruction technique is implemented to reach the global convergence and stability of the inversion. Numerical simulations indicate that the improved pulse sequence leads to the same result as CPMG, but with lower echo numbers and computational time. The proposed method is a promising technique for geophysical prospecting and other related fields in future.

Wavelet-promoted sparsity for non-invasive reconstruction of electrical activity of the heart.

PubMed

Cluitmans, Matthijs; Karel, Joël; Bonizzi, Pietro; Volders, Paul; Westra, Ronald; Peeters, Ralf

2018-05-12

We investigated a novel sparsity-based regularization method in the wavelet domain of the inverse problem of electrocardiography that aims at preserving the spatiotemporal characteristics of heart-surface potentials. In three normal, anesthetized dogs, electrodes were implanted around the epicardium and body-surface electrodes were attached to the torso. Potential recordings were obtained simultaneously on the body surface and on the epicardium. A CT scan was used to digitize a homogeneous geometry which consisted of the body-surface electrodes and the epicardial surface. A novel multitask elastic-net-based method was introduced to regularize the ill-posed inverse problem. The method simultaneously pursues a sparse wavelet representation in time-frequency and exploits correlations in space. Performance was assessed in terms of quality of reconstructed epicardial potentials, estimated activation and recovery time, and estimated locations of pacing, and compared with performance of Tikhonov zeroth-order regularization. Results in the wavelet domain obtained higher sparsity than those in the time domain. Epicardial potentials were non-invasively reconstructed with higher accuracy than with Tikhonov zeroth-order regularization (p < 0.05), and recovery times were improved (p < 0.05). No significant improvement was found in terms of activation times and localization of origin of pacing. Next to improved estimation of recovery isochrones, which is important when assessing substrate for cardiac arrhythmias, this novel technique opens potentially powerful opportunities for clinical application, by allowing to choose wavelet bases that are optimized for specific clinical questions. Graphical Abstract The inverse problem of electrocardiography is to reconstruct heart-surface potentials from recorded bodysurface electrocardiograms (ECGs) and a torso-heart geometry. However, it is ill-posed and solving it requires additional constraints for regularization. We introduce a regularization method that simultaneously pursues a sparse wavelet representation in time-frequency and exploits correlations in space. Our approach reconstructs epicardial (heart-surface) potentials with higher accuracy than common methods. It also improves the reconstruction of recovery isochrones, which is important when assessing substrate for cardiac arrhythmias. This novel technique opens potentially powerful opportunities for clinical application, by allowing to choose wavelet bases that are optimized for specific clinical questions.

Efficient Bayesian parameter estimation with implicit sampling and surrogate modeling for a vadose zone hydrological problem

NASA Astrophysics Data System (ADS)

Liu, Y.; Pau, G. S. H.; Finsterle, S.

2015-12-01

Parameter inversion involves inferring the model parameter values based on sparse observations of some observables. To infer the posterior probability distributions of the parameters, Markov chain Monte Carlo (MCMC) methods are typically used. However, the large number of forward simulations needed and limited computational resources limit the complexity of the hydrological model we can use in these methods. In view of this, we studied the implicit sampling (IS) method, an efficient importance sampling technique that generates samples in the high-probability region of the posterior distribution and thus reduces the number of forward simulations that we need to run. For a pilot-point inversion of a heterogeneous permeability field based on a synthetic ponded infiltration experiment simu­lated with TOUGH2 (a subsurface modeling code), we showed that IS with linear map provides an accurate Bayesian description of the parameterized permeability field at the pilot points with just approximately 500 forward simulations. We further studied the use of surrogate models to improve the computational efficiency of parameter inversion. We implemented two reduced-order models (ROMs) for the TOUGH2 forward model. One is based on polynomial chaos expansion (PCE), of which the coefficients are obtained using the sparse Bayesian learning technique to mitigate the "curse of dimensionality" of the PCE terms. The other model is Gaussian process regression (GPR) for which different covariance, likelihood and inference models are considered. Preliminary results indicate that ROMs constructed based on the prior parameter space perform poorly. It is thus impractical to replace this hydrological model by a ROM directly in a MCMC method. However, the IS method can work with a ROM constructed for parameters in the close vicinity of the maximum a posteriori probability (MAP) estimate. We will discuss the accuracy and computational efficiency of using ROMs in the implicit sampling procedure for the hydrological problem considered. This work was supported, in part, by the U.S. Dept. of Energy under Contract No. DE-AC02-05CH11231

A performance study of sparse Cholesky factorization on INTEL iPSC/860

NASA Technical Reports Server (NTRS)

Zubair, M.; Ghose, M.

1992-01-01

The problem of Cholesky factorization of a sparse matrix has been very well investigated on sequential machines. A number of efficient codes exist for factorizing large unstructured sparse matrices. However, there is a lack of such efficient codes on parallel machines in general, and distributed machines in particular. Some of the issues that are critical to the implementation of sparse Cholesky factorization on a distributed memory parallel machine are ordering, partitioning and mapping, load balancing, and ordering of various tasks within a processor. Here, we focus on the effect of various partitioning schemes on the performance of sparse Cholesky factorization on the Intel iPSC/860. Also, a new partitioning heuristic for structured as well as unstructured sparse matrices is proposed, and its performance is compared with other schemes.

Non-convex Statistical Optimization for Sparse Tensor Graphical Model

PubMed Central

Sun, Wei; Wang, Zhaoran; Liu, Han; Cheng, Guang

2016-01-01

We consider the estimation of sparse graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we assume the data follow a tensor normal distribution whose covariance has a Kronecker product structure. The penalized maximum likelihood estimation of this model involves minimizing a non-convex objective function. In spite of the non-convexity of this estimation problem, we prove that an alternating minimization algorithm, which iteratively estimates each sparse precision matrix while fixing the others, attains an estimator with the optimal statistical rate of convergence as well as consistent graph recovery. Notably, such an estimator achieves estimation consistency with only one tensor sample, which is unobserved in previous work. Our theoretical results are backed by thorough numerical studies. PMID:28316459

Determination of eigenvalues of dynamical systems by symbolic computation

NASA Technical Reports Server (NTRS)

Howard, J. C.

1982-01-01

A symbolic computation technique for determining the eigenvalues of dynamical systems is described wherein algebraic operations, symbolic differentiation, matrix formulation and inversion, etc., can be performed on a digital computer equipped with a formula-manipulation compiler. An example is included that demonstrates the facility with which the system dynamics matrix and the control distribution matrix from the state space formulation of the equations of motion can be processed to obtain eigenvalue loci as a function of a system parameter. The example chosen to demonstrate the technique is a fourth-order system representing the longitudinal response of a DC 8 aircraft to elevator inputs. This simplified system has two dominant modes, one of which is lightly damped and the other well damped. The loci may be used to determine the value of the controlling parameter that satisfied design requirements. The results were obtained using the MACSYMA symbolic manipulation system.

Securing image information using double random phase encoding and parallel compressive sensing with updated sampling processes

NASA Astrophysics Data System (ADS)

Hu, Guiqiang; Xiao, Di; Wang, Yong; Xiang, Tao; Zhou, Qing

2017-11-01

Recently, a new kind of image encryption approach using compressive sensing (CS) and double random phase encoding has received much attention due to the advantages such as compressibility and robustness. However, this approach is found to be vulnerable to chosen plaintext attack (CPA) if the CS measurement matrix is re-used. Therefore, designing an efficient measurement matrix updating mechanism that ensures resistance to CPA is of practical significance. In this paper, we provide a novel solution to update the CS measurement matrix by altering the secret sparse basis with the help of counter mode operation. Particularly, the secret sparse basis is implemented by a reality-preserving fractional cosine transform matrix. Compared with the conventional CS-based cryptosystem that totally generates all the random entries of measurement matrix, our scheme owns efficiency superiority while guaranteeing resistance to CPA. Experimental and analysis results show that the proposed scheme has a good security performance and has robustness against noise and occlusion.

Exploiting Multiple Levels of Parallelism in Sparse Matrix-Matrix Multiplication

DOE PAGES

Azad, Ariful; Ballard, Grey; Buluc, Aydin; ...

2016-11-08

Sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high-performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. The scaling of existing parallel implementations of SpGEMM is heavily bound by communication. Even though 3D (or 2.5D) algorithms have been proposed and theoretically analyzed in the flat MPI model on Erdös-Rényi matrices, those algorithms had not been implemented in practice and their complexities had not been analyzed for the general case. In this work, we present the first implementation of the 3D SpGEMM formulation that exploits multiple (intranode and internode) levels of parallelism, achievingmore » significant speedups over the state-of-the-art publicly available codes at all levels of concurrencies. We extensively evaluate our implementation and identify bottlenecks that should be subject to further research.« less

Prolongation structures of nonlinear evolution equations

NASA Technical Reports Server (NTRS)

Wahlquist, H. D.; Estabrook, F. B.

1975-01-01

A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.

A Higher Order Iterative Method for Computing the Drazin Inverse

PubMed Central

Soleymani, F.; Stanimirović, Predrag S.

2013-01-01

A method with high convergence rate for finding approximate inverses of nonsingular matrices is suggested and established analytically. An extension of the introduced computational scheme to general square matrices is defined. The extended method could be used for finding the Drazin inverse. The application of the scheme on large sparse test matrices alongside the use in preconditioning of linear system of equations will be presented to clarify the contribution of the paper. PMID:24222747

A Space-Time-Frequency Dictionary for Sparse Cortical Source Localization.

PubMed

Korats, Gundars; Le Cam, Steven; Ranta, Radu; Louis-Dorr, Valerie

2016-09-01

Cortical source imaging aims at identifying activated cortical areas on the surface of the cortex from the raw electroencephalogram (EEG) data. This problem is ill posed, the number of channels being very low compared to the number of possible source positions. In some realistic physiological situations, the active areas are sparse in space and of short time durations, and the amount of spatio-temporal data to carry the inversion is then limited. In this study, we propose an original data driven space-time-frequency (STF) dictionary which takes into account simultaneously both spatial and time-frequency sparseness while preserving smoothness in the time frequency (i.e., nonstationary smooth time courses in sparse locations). Based on these assumptions, we take benefit of the matching pursuit (MP) framework for selecting the most relevant atoms in this highly redundant dictionary. We apply two recent MP algorithms, single best replacement (SBR) and source deflated matching pursuit, and we compare the results using a spatial dictionary and the proposed STF dictionary to demonstrate the improvements of our multidimensional approach. We also provide comparison using well-established inversion methods, FOCUSS and RAP-MUSIC, analyzing performances under different degrees of nonstationarity and signal to noise ratio. Our STF dictionary combined with the SBR approach provides robust performances on realistic simulations. From a computational point of view, the algorithm is embedded in the wavelet domain, ensuring high efficiency in term of computation time. The proposed approach ensures fast and accurate sparse cortical localizations on highly nonstationary and noisy data.

A matrix-inversion method for gamma-source mapping from gamma-count data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adsley, Ian; Burgess, Claire; Bull, Richard K

In a previous paper it was proposed that a simple matrix inversion method could be used to extract source distributions from gamma-count maps, using simple models to calculate the response matrix. The method was tested using numerically generated count maps. In the present work a 100 kBq Co{sup 60} source has been placed on a gridded surface and the count rate measured using a NaI scintillation detector. The resulting map of gamma counts was used as input to the matrix inversion procedure and the source position recovered. A multi-source array was simulated by superposition of several single-source count maps andmore » the source distribution was again recovered using matrix inversion. The measurements were performed for several detector heights. The effects of uncertainties in source-detector distances on the matrix inversion method are also examined. The results from this work give confidence in the application of the method to practical applications, such as the segregation of highly active objects amongst fuel-element debris. (authors)« less

Discovering mutated driver genes through a robust and sparse co-regularized matrix factorization framework with prior information from mRNA expression patterns and interaction network.

PubMed

Xi, Jianing; Wang, Minghui; Li, Ao

2018-06-05

Discovery of mutated driver genes is one of the primary objective for studying tumorigenesis. To discover some relatively low frequently mutated driver genes from somatic mutation data, many existing methods incorporate interaction network as prior information. However, the prior information of mRNA expression patterns are not exploited by these existing network-based methods, which is also proven to be highly informative of cancer progressions. To incorporate prior information from both interaction network and mRNA expressions, we propose a robust and sparse co-regularized nonnegative matrix factorization to discover driver genes from mutation data. Furthermore, our framework also conducts Frobenius norm regularization to overcome overfitting issue. Sparsity-inducing penalty is employed to obtain sparse scores in gene representations, of which the top scored genes are selected as driver candidates. Evaluation experiments by known benchmarking genes indicate that the performance of our method benefits from the two type of prior information. Our method also outperforms the existing network-based methods, and detect some driver genes that are not predicted by the competing methods. In summary, our proposed method can improve the performance of driver gene discovery by effectively incorporating prior information from interaction network and mRNA expression patterns into a robust and sparse co-regularized matrix factorization framework.

Large-region acoustic source mapping using a movable array and sparse covariance fitting.

PubMed

Zhao, Shengkui; Tuna, Cagdas; Nguyen, Thi Ngoc Tho; Jones, Douglas L

2017-01-01

Large-region acoustic source mapping is important for city-scale noise monitoring. Approaches using a single-position measurement scheme to scan large regions using small arrays cannot provide clean acoustic source maps, while deploying large arrays spanning the entire region of interest is prohibitively expensive. A multiple-position measurement scheme is applied to scan large regions at multiple spatial positions using a movable array of small size. Based on the multiple-position measurement scheme, a sparse-constrained multiple-position vectorized covariance matrix fitting approach is presented. In the proposed approach, the overall sample covariance matrix of the incoherent virtual array is first estimated using the multiple-position array data and then vectorized using the Khatri-Rao (KR) product. A linear model is then constructed for fitting the vectorized covariance matrix and a sparse-constrained reconstruction algorithm is proposed for recovering source powers from the model. The user parameter settings are discussed. The proposed approach is tested on a 30 m × 40 m region and a 60 m × 40 m region using simulated and measured data. Much cleaner acoustic source maps and lower sound pressure level errors are obtained compared to the beamforming approaches and the previous sparse approach [Zhao, Tuna, Nguyen, and Jones, Proc. IEEE Intl. Conf. on Acoustics, Speech and Signal Processing (ICASSP) (2016)].

Dynamic Textures Modeling via Joint Video Dictionary Learning.

PubMed

Wei, Xian; Li, Yuanxiang; Shen, Hao; Chen, Fang; Kleinsteuber, Martin; Wang, Zhongfeng

2017-04-06

Video representation is an important and challenging task in the computer vision community. In this paper, we consider the problem of modeling and classifying video sequences of dynamic scenes which could be modeled in a dynamic textures (DT) framework. At first, we assume that image frames of a moving scene can be modeled as a Markov random process. We propose a sparse coding framework, named joint video dictionary learning (JVDL), to model a video adaptively. By treating the sparse coefficients of image frames over a learned dictionary as the underlying "states", we learn an efficient and robust linear transition matrix between two adjacent frames of sparse events in time series. Hence, a dynamic scene sequence is represented by an appropriate transition matrix associated with a dictionary. In order to ensure the stability of JVDL, we impose several constraints on such transition matrix and dictionary. The developed framework is able to capture the dynamics of a moving scene by exploring both sparse properties and the temporal correlations of consecutive video frames. Moreover, such learned JVDL parameters can be used for various DT applications, such as DT synthesis and recognition. Experimental results demonstrate the strong competitiveness of the proposed JVDL approach in comparison with state-of-the-art video representation methods. Especially, it performs significantly better in dealing with DT synthesis and recognition on heavily corrupted data.

Isotope Inversion Experiment evaluating the suitability of calibration in surrogate matrix for quantification via LC-MS/MS-Exemplary application for a steroid multi-method.

PubMed

Suhr, Anna Catharina; Vogeser, Michael; Grimm, Stefanie H

2016-05-30

For quotable quantitative analysis of endogenous analytes in complex biological samples by isotope dilution LC-MS/MS, the creation of appropriate calibrators is a challenge, since analyte-free authentic material is in general not available. Thus, surrogate matrices are often used to prepare calibrators and controls. However, currently employed validation protocols do not include specific experiments to verify the suitability of a surrogate matrix calibration for quantification of authentic matrix samples. The aim of the study was the development of a novel validation experiment to test whether surrogate matrix based calibrators enable correct quantification of authentic matrix samples. The key element of the novel validation experiment is the inversion of nonlabelled analytes and their stable isotope labelled (SIL) counterparts in respect to their functions, i.e. SIL compound is the analyte and nonlabelled substance is employed as internal standard. As a consequence, both surrogate and authentic matrix are analyte-free regarding SIL analytes, which allows a comparison of both matrices. We called this approach Isotope Inversion Experiment. As figure of merit we defined the accuracy of inverse quality controls in authentic matrix quantified by means of a surrogate matrix calibration curve. As a proof-of-concept application a LC-MS/MS assay addressing six corticosteroids (cortisol, cortisone, corticosterone, 11-deoxycortisol, 11-deoxycorticosterone, and 17-OH-progesterone) was chosen. The integration of the Isotope Inversion Experiment in the validation protocol for the steroid assay was successfully realized. The accuracy results of the inverse quality controls were all in all very satisfying. As a consequence the suitability of a surrogate matrix calibration for quantification of the targeted steroids in human serum as authentic matrix could be successfully demonstrated. The Isotope Inversion Experiment fills a gap in the validation process for LC-MS/MS assays quantifying endogenous analytes. We consider it a valuable and convenient tool to evaluate the correct quantification of authentic matrix samples based on a calibration curve in surrogate matrix. Copyright © 2016 Elsevier B.V. All rights reserved.

Direct Iterative Nonlinear Inversion by Multi-frequency T-matrix Completion

NASA Astrophysics Data System (ADS)

Jakobsen, M.; Wu, R. S.

2016-12-01

Researchers in the mathematical physics community have recently proposed a conceptually new method for solving nonlinear inverse scattering problems (like FWI) which is inspired by the theory of nonlocality of physical interactions. The conceptually new method, which may be referred to as the T-matrix completion method, is very interesting since it is not based on linearization at any stage. Also, there are no gradient vectors or (inverse) Hessian matrices to calculate. However, the convergence radius of this promising T-matrix completion method is seriously restricted by it's use of single-frequency scattering data only. In this study, we have developed a modified version of the T-matrix completion method which we believe is more suitable for applications to nonlinear inverse scattering problems in (exploration) seismology, because it makes use of multi-frequency data. Essentially, we have simplified the single-frequency T-matrix completion method of Levinson and Markel and combined it with the standard sequential frequency inversion (multi-scale regularization) method. For each frequency, we first estimate the experimental T-matrix by using the Moore-Penrose pseudo inverse concept. Then this experimental T-matrix is used to initiate an iterative procedure for successive estimation of the scattering potential and the T-matrix using the Lippmann-Schwinger for the nonlinear relation between these two quantities. The main physical requirements in the basic iterative cycle is that the T-matrix should be data-compatible and the scattering potential operator should be dominantly local; although a non-local scattering potential operator is allowed in the intermediate iterations. In our simplified T-matrix completion strategy, we ensure that the T-matrix updates are always data compatible simply by adding a suitable correction term in the real space coordinate representation. The use of singular-value decomposition representations are not required in our formulation since we have developed an efficient domain decomposition method. The results of several numerical experiments for the SEG/EAGE salt model illustrate the importance of using multi-frequency data when performing frequency domain full waveform inversion in strongly scattering media via the new concept of T-matrix completion.

Thermal stress effects in intermetallic matrix composites

NASA Technical Reports Server (NTRS)

Wright, P. K.; Sensmeier, M. D.; Kupperman, D. S.; Wadley, H. N. G.

1993-01-01

Intermetallic matrix composites develop residual stresses from the large thermal expansion mismatch (delta-alpha) between the fibers and matrix. This work was undertaken to: establish improved techniques to measure these thermal stresses in IMC's; determine residual stresses in a variety of IMC systems by experiments and modeling; and, determine the effect of residual stresses on selected mechanical properties of an IMC. X ray diffraction (XRD), neutron diffraction (ND), synchrotron XRD (SXRD), and ultrasonics (US) techniques for measuring thermal stresses in IMC were examined and ND was selected as the most promising technique. ND was demonstrated on a variety of IMC systems encompassing Ti- and Ni-base matrices, SiC, W, and Al2O3 fibers, and different fiber fractions (Vf). Experimental results on these systems agreed with predictions of a concentric cylinder model. In SiC/Ti-base systems, little yielding was found and stresses were controlled primarily by delta-alpha and Vf. In Ni-base matrix systems, yield strength of the matrix and Vf controlled stress levels. The longitudinal residual stresses in SCS-6/Ti-24Al-llNb composite were modified by thermomechanical processing. Increasing residual stress decreased ultimate tensile strength in agreement with model predictions. Fiber pushout strength showed an unexpected inverse correlation with residual stress. In-plane shear yield strength showed no dependence on residual stress. Higher levels of residual tension led to higher fatigue crack growth rates, as suggested by matrix mean stress effects.

Matrix decomposition graphics processing unit solver for Poisson image editing

NASA Astrophysics Data System (ADS)

Lei, Zhao; Wei, Li

2012-10-01

In recent years, gradient-domain methods have been widely discussed in the image processing field, including seamless cloning and image stitching. These algorithms are commonly carried out by solving a large sparse linear system: the Poisson equation. However, solving the Poisson equation is a computational and memory intensive task which makes it not suitable for real-time image editing. A new matrix decomposition graphics processing unit (GPU) solver (MDGS) is proposed to settle the problem. A matrix decomposition method is used to distribute the work among GPU threads, so that MDGS will take full advantage of the computing power of current GPUs. Additionally, MDGS is a hybrid solver (combines both the direct and iterative techniques) and has two-level architecture. These enable MDGS to generate identical solutions with those of the common Poisson methods and achieve high convergence rate in most cases. This approach is advantageous in terms of parallelizability, enabling real-time image processing, low memory-taken and extensive applications.

Strategies to Enhance the Model Update in Regions of Weak Sensitivities for Use in Full Waveform Inversion

NASA Astrophysics Data System (ADS)

Nuber, André; Manukyan, Edgar; Maurer, Hansruedi

2014-05-01

Conventional methods of interpreting seismic data rely on filtering and processing limited portions of the recorded wavefield. Typically, either reflections, refractions or surface waves are considered in isolation. Particularly in near-surface engineering and environmental investigations (depths less than, say 100 m), these wave types often overlap in time and are difficult to separate. Full waveform inversion is a technique that seeks to exploit and interpret the full information content of the seismic records without the need for separating events first; it yields models of the subsurface at sub-wavelength resolution. We use a finite element modelling code to solve the 2D elastic isotropic wave equation in the frequency domain. This code is part of a Gauss-Newton inversion scheme which we employ to invert for the P- and S-wave velocities as well as for density in the subsurface. For shallow surface data the use of an elastic forward solver is essential because surface waves often dominate the seismograms. This leads to high sensitivities (partial derivatives contained in the Jacobian matrix of the Gauss-Newton inversion scheme) and thus large model updates close to the surface. Reflections from deeper structures may also include useful information, but the large sensitivities of the surface waves often preclude this information from being fully exploited. We have developed two methods that balance the sensitivity distributions and thus may help resolve the deeper structures. The first method includes equilibrating the columns of the Jacobian matrix prior to every inversion step by multiplying them with individual scaling factors. This is expected to also balance the model updates throughout the entire subsurface model. It can be shown that this procedure is mathematically equivalent to balancing the regularization weights of the individual model parameters. A proper choice of the scaling factors required to balance the Jacobian matrix is critical. We decided to normalise the columns of the Jacobian based on their absolute column sum, but defining an upper threshold for the scaling factors. This avoids particularly small and therefore insignificant sensitivities being over-boosted, which would produce unstable results. The second method proposed includes adjusting the inversion cell size with depth. Multiple cells of the forward modelling grid are merged to form larger inversion cells (typical ratios between forward and inversion cells are in the order of 1:100). The irregular inversion grid is adapted to the expected resolution power of full waveform inversion. Besides stabilizing the inversion, this approach also reduces the number of model parameters to be recovered. Consequently, the computational costs and the memory consumption are reduced significantly. This is particularly critical when Gauss-Newton type inversion schemes are employed. Extensive tests with synthetic data demonstrated that both methods stabilise the inversion and improve the inversion results. The two methods have some redundancy, which can be seen when both are applied simultaneously, that is, when scaling of the Jacobian matrix is applied to an irregular inversion grid. The calculated scaling factors are quite balanced and span a much smaller range than in the case of a regular inversion grid.

Estimation of near-surface shear-wave velocity by inversion of Rayleigh waves

USGS Publications Warehouse

Xia, J.; Miller, R.D.; Park, C.B.

1999-01-01

The shear-wave (S-wave) velocity of near-surface materials (soil, rocks, pavement) and its effect on seismic-wave propagation are of fundamental interest in many groundwater, engineering, and environmental studies. Rayleigh-wave phase velocity of a layered-earth model is a function of frequency and four groups of earth properties: P-wave velocity, S-wave velocity, density, and thickness of layers. Analysis of the Jacobian matrix provides a measure of dispersion-curve sensitivity to earth properties. S-wave velocities are the dominant influence on a dispersion curve in a high-frequency range (>5 Hz) followed by layer thickness. An iterative solution technique to the weighted equation proved very effective in the high-frequency range when using the Levenberg-Marquardt and singular-value decomposition techniques. Convergence of the weighted solution is guaranteed through selection of the damping factor using the Levenberg-Marquardt method. Synthetic examples demonstrated calculation efficiency and stability of inverse procedures. We verify our method using borehole S-wave velocity measurements.Iterative solutions to the weighted equation by the Levenberg-Marquardt and singular-value decomposition techniques are derived to estimate near-surface shear-wave velocity. Synthetic and real examples demonstrate the calculation efficiency and stability of the inverse procedure. The inverse results of the real example are verified by borehole S-wave velocity measurements.

Polymer sol-gel composite inverse opal structures.

PubMed

Zhang, Xiaoran; Blanchard, G J

2015-03-25

We report on the formation of composite inverse opal structures where the matrix used to form the inverse opal contains both silica, formed using sol-gel chemistry, and poly(ethylene glycol), PEG. We find that the morphology of the inverse opal structure depends on both the amount of PEG incorporated into the matrix and its molecular weight. The extent of organization in the inverse opal structure, which is characterized by scanning electron microscopy and optical reflectance data, is mediated by the chemical bonding interactions between the silica and PEG constituents in the hybrid matrix. Both polymer chain terminus Si-O-C bonding and hydrogen bonding between the polymer backbone oxygens and silanol functionalities can contribute, with the polymer mediating the extent to which Si-O-Si bonds can form within the silica regions of the matrix due to hydrogen-bonding interactions.

Global high-frequency source imaging accounting for complexity in Green's functions

NASA Astrophysics Data System (ADS)

Lambert, V.; Zhan, Z.

2017-12-01

The general characterization of earthquake source processes at long periods has seen great success via seismic finite fault inversion/modeling. Complementary techniques, such as seismic back-projection, extend the capabilities of source imaging to higher frequencies and reveal finer details of the rupture process. However, such high frequency methods are limited by the implicit assumption of simple Green's functions, which restricts the use of global arrays and introduces artifacts (e.g., sweeping effects, depth/water phases) that require careful attention. This motivates the implementation of an imaging technique that considers the potential complexity of Green's functions at high frequencies. We propose an alternative inversion approach based on the modest assumption that the path effects contributing to signals within high-coherency subarrays share a similar form. Under this assumption, we develop a method that can combine multiple high-coherency subarrays to invert for a sparse set of subevents. By accounting for potential variability in the Green's functions among subarrays, our method allows for the utilization of heterogeneous global networks for robust high resolution imaging of the complex rupture process. The approach also provides a consistent framework for examining frequency-dependent radiation across a broad frequency spectrum.

Smoothed low rank and sparse matrix recovery by iteratively reweighted least squares minimization.

PubMed

Lu, Canyi; Lin, Zhouchen; Yan, Shuicheng

2015-02-01

This paper presents a general framework for solving the low-rank and/or sparse matrix minimization problems, which may involve multiple nonsmooth terms. The iteratively reweighted least squares (IRLSs) method is a fast solver, which smooths the objective function and minimizes it by alternately updating the variables and their weights. However, the traditional IRLS can only solve a sparse only or low rank only minimization problem with squared loss or an affine constraint. This paper generalizes IRLS to solve joint/mixed low-rank and sparse minimization problems, which are essential formulations for many tasks. As a concrete example, we solve the Schatten-p norm and l2,q-norm regularized low-rank representation problem by IRLS, and theoretically prove that the derived solution is a stationary point (globally optimal if p,q ≥ 1). Our convergence proof of IRLS is more general than previous one that depends on the special properties of the Schatten-p norm and l2,q-norm. Extensive experiments on both synthetic and real data sets demonstrate that our IRLS is much more efficient.

Evaluation of several non-reflecting computational boundary conditions for duct acoustics

NASA Technical Reports Server (NTRS)

Watson, Willie R.; Zorumski, William E.; Hodge, Steve L.

1994-01-01

Several non-reflecting computational boundary conditions that meet certain criteria and have potential applications to duct acoustics are evaluated for their effectiveness. The same interior solution scheme, grid, and order of approximation are used to evaluate each condition. Sparse matrix solution techniques are applied to solve the matrix equation resulting from the discretization. Modal series solutions for the sound attenuation in an infinite duct are used to evaluate the accuracy of each non-reflecting boundary conditions. The evaluations are performed for sound propagation in a softwall duct, for several sources, sound frequencies, and duct lengths. It is shown that a recently developed nonlocal boundary condition leads to sound attenuation predictions considerably more accurate for short ducts. This leads to a substantial reduction in the number of grid points when compared to other non-reflecting conditions.

BinTree Seeking: A Novel Approach to Mine Both Bi-Sparse and Cohesive Modules in Protein Interaction Networks

PubMed Central

Shen, Hong-Bin

2011-01-01

Modern science of networks has brought significant advances to our understanding of complex systems biology. As a representative model of systems biology, Protein Interaction Networks (PINs) are characterized by a remarkable modular structures, reflecting functional associations between their components. Many methods were proposed to capture cohesive modules so that there is a higher density of edges within modules than those across them. Recent studies reveal that cohesively interacting modules of proteins is not a universal organizing principle in PINs, which has opened up new avenues for revisiting functional modules in PINs. In this paper, functional clusters in PINs are found to be able to form unorthodox structures defined as bi-sparse module. In contrast to the traditional cohesive module, the nodes in the bi-sparse module are sparsely connected internally and densely connected with other bi-sparse or cohesive modules. We present a novel protocol called the BinTree Seeking (BTS) for mining both bi-sparse and cohesive modules in PINs based on Edge Density of Module (EDM) and matrix theory. BTS detects modules by depicting links and nodes rather than nodes alone and its derivation procedure is totally performed on adjacency matrix of networks. The number of modules in a PIN can be automatically determined in the proposed BTS approach. BTS is tested on three real PINs and the results demonstrate that functional modules in PINs are not dominantly cohesive but can be sparse. BTS software and the supporting information are available at: www.csbio.sjtu.edu.cn/bioinf/BTS/. PMID:22140454

Fast polar decomposition of an arbitrary matrix

NASA Technical Reports Server (NTRS)

Higham, Nicholas J.; Schreiber, Robert S.

1988-01-01

The polar decomposition of an m x n matrix A of full rank, where m is greater than or equal to n, can be computed using a quadratically convergent algorithm. The algorithm is based on a Newton iteration involving a matrix inverse. With the use of a preliminary complete orthogonal decomposition the algorithm can be extended to arbitrary A. How to use the algorithm to compute the positive semi-definite square root of a Hermitian positive semi-definite matrix is described. A hybrid algorithm which adaptively switches from the matrix inversion based iteration to a matrix multiplication based iteration due to Kovarik, and to Bjorck and Bowie is formulated. The decision when to switch is made using a condition estimator. This matrix multiplication rich algorithm is shown to be more efficient on machines for which matrix multiplication can be executed 1.5 times faster than matrix inversion.

A Spectral Algorithm for Envelope Reduction of Sparse Matrices

NASA Technical Reports Server (NTRS)

Barnard, Stephen T.; Pothen, Alex; Simon, Horst D.

1993-01-01

The problem of reordering a sparse symmetric matrix to reduce its envelope size is considered. A new spectral algorithm for computing an envelope-reducing reordering is obtained by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. This Laplacian eigenvector solves a continuous relaxation of a discrete problem related to envelope minimization called the minimum 2-sum problem. The permutation vector computed by the spectral algorithm is a closest permutation vector to the specified Laplacian eigenvector. Numerical results show that the new reordering algorithm usually computes smaller envelope sizes than those obtained from the current standard algorithms such as Gibbs-Poole-Stockmeyer (GPS) or SPARSPAK reverse Cuthill-McKee (RCM), in some cases reducing the envelope by more than a factor of two.

Optimization of computations for adjoint field and Jacobian needed in 3D CSEM inversion

NASA Astrophysics Data System (ADS)

Dehiya, Rahul; Singh, Arun; Gupta, Pravin K.; Israil, M.

2017-01-01

We present the features and results of a newly developed code, based on Gauss-Newton optimization technique, for solving three-dimensional Controlled-Source Electromagnetic inverse problem. In this code a special emphasis has been put on representing the operations by block matrices for conjugate gradient iteration. We show how in the computation of Jacobian, the matrix formed by differentiation of system matrix can be made independent of frequency to optimize the operations at conjugate gradient step. The coarse level parallel computing, using OpenMP framework, is used primarily due to its simplicity in implementation and accessibility of shared memory multi-core computing machine to almost anyone. We demonstrate how the coarseness of modeling grid in comparison to source (comp`utational receivers) spacing can be exploited for efficient computing, without compromising the quality of the inverted model, by reducing the number of adjoint calls. It is also demonstrated that the adjoint field can even be computed on a grid coarser than the modeling grid without affecting the inversion outcome. These observations were reconfirmed using an experiment design where the deviation of source from straight tow line is considered. Finally, a real field data inversion experiment is presented to demonstrate robustness of the code.

Parallel solution of the symmetric tridiagonal eigenproblem. Research report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jessup, E.R.

1989-10-01

This thesis discusses methods for computing all eigenvalues and eigenvectors of a symmetric tridiagonal matrix on a distributed-memory Multiple Instruction, Multiple Data multiprocessor. Only those techniques having the potential for both high numerical accuracy and significant large-grained parallelism are investigated. These include the QL method or Cuppen's divide and conquer method based on rank-one updating to compute both eigenvalues and eigenvectors, bisection to determine eigenvalues and inverse iteration to compute eigenvectors. To begin, the methods are compared with respect to computation time, communication time, parallel speed up, and accuracy. Experiments on an IPSC hypercube multiprocessor reveal that Cuppen's method ismore » the most accurate approach, but bisection with inverse iteration is the fastest and most parallel. Because the accuracy of the latter combination is determined by the quality of the computed eigenvectors, the factors influencing the accuracy of inverse iteration are examined. This includes, in part, statistical analysis of the effect of a starting vector with random components. These results are used to develop an implementation of inverse iteration producing eigenvectors with lower residual error and better orthogonality than those generated by the EISPACK routine TINVIT. This thesis concludes with adaptions of methods for the symmetric tridiagonal eigenproblem to the related problem of computing the singular value decomposition (SVD) of a bidiagonal matrix.« less

Parallel solution of the symmetric tridiagonal eigenproblem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jessup, E.R.

1989-01-01

This thesis discusses methods for computing all eigenvalues and eigenvectors of a symmetric tridiagonal matrix on a distributed memory MIMD multiprocessor. Only those techniques having the potential for both high numerical accuracy and significant large-grained parallelism are investigated. These include the QL method or Cuppen's divide and conquer method based on rank-one updating to compute both eigenvalues and eigenvectors, bisection to determine eigenvalues, and inverse iteration to compute eigenvectors. To begin, the methods are compared with respect to computation time, communication time, parallel speedup, and accuracy. Experiments on an iPSC hyper-cube multiprocessor reveal that Cuppen's method is the most accuratemore » approach, but bisection with inverse iteration is the fastest and most parallel. Because the accuracy of the latter combination is determined by the quality of the computed eigenvectors, the factors influencing the accuracy of inverse iteration are examined. This includes, in part, statistical analysis of the effects of a starting vector with random components. These results are used to develop an implementation of inverse iteration producing eigenvectors with lower residual error and better orthogonality than those generated by the EISPACK routine TINVIT. This thesis concludes with adaptations of methods for the symmetric tridiagonal eigenproblem to the related problem of computing the singular value decomposition (SVD) of a bidiagonal matrix.« less

Numerical solution of quadratic matrix equations for free vibration analysis of structures

NASA Technical Reports Server (NTRS)

Gupta, K. K.

1975-01-01

This paper is concerned with the efficient and accurate solution of the eigenvalue problem represented by quadratic matrix equations. Such matrix forms are obtained in connection with the free vibration analysis of structures, discretized by finite 'dynamic' elements, resulting in frequency-dependent stiffness and inertia matrices. The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors. An alternative procedure based on a simultaneous iteration procedure is also described when only the first few modes are the usual requirement. The employment of finite dynamic elements in conjunction with the presently developed eigenvalue routines results in a most significant economy in the dynamic analysis of structures.

A Geophysical Inversion Model Enhancement Technique Based on the Blind Deconvolution

NASA Astrophysics Data System (ADS)

Zuo, B.; Hu, X.; Li, H.

2011-12-01

A model-enhancement technique is proposed to enhance the geophysical inversion model edges and details without introducing any additional information. Firstly, the theoretic correctness of the proposed geophysical inversion model-enhancement technique is discussed. An inversion MRM (model resolution matrix) convolution approximating PSF (Point Spread Function) method is designed to demonstrate the correctness of the deconvolution model enhancement method. Then, a total-variation regularization blind deconvolution geophysical inversion model-enhancement algorithm is proposed. In previous research, Oldenburg et al. demonstrate the connection between the PSF and the geophysical inverse solution. Alumbaugh et al. propose that more information could be provided by the PSF if we return to the idea of it behaving as an averaging or low pass filter. We consider the PSF as a low pass filter to enhance the inversion model basis on the theory of the PSF convolution approximation. Both the 1D linear and the 2D magnetotelluric inversion examples are used to analyze the validity of the theory and the algorithm. To prove the proposed PSF convolution approximation theory, the 1D linear inversion problem is considered. It shows the ratio of convolution approximation error is only 0.15%. The 2D synthetic model enhancement experiment is presented. After the deconvolution enhancement, the edges of the conductive prism and the resistive host become sharper, and the enhancement result is closer to the actual model than the original inversion model according the numerical statistic analysis. Moreover, the artifacts in the inversion model are suppressed. The overall precision of model increases 75%. All of the experiments show that the structure details and the numerical precision of inversion model are significantly improved, especially in the anomalous region. The correlation coefficient between the enhanced inversion model and the actual model are shown in Fig. 1. The figure illustrates that more information and details structure of the actual model are enhanced through the proposed enhancement algorithm. Using the proposed enhancement method can help us gain a clearer insight into the results of the inversions and help make better informed decisions.

A pressure flux-split technique for computation of inlet flow behavior

NASA Technical Reports Server (NTRS)

Pordal, H. S.; Khosla, P. K.; Rubin, S. G.

1991-01-01

A method for calculating the flow field in aircraft engine inlets is presented. The phenomena of inlet unstart and restart are investigated. Solutions of the reduced Navier-Stokes (RNS) equations are obtained with a time consistent direct sparse matrix solver that computes the transient flow field both internal and external to the inlet. Time varying shocks and time varying recirculation regions can be efficiently analyzed. The code is quite general and is suitable for the computation of flow for a wide variety of geometries and over a wide range of Mach and Reynolds numbers.

Variational Assimilation of Sparse and Uncertain Satellite Data For 1D Saint-Venant River Models

NASA Astrophysics Data System (ADS)

Garambois, P. A.; Brisset, P.; Monnier, J.; Roux, H.

2016-12-01

Profusion of satellites are providing increasingly accurate measurements of continental water cyle, and water bodies variations while in situ observability is declining. The future Surface Water and Ocean Topography (SWOT) mission will provide maps of river surface elevations widths and slopes with an almost global coverage and temporal revisits. This will offer the possibility to address a larger variety of inverse problems in surface hydrology. Data assimilation techniques, that are broadly used in several scientific fields, aim to optimally combine models, system observations and prior information. Variational assimilation consists in iterative minimization of a discrepency measure between model outputs and observations, here for retrieving boundary conditions and parameters of a 1D Saint Venant model. Nevertheless, inferring river discharge and hydraulic parameters thanks to the observation of river surface is not straightforward. This is particularly true in the case of sparse and uncertain observations of flow state variables since they are governed by nonlinear physical processes. This paper investigates the identifiability of hydraulic controls given sparse and uncertain satellite observations of a river. The identifiability of river discharge alone and with roughness is tested for several spatio temporal patterns of river observations, including SWOT like observations. A new 1D Shallow water model with variational data assimilation, within the DassFlow chain is presented as well as postprocessing and observation operator dedicated to the future SWOT and SWOT simulator data. In view to decrease inverse problem dimensionality discharge is represented in a reduced basis. Moreover we introduce an original and reduced parametrization of the flow resistance that can account for various flow regimes along with a cross section design dedicated to remote sensing. We show which discharge temporal frequencies can be identified w.r.t observation ones and at which accuracy. Eventually the important question of the discharge identifiability potential between observation times and depending on the spatio-temporal sampling is adressed with respect to the wave lengths of the hydrological signals.

The application of nonlinear programming and collocation to optimal aeroassisted orbital transfers

NASA Astrophysics Data System (ADS)

Shi, Y. Y.; Nelson, R. L.; Young, D. H.; Gill, P. E.; Murray, W.; Saunders, M. A.

1992-01-01

Sequential quadratic programming (SQP) and collocation of the differential equations of motion were applied to optimal aeroassisted orbital transfers. The Optimal Trajectory by Implicit Simulation (OTIS) computer program codes with updated nonlinear programming code (NZSOL) were used as a testbed for the SQP nonlinear programming (NLP) algorithms. The state-of-the-art sparse SQP method is considered to be effective for solving large problems with a sparse matrix. Sparse optimizers are characterized in terms of memory requirements and computational efficiency. For the OTIS problems, less than 10 percent of the Jacobian matrix elements are nonzero. The SQP method encompasses two phases: finding an initial feasible point by minimizing the sum of infeasibilities and minimizing the quadratic objective function within the feasible region. The orbital transfer problem under consideration involves the transfer from a high energy orbit to a low energy orbit.

A Fast Gradient Method for Nonnegative Sparse Regression With Self-Dictionary

NASA Astrophysics Data System (ADS)

Gillis, Nicolas; Luce, Robert

2018-01-01

A nonnegative matrix factorization (NMF) can be computed efficiently under the separability assumption, which asserts that all the columns of the given input data matrix belong to the cone generated by a (small) subset of them. The provably most robust methods to identify these conic basis columns are based on nonnegative sparse regression and self dictionaries, and require the solution of large-scale convex optimization problems. In this paper we study a particular nonnegative sparse regression model with self dictionary. As opposed to previously proposed models, this model yields a smooth optimization problem where the sparsity is enforced through linear constraints. We show that the Euclidean projection on the polyhedron defined by these constraints can be computed efficiently, and propose a fast gradient method to solve our model. We compare our algorithm with several state-of-the-art methods on synthetic data sets and real-world hyperspectral images.

Sparse Covariance Matrix Estimation by DCA-Based Algorithms.

PubMed

Phan, Duy Nhat; Le Thi, Hoai An; Dinh, Tao Pham

2017-11-01

This letter proposes a novel approach using the [Formula: see text]-norm regularization for the sparse covariance matrix estimation (SCME) problem. The objective function of SCME problem is composed of a nonconvex part and the [Formula: see text] term, which is discontinuous and difficult to tackle. Appropriate DC (difference of convex functions) approximations of [Formula: see text]-norm are used that result in approximation SCME problems that are still nonconvex. DC programming and DCA (DC algorithm), powerful tools in nonconvex programming framework, are investigated. Two DC formulations are proposed and corresponding DCA schemes developed. Two applications of the SCME problem that are considered are classification via sparse quadratic discriminant analysis and portfolio optimization. A careful empirical experiment is performed through simulated and real data sets to study the performance of the proposed algorithms. Numerical results showed their efficiency and their superiority compared with seven state-of-the-art methods.

Automatic segmentation of right ventricular ultrasound images using sparse matrix transform and a level set

NASA Astrophysics Data System (ADS)

Qin, Xulei; Cong, Zhibin; Fei, Baowei

2013-11-01

An automatic segmentation framework is proposed to segment the right ventricle (RV) in echocardiographic images. The method can automatically segment both epicardial and endocardial boundaries from a continuous echocardiography series by combining sparse matrix transform, a training model, and a localized region-based level set. First, the sparse matrix transform extracts main motion regions of the myocardium as eigen-images by analyzing the statistical information of the images. Second, an RV training model is registered to the eigen-images in order to locate the position of the RV. Third, the training model is adjusted and then serves as an optimized initialization for the segmentation of each image. Finally, based on the initializations, a localized, region-based level set algorithm is applied to segment both epicardial and endocardial boundaries in each echocardiograph. Three evaluation methods were used to validate the performance of the segmentation framework. The Dice coefficient measures the overall agreement between the manual and automatic segmentation. The absolute distance and the Hausdorff distance between the boundaries from manual and automatic segmentation were used to measure the accuracy of the segmentation. Ultrasound images of human subjects were used for validation. For the epicardial and endocardial boundaries, the Dice coefficients were 90.8 ± 1.7% and 87.3 ± 1.9%, the absolute distances were 2.0 ± 0.42 mm and 1.79 ± 0.45 mm, and the Hausdorff distances were 6.86 ± 1.71 mm and 7.02 ± 1.17 mm, respectively. The automatic segmentation method based on a sparse matrix transform and level set can provide a useful tool for quantitative cardiac imaging.

LSRN: A PARALLEL ITERATIVE SOLVER FOR STRONGLY OVER- OR UNDERDETERMINED SYSTEMS*

PubMed Central

Meng, Xiangrui; Saunders, Michael A.; Mahoney, Michael W.

2014-01-01

We describe a parallel iterative least squares solver named LSRN that is based on random normal projection. LSRN computes the min-length solution to minx∈ℝn ‖Ax − b‖2, where A ∈ ℝm × n with m ≫ n or m ≪ n, and where A may be rank-deficient. Tikhonov regularization may also be included. Since A is involved only in matrix-matrix and matrix-vector multiplications, it can be a dense or sparse matrix or a linear operator, and LSRN automatically speeds up when A is sparse or a fast linear operator. The preconditioning phase consists of a random normal projection, which is embarrassingly parallel, and a singular value decomposition of size ⌈γ min(m, n)⌉ × min(m, n), where γ is moderately larger than 1, e.g., γ = 2. We prove that the preconditioned system is well-conditioned, with a strong concentration result on the extreme singular values, and hence that the number of iterations is fully predictable when we apply LSQR or the Chebyshev semi-iterative method. As we demonstrate, the Chebyshev method is particularly efficient for solving large problems on clusters with high communication cost. Numerical results show that on a shared-memory machine, LSRN is very competitive with LAPACK’s DGELSD and a fast randomized least squares solver called Blendenpik on large dense problems, and it outperforms the least squares solver from SuiteSparseQR on sparse problems without sparsity patterns that can be exploited to reduce fill-in. Further experiments show that LSRN scales well on an Amazon Elastic Compute Cloud cluster. PMID:25419094

Modeling the 16 September 2015 Chile tsunami source with the inversion of deep-ocean tsunami records by means of the r - solution method

NASA Astrophysics Data System (ADS)

Voronina, Tatyana; Romanenko, Alexey; Loskutov, Artem

2017-04-01

The key point in the state-of-the-art in the tsunami forecasting is constructing a reliable tsunami source. In this study, we present an application of the original numerical inversion technique to modeling the tsunami sources of the 16 September 2015 Chile tsunami. The problem of recovering a tsunami source from remote measurements of the incoming wave in the deep-water tsunameters is considered as an inverse problem of mathematical physics in the class of ill-posed problems. This approach is based on the least squares and the truncated singular value decomposition techniques. The tsunami wave propagation is considered within the scope of the linear shallow-water theory. As in inverse seismic problem, the numerical solutions obtained by mathematical methods become unstable due to the presence of noise in real data. A method of r-solutions makes it possible to avoid instability in the solution to the ill-posed problem under study. This method seems to be attractive from the computational point of view since the main efforts are required only once for calculating the matrix whose columns consist of computed waveforms for each harmonic as a source (an unknown tsunami source is represented as a part of a spatial harmonics series in the source area). Furthermore, analyzing the singular spectra of the matrix obtained in the course of numerical calculations one can estimate the future inversion by a certain observational system that will allow offering a more effective disposition for the tsunameters with the help of precomputations. In other words, the results obtained allow finding a way to improve the inversion by selecting the most informative set of available recording stations. The case study of the 6 February 2013 Solomon Islands tsunami highlights a critical role of arranging deep-water tsunameters for obtaining the inversion results. Implementation of the proposed methodology to the 16 September 2015 Chile tsunami has successfully produced tsunami source model. The function recovered by the method proposed can find practical applications both as an initial condition for various optimization approaches and for computer calculation of the tsunami wave propagation.

Image Fusion of CT and MR with Sparse Representation in NSST Domain

PubMed Central

Qiu, Chenhui; Wang, Yuanyuan; Zhang, Huan

2017-01-01

Multimodal image fusion techniques can integrate the information from different medical images to get an informative image that is more suitable for joint diagnosis, preoperative planning, intraoperative guidance, and interventional treatment. Fusing images of CT and different MR modalities are studied in this paper. Firstly, the CT and MR images are both transformed to nonsubsampled shearlet transform (NSST) domain. So the low-frequency components and high-frequency components are obtained. Then the high-frequency components are merged using the absolute-maximum rule, while the low-frequency components are merged by a sparse representation- (SR-) based approach. And the dynamic group sparsity recovery (DGSR) algorithm is proposed to improve the performance of the SR-based approach. Finally, the fused image is obtained by performing the inverse NSST on the merged components. The proposed fusion method is tested on a number of clinical CT and MR images and compared with several popular image fusion methods. The experimental results demonstrate that the proposed fusion method can provide better fusion results in terms of subjective quality and objective evaluation. PMID:29250134

Image Fusion of CT and MR with Sparse Representation in NSST Domain.

PubMed

Qiu, Chenhui; Wang, Yuanyuan; Zhang, Huan; Xia, Shunren

2017-01-01

Multimodal image fusion techniques can integrate the information from different medical images to get an informative image that is more suitable for joint diagnosis, preoperative planning, intraoperative guidance, and interventional treatment. Fusing images of CT and different MR modalities are studied in this paper. Firstly, the CT and MR images are both transformed to nonsubsampled shearlet transform (NSST) domain. So the low-frequency components and high-frequency components are obtained. Then the high-frequency components are merged using the absolute-maximum rule, while the low-frequency components are merged by a sparse representation- (SR-) based approach. And the dynamic group sparsity recovery (DGSR) algorithm is proposed to improve the performance of the SR-based approach. Finally, the fused image is obtained by performing the inverse NSST on the merged components. The proposed fusion method is tested on a number of clinical CT and MR images and compared with several popular image fusion methods. The experimental results demonstrate that the proposed fusion method can provide better fusion results in terms of subjective quality and objective evaluation.

Indexing amyloid peptide diffraction from serial femtosecond crystallography: New algorithms for sparse patterns

DOE PAGES

Brewster, Aaron S.; Sawaya, Michael R.; Rodriguez, Jose; ...

2015-01-23

Still diffraction patterns from peptide nanocrystals with small unit cells are challenging to index using conventional methods owing to the limited number of spots and the lack of crystal orientation information for individual images. New indexing algorithms have been developed as part of the Computational Crystallography Toolbox( cctbx) to overcome these challenges. Accurate unit-cell information derived from an aggregate data set from thousands of diffraction patterns can be used to determine a crystal orientation matrix for individual images with as few as five reflections. These algorithms are potentially applicable not only to amyloid peptides but also to any set ofmore » diffraction patterns with sparse properties, such as low-resolution virus structures or high-throughput screening of still images captured by raster-scanning at synchrotron sources. As a proof of concept for this technique, successful integration of X-ray free-electron laser (XFEL) data to 2.5 Å resolution for the amyloid segment GNNQQNY from the Sup35 yeast prion is presented.« less

Joint Feature Extraction and Classifier Design for ECG-Based Biometric Recognition.

PubMed

Gutta, Sandeep; Cheng, Qi

2016-03-01

Traditional biometric recognition systems often utilize physiological traits such as fingerprint, face, iris, etc. Recent years have seen a growing interest in electrocardiogram (ECG)-based biometric recognition techniques, especially in the field of clinical medicine. In existing ECG-based biometric recognition methods, feature extraction and classifier design are usually performed separately. In this paper, a multitask learning approach is proposed, in which feature extraction and classifier design are carried out simultaneously. Weights are assigned to the features within the kernel of each task. We decompose the matrix consisting of all the feature weights into sparse and low-rank components. The sparse component determines the features that are relevant to identify each individual, and the low-rank component determines the common feature subspace that is relevant to identify all the subjects. A fast optimization algorithm is developed, which requires only the first-order information. The performance of the proposed approach is demonstrated through experiments using the MIT-BIH Normal Sinus Rhythm database.

A robust method of computing finite difference coefficients based on Vandermonde matrix

NASA Astrophysics Data System (ADS)

Zhang, Yijie; Gao, Jinghuai; Peng, Jigen; Han, Weimin

2018-05-01

When the finite difference (FD) method is employed to simulate the wave propagation, high-order FD method is preferred in order to achieve better accuracy. However, if the order of FD scheme is high enough, the coefficient matrix of the formula for calculating finite difference coefficients is close to be singular. In this case, when the FD coefficients are computed by matrix inverse operator of MATLAB, inaccuracy can be produced. In order to overcome this problem, we have suggested an algorithm based on Vandermonde matrix in this paper. After specified mathematical transformation, the coefficient matrix is transformed into a Vandermonde matrix. Then the FD coefficients of high-order FD method can be computed by the algorithm of Vandermonde matrix, which prevents the inverse of the singular matrix. The dispersion analysis and numerical results of a homogeneous elastic model and a geophysical model of oil and gas reservoir demonstrate that the algorithm based on Vandermonde matrix has better accuracy compared with matrix inverse operator of MATLAB.

Composition of fibrin glues significantly influences axial vascularization and degradation in isolation chamber model.

PubMed

Arkudas, Andreas; Pryymachuk, Galyna; Hoereth, Tobias; Beier, Justus P; Polykandriotis, Elias; Bleiziffer, Oliver; Gulle, Heinz; Horch, Raymund E; Kneser, Ulrich

2012-07-01

In this study, different fibrin sealants with varying concentrations of the fibrin components were evaluated in terms of matrix degradation and vascularization in the arteriovenous loop (AVL) model of the rat. An AVL was placed in a Teflon isolation chamber filled with 500 μl fibrin gel. The matrix was composed of commercially available fibrin gels, namely Beriplast (Behring GmbH, Marburg, Germany) (group A), Evicel (Omrix Biopharmaceuticals S.A., Somerville, New Jersey, USA) (group B), Tisseel VH S/D (Baxter, Vienna, Austria) with a thrombin concentration of 4 IU/ml and a fibrinogen concentration of 80 mg/ml [Tisseel S F80 (Baxter), group C] and with an fibrinogen concentration of 20 mg/ml [Tisseel S F20 (Baxter), group D]. After 2 and 4 weeks, five constructs per group and time point were investigated using micro-computed tomography, and histological and morphometrical analysis techniques. The aprotinin, factor XIII and thrombin concentration did not affect the degree of clot degradation. An inverse relationship was found between fibrin matrix degradation and sprouting of blood vessels. By reducing the fibrinogen concentration in group D, a significantly decreased construct weight and an increased generation of vascularized connective tissue were detected. There was an inverse relationship between matrix degradation and vascularization detectable. Fibrinogen as the major matrix component showed a significant impact on the matrix properties. Alteration of fibrin gel properties might optimize formation of blood vessels.

Computing the Moore-Penrose Inverse of a Matrix with a Computer Algebra System

ERIC Educational Resources Information Center

Schmidt, Karsten

2008-01-01

In this paper "Derive" functions are provided for the computation of the Moore-Penrose inverse of a matrix, as well as for solving systems of linear equations by means of the Moore-Penrose inverse. Making it possible to compute the Moore-Penrose inverse easily with one of the most commonly used Computer Algebra Systems--and to have the blueprint…

Geographic patterns and dynamics of Alaskan climate interpolated from a sparse station record

USGS Publications Warehouse

Fleming, Michael D.; Chapin, F. Stuart; Cramer, W.; Hufford, Gary L.; Serreze, Mark C.

2000-01-01

Data from a sparse network of climate stations in Alaska were interpolated to provide 1-km resolution maps of mean monthly temperature and precipitation-variables that are required at high spatial resolution for input into regional models of ecological processes and resource management. The interpolation model is based on thin-plate smoothing splines, which uses the spatial data along with a digital elevation model to incorporate local topography. The model provides maps that are consistent with regional climatology and with patterns recognized by experienced weather forecasters. The broad patterns of Alaskan climate are well represented and include latitudinal and altitudinal trends in temperature and precipitation and gradients in continentality. Variations within these broad patterns reflect both the weakening and reduction in frequency of low-pressure centres in their eastward movement across southern Alaska during the summer, and the shift of the storm tracks into central and northern Alaska in late summer. Not surprisingly, apparent artifacts of the interpolated climate occur primarily in regions with few or no stations. The interpolation model did not accurately represent low-level winter temperature inversions that occur within large valleys and basins. Along with well-recognized climate patterns, the model captures local topographic effects that would not be depicted using standard interpolation techniques. This suggests that similar procedures could be used to generate high-resolution maps for other high-latitude regions with a sparse density of data.

A Subspace Pursuit–based Iterative Greedy Hierarchical Solution to the Neuromagnetic Inverse Problem

PubMed Central

Babadi, Behtash; Obregon-Henao, Gabriel; Lamus, Camilo; Hämäläinen, Matti S.; Brown, Emery N.; Purdon, Patrick L.

2013-01-01

Magnetoencephalography (MEG) is an important non-invasive method for studying activity within the human brain. Source localization methods can be used to estimate spatiotemporal activity from MEG measurements with high temporal resolution, but the spatial resolution of these estimates is poor due to the ill-posed nature of the MEG inverse problem. Recent developments in source localization methodology have emphasized temporal as well as spatial constraints to improve source localization accuracy, but these methods can be computationally intense. Solutions emphasizing spatial sparsity hold tremendous promise, since the underlying neurophysiological processes generating MEG signals are often sparse in nature, whether in the form of focal sources, or distributed sources representing large-scale functional networks. Recent developments in the theory of compressed sensing (CS) provide a rigorous framework to estimate signals with sparse structure. In particular, a class of CS algorithms referred to as greedy pursuit algorithms can provide both high recovery accuracy and low computational complexity. Greedy pursuit algorithms are difficult to apply directly to the MEG inverse problem because of the high-dimensional structure of the MEG source space and the high spatial correlation in MEG measurements. In this paper, we develop a novel greedy pursuit algorithm for sparse MEG source localization that overcomes these fundamental problems. This algorithm, which we refer to as the Subspace Pursuit-based Iterative Greedy Hierarchical (SPIGH) inverse solution, exhibits very low computational complexity while achieving very high localization accuracy. We evaluate the performance of the proposed algorithm using comprehensive simulations, as well as the analysis of human MEG data during spontaneous brain activity and somatosensory stimuli. These studies reveal substantial performance gains provided by the SPIGH algorithm in terms of computational complexity, localization accuracy, and robustness. PMID:24055554

Direction of Arrival Estimation for MIMO Radar via Unitary Nuclear Norm Minimization

PubMed Central

Wang, Xianpeng; Huang, Mengxing; Wu, Xiaoqin; Bi, Guoan

2017-01-01

In this paper, we consider the direction of arrival (DOA) estimation issue of noncircular (NC) source in multiple-input multiple-output (MIMO) radar and propose a novel unitary nuclear norm minimization (UNNM) algorithm. In the proposed method, the noncircular properties of signals are used to double the virtual array aperture, and the real-valued data are obtained by utilizing unitary transformation. Then a real-valued block sparse model is established based on a novel over-complete dictionary, and a UNNM algorithm is formulated for recovering the block-sparse matrix. In addition, the real-valued NC-MUSIC spectrum is used to design a weight matrix for reweighting the nuclear norm minimization to achieve the enhanced sparsity of solutions. Finally, the DOA is estimated by searching the non-zero blocks of the recovered matrix. Because of using the noncircular properties of signals to extend the virtual array aperture and an additional real structure to suppress the noise, the proposed method provides better performance compared with the conventional sparse recovery based algorithms. Furthermore, the proposed method can handle the case of underdetermined DOA estimation. Simulation results show the effectiveness and advantages of the proposed method. PMID:28441770

Yielding physically-interpretable emulators - A Sparse PCA approach

NASA Astrophysics Data System (ADS)

Galelli, S.; Alsahaf, A.; Giuliani, M.; Castelletti, A.

2015-12-01

Projection-based techniques, such as Principal Orthogonal Decomposition (POD), are a common approach to surrogate high-fidelity process-based models by lower order dynamic emulators. With POD, the dimensionality reduction is achieved by using observations, or 'snapshots' - generated with the high-fidelity model -, to project the entire set of input and state variables of this model onto a smaller set of basis functions that account for most of the variability in the data. While reduction efficiency and variance control of POD techniques are usually very high, the resulting emulators are structurally highly complex and can hardly be given a physically meaningful interpretation as each basis is a projection of the entire set of inputs and states. In this work, we propose a novel approach based on Sparse Principal Component Analysis (SPCA) that combines the several assets of POD methods with the potential for ex-post interpretation of the emulator structure. SPCA reduces the number of non-zero coefficients in the basis functions by identifying a sparse matrix of coefficients. While the resulting set of basis functions may retain less variance of the snapshots, the presence of a few non-zero coefficients assists in the interpretation of the underlying physical processes. The SPCA approach is tested on the reduction of a 1D hydro-ecological model (DYRESM-CAEDYM) used to describe the main ecological and hydrodynamic processes in Tono Dam, Japan. An experimental comparison against a standard POD approach shows that SPCA achieves the same accuracy in emulating a given output variable - for the same level of dimensionality reduction - while yielding better insights of the main process dynamics.

The shifting zoom: new possibilities for inverse scattering on electrically large domains

NASA Astrophysics Data System (ADS)

Persico, Raffaele; Ludeno, Giovanni; Soldovieri, Francesco; De Coster, Alberic; Lambot, Sebastien

2017-04-01

Inverse scattering is a subject of great interest in diagnostic problems, which are in their turn of interest for many applicative problems as investigation of cultural heritage, characterization of foundations or subservices, identification of unexploded ordnances and so on [1-4]. In particular, GPR data are usually focused by means of migration algorithms, essentially based on a linear approximation of the scattering phenomenon. Migration algorithms are popular because they are computationally efficient and do not require the inversion of a matrix, neither the calculation of the elements of a matrix. In fact, they are essentially based on the adjoint of the linearised scattering operator, which allows in the end to write the inversion formula as a suitably weighted integral of the data [5]. In particular, this makes a migration algorithm more suitable than a linear microwave tomography inversion algorithm for the reconstruction of an electrically large investigation domain. However, this computational challenge can be overcome by making use of investigation domains joined side by side, as proposed e.g. in ref. [3]. This allows to apply a microwave tomography algorithm even to large investigation domains. However, the joining side by side of sequential investigation domains introduces a problem of limited (and asymmetric) maximum view angle with regard to the targets occurring close to the edges between two adjacent domains, or possibly crossing these edges. The shifting zoom is a method that allows to overcome this difficulty by means of overlapped investigation and observation domains [6-7]. It requires more sequential inversion with respect to adjacent investigation domains, but the really required extra-time is minimal because the matrix to be inverted is calculated ones and for all, as well as its singular value decomposition: what is repeated more time is only a fast matrix-vector multiplication. References [1] M. Pieraccini, L. Noferini, D. Mecatti, C. Atzeni, R. Persico, F. Soldovieri, Advanced Processing Techniques for Step-frequency Continuous-Wave Penetrating Radar: the Case Study of "Palazzo Vecchio" Walls (Firenze, Italy), Research on Nondestructive Evaluation, vol. 17, pp. 71-83, 2006. [2] N. Masini, R. Persico, E. Rizzo, A. Calia, M. T. Giannotta, G. Quarta, A. Pagliuca, "Integrated Techniques for Analysis and Monitoring of Historical Monuments: the case of S.Giovanni al Sepolcro in Brindisi (Southern Italy)." Near Surface Geophysics, vol. 8 (5), pp. 423-432, 2010. [3] E. Pettinelli, A. Di Matteo, E. Mattei, L. Crocco, F. Soldovieri, J. D. Redman, and A. P. Annan, "GPR response from buried pipes: Measurement on field site and tomographic reconstructions", IEEE Transactions on Geoscience and Remote Sensing, vol. 47, n. 8, 2639-2645, Aug. 2009. [4] O. Lopera, E. C. Slob, N. Milisavljevic and S. Lambot, "Filtering soil surface and antenna effects from GPR data to enhance landmine detection", IEEE Transactions on Geoscience and Remote Sensing, vol. 45, n. 3, pp.707-717, 2007. [5] R. Persico, "Introduction to Ground Penetrating Radar: Inverse Scattering and Data Processing". Wiley, 2014. [6] R. Persico, J. Sala, "The problem of the investigation domain subdivision in 2D linear inversions for large scale GPR data", IEEE Geoscience and Remote Sensing Letters, vol. 11, n. 7, pp. 1215-1219, doi 10.1109/LGRS.2013.2290008, July 2014. [7] R. Persico, F. Soldovieri, S. Lambot, Shifting zoom in 2D linear inversions performed on GPR data gathered along an electrically large investigation domain, Proc. 16th International Conference on Ground Penetrating Radar GPR2016, Honk-Kong, June 13-16, 2016

A new global approach to obtain three-dimensional displacement maps by integrating GPS and DInSAR data

NASA Astrophysics Data System (ADS)

Guglielmino, F.; Nunnari, G.; Puglisi, G.; Spata, A.

2009-04-01

We propose a new technique, based on the elastic theory, to efficiently produce an estimate of three-dimensional surface displacement maps by integrating sparse Global Position System (GPS) measurements of deformations and Differential Interferometric Synthetic Aperture Radar (DInSAR) maps of movements of the Earth's surface. The previous methodologies known in literature, for combining data from GPS and DInSAR surveys, require two steps: the first, in which sparse GPS measurements are interpolated in order to fill in GPS displacements at the DInSAR grid, and the second, to estimate the three-dimensional surface displacement maps by using a suitable optimization technique. One of the advantages of the proposed approach is that both these steps are unified. We propose a linear matrix equation which accounts for both GPS and DInSAR data whose solution provide simultaneously the strain tensor, the displacement field and the rigid body rotation tensor throughout the entire investigated area. The mentioned linear matrix equation is solved by using the Weighted Least Square (WLS) thus assuring both numerical robustness and high computation efficiency. The proposed methodology was tested on both synthetic and experimental data, these last from GPS and DInSAR measurements carried out on Mt. Etna. The goodness of the results has been evaluated by using standard errors. These tests also allow optimising the choice of specific parameters of this algorithm. This "open" structure of the method will allow in the near future to take account of other available data sets, such as additional interferograms, or other geodetic data (e.g. levelling, tilt, etc.), in order to achieve even higher accuracy.

Using artificial neural networks (ANN) for open-loop tomography

NASA Astrophysics Data System (ADS)

Osborn, James; De Cos Juez, Francisco Javier; Guzman, Dani; Butterley, Timothy; Myers, Richard; Guesalaga, Andres; Laine, Jesus

2011-09-01

The next generation of adaptive optics (AO) systems require tomographic techniques in order to correct for atmospheric turbulence along lines of sight separated from the guide stars. Multi-object adaptive optics (MOAO) is one such technique. Here, we present a method which uses an artificial neural network (ANN) to reconstruct the target phase given off-axis references sources. This method does not require any input of the turbulence profile and is therefore less susceptible to changing conditions than some existing methods. We compare our ANN method with a standard least squares type matrix multiplication method (MVM) in simulation and find that the tomographic error is similar to the MVM method. In changing conditions the tomographic error increases for MVM but remains constant with the ANN model and no large matrix inversions are required.

A highly efficient approach to protein interactome mapping based on collaborative filtering framework.

PubMed

Luo, Xin; You, Zhuhong; Zhou, Mengchu; Li, Shuai; Leung, Hareton; Xia, Yunni; Zhu, Qingsheng

2015-01-09

The comprehensive mapping of protein-protein interactions (PPIs) is highly desired for one to gain deep insights into both fundamental cell biology processes and the pathology of diseases. Finely-set small-scale experiments are not only very expensive but also inefficient to identify numerous interactomes despite their high accuracy. High-throughput screening techniques enable efficient identification of PPIs; yet the desire to further extract useful knowledge from these data leads to the problem of binary interactome mapping. Network topology-based approaches prove to be highly efficient in addressing this problem; however, their performance deteriorates significantly on sparse putative PPI networks. Motivated by the success of collaborative filtering (CF)-based approaches to the problem of personalized-recommendation on large, sparse rating matrices, this work aims at implementing a highly efficient CF-based approach to binary interactome mapping. To achieve this, we first propose a CF framework for it. Under this framework, we model the given data into an interactome weight matrix, where the feature-vectors of involved proteins are extracted. With them, we design the rescaled cosine coefficient to model the inter-neighborhood similarity among involved proteins, for taking the mapping process. Experimental results on three large, sparse datasets demonstrate that the proposed approach outperforms several sophisticated topology-based approaches significantly.

A Highly Efficient Approach to Protein Interactome Mapping Based on Collaborative Filtering Framework

PubMed Central

Luo, Xin; You, Zhuhong; Zhou, Mengchu; Li, Shuai; Leung, Hareton; Xia, Yunni; Zhu, Qingsheng

2015-01-01

The comprehensive mapping of protein-protein interactions (PPIs) is highly desired for one to gain deep insights into both fundamental cell biology processes and the pathology of diseases. Finely-set small-scale experiments are not only very expensive but also inefficient to identify numerous interactomes despite their high accuracy. High-throughput screening techniques enable efficient identification of PPIs; yet the desire to further extract useful knowledge from these data leads to the problem of binary interactome mapping. Network topology-based approaches prove to be highly efficient in addressing this problem; however, their performance deteriorates significantly on sparse putative PPI networks. Motivated by the success of collaborative filtering (CF)-based approaches to the problem of personalized-recommendation on large, sparse rating matrices, this work aims at implementing a highly efficient CF-based approach to binary interactome mapping. To achieve this, we first propose a CF framework for it. Under this framework, we model the given data into an interactome weight matrix, where the feature-vectors of involved proteins are extracted. With them, we design the rescaled cosine coefficient to model the inter-neighborhood similarity among involved proteins, for taking the mapping process. Experimental results on three large, sparse datasets demonstrate that the proposed approach outperforms several sophisticated topology-based approaches significantly. PMID:25572661

Indexing amyloid peptide diffraction from serial femtosecond crystallography: new algorithms for sparse patterns

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brewster, Aaron S.; Sawaya, Michael R.; University of California, Los Angeles, CA 90095-1570

2015-02-01

Special methods are required to interpret sparse diffraction patterns collected from peptide crystals at X-ray free-electron lasers. Bragg spots can be indexed from composite-image powder rings, with crystal orientations then deduced from a very limited number of spot positions. Still diffraction patterns from peptide nanocrystals with small unit cells are challenging to index using conventional methods owing to the limited number of spots and the lack of crystal orientation information for individual images. New indexing algorithms have been developed as part of the Computational Crystallography Toolbox (cctbx) to overcome these challenges. Accurate unit-cell information derived from an aggregate data setmore » from thousands of diffraction patterns can be used to determine a crystal orientation matrix for individual images with as few as five reflections. These algorithms are potentially applicable not only to amyloid peptides but also to any set of diffraction patterns with sparse properties, such as low-resolution virus structures or high-throughput screening of still images captured by raster-scanning at synchrotron sources. As a proof of concept for this technique, successful integration of X-ray free-electron laser (XFEL) data to 2.5 Å resolution for the amyloid segment GNNQQNY from the Sup35 yeast prion is presented.« less

A Highly Efficient Approach to Protein Interactome Mapping Based on Collaborative Filtering Framework

NASA Astrophysics Data System (ADS)

Luo, Xin; You, Zhuhong; Zhou, Mengchu; Li, Shuai; Leung, Hareton; Xia, Yunni; Zhu, Qingsheng

2015-01-01

The comprehensive mapping of protein-protein interactions (PPIs) is highly desired for one to gain deep insights into both fundamental cell biology processes and the pathology of diseases. Finely-set small-scale experiments are not only very expensive but also inefficient to identify numerous interactomes despite their high accuracy. High-throughput screening techniques enable efficient identification of PPIs; yet the desire to further extract useful knowledge from these data leads to the problem of binary interactome mapping. Network topology-based approaches prove to be highly efficient in addressing this problem; however, their performance deteriorates significantly on sparse putative PPI networks. Motivated by the success of collaborative filtering (CF)-based approaches to the problem of personalized-recommendation on large, sparse rating matrices, this work aims at implementing a highly efficient CF-based approach to binary interactome mapping. To achieve this, we first propose a CF framework for it. Under this framework, we model the given data into an interactome weight matrix, where the feature-vectors of involved proteins are extracted. With them, we design the rescaled cosine coefficient to model the inter-neighborhood similarity among involved proteins, for taking the mapping process. Experimental results on three large, sparse datasets demonstrate that the proposed approach outperforms several sophisticated topology-based approaches significantly.

Using Perturbed QR Factorizations To Solve Linear Least-Squares Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Avron, Haim; Ng, Esmond G.; Toledo, Sivan

2008-03-21

We propose and analyze a new tool to help solve sparse linear least-squares problems min{sub x} {parallel}Ax-b{parallel}{sub 2}. Our method is based on a sparse QR factorization of a low-rank perturbation {cflx A} of A. More precisely, we show that the R factor of {cflx A} is an effective preconditioner for the least-squares problem min{sub x} {parallel}Ax-b{parallel}{sub 2}, when solved using LSQR. We propose applications for the new technique. When A is rank deficient we can add rows to ensure that the preconditioner is well-conditioned without column pivoting. When A is sparse except for a few dense rows we canmore » drop these dense rows from A to obtain {cflx A}. Another application is solving an updated or downdated problem. If R is a good preconditioner for the original problem A, it is a good preconditioner for the updated/downdated problem {cflx A}. We can also solve what-if scenarios, where we want to find the solution if a column of the original matrix is changed/removed. We present a spectral theory that analyzes the generalized spectrum of the pencil (A*A,R*R) and analyze the applications.« less

Identifing Atmospheric Pollutant Sources Using Artificial Neural Networks

NASA Astrophysics Data System (ADS)

Paes, F. F.; Campos, H. F.; Luz, E. P.; Carvalho, A. R.

2008-05-01

The estimation of the area source pollutant strength is a relevant issue for atmospheric environment. This characterizes an inverse problem in the atmospheric pollution dispersion. In the inverse analysis, an area source domain is considered, where the strength of such area source term is assumed unknown. The inverse problem is solved by using a supervised artificial neural network: multi-layer perceptron. The conection weights of the neural network are computed from delta rule - learning process. The neural network inversion is compared with results from standard inverse analysis (regularized inverse solution). In the regularization method, the inverse problem is formulated as a non-linear optimization approach, whose the objective function is given by the square difference between the measured pollutant concentration and the mathematical models, associated with a regularization operator. In our numerical experiments, the forward problem is addressed by a source-receptor scheme, where a regressive Lagrangian model is applied to compute the transition matrix. The second order maximum entropy regularization is used, and the regularization parameter is calculated by the L-curve technique. The objective function is minimized employing a deterministic scheme (a quasi-Newton algorithm) [1] and a stochastic technique (PSO: particle swarm optimization) [2]. The inverse problem methodology is tested with synthetic observational data, from six measurement points in the physical domain. The best inverse solutions were obtained with neural networks. References: [1] D. R. Roberti, D. Anfossi, H. F. Campos Velho, G. A. Degrazia (2005): Estimating Emission Rate and Pollutant Source Location, Ciencia e Natura, p. 131-134. [2] E.F.P. da Luz, H.F. de Campos Velho, J.C. Becceneri, D.R. Roberti (2007): Estimating Atmospheric Area Source Strength Through Particle Swarm Optimization. Inverse Problems, Desing and Optimization Symposium IPDO-2007, April 16-18, Miami (FL), USA, vol 1, p. 354-359.

Groupwise registration of MR brain images with tumors.

PubMed

Tang, Zhenyu; Wu, Yihong; Fan, Yong

2017-08-04

A novel groupwise image registration framework is developed for registering MR brain images with tumors. Our method iteratively estimates a normal-appearance counterpart for each tumor image to be registered and constructs a directed graph (digraph) of normal-appearance images to guide the groupwise image registration. Particularly, our method maps each tumor image to its normal appearance counterpart by identifying and inpainting brain tumor regions with intensity information estimated using a low-rank plus sparse matrix decomposition based image representation technique. The estimated normal-appearance images are groupwisely registered to a group center image guided by a digraph of images so that the total length of 'image registration paths' to be the minimum, and then the original tumor images are warped to the group center image using the resulting deformation fields. We have evaluated our method based on both simulated and real MR brain tumor images. The registration results were evaluated with overlap measures of corresponding brain regions and average entropy of image intensity information, and Wilcoxon signed rank tests were adopted to compare different methods with respect to their regional overlap measures. Compared with a groupwise image registration method that is applied to normal-appearance images estimated using the traditional low-rank plus sparse matrix decomposition based image inpainting, our method achieved higher image registration accuracy with statistical significance (p  =  7.02  ×  10 -9 ).

Data-resolution matrix and model-resolution matrix for Rayleigh-wave inversion using a damped least-squares method

USGS Publications Warehouse

Xia, J.; Miller, R.D.; Xu, Y.

2008-01-01

Inversion of multimode surface-wave data is of increasing interest in the near-surface geophysics community. For a given near-surface geophysical problem, it is essential to understand how well the data, calculated according to a layered-earth model, might match the observed data. A data-resolution matrix is a function of the data kernel (determined by a geophysical model and a priori information applied to the problem), not the data. A data-resolution matrix of high-frequency (>2 Hz) Rayleigh-wave phase velocities, therefore, offers a quantitative tool for designing field surveys and predicting the match between calculated and observed data. We employed a data-resolution matrix to select data that would be well predicted and we find that there are advantages of incorporating higher modes in inversion. The resulting discussion using the data-resolution matrix provides insight into the process of inverting Rayleigh-wave phase velocities with higher-mode data to estimate S-wave velocity structure. Discussion also suggested that each near-surface geophysical target can only be resolved using Rayleigh-wave phase velocities within specific frequency ranges, and higher-mode data are normally more accurately predicted than fundamental-mode data because of restrictions on the data kernel for the inversion system. We used synthetic and real-world examples to demonstrate that selected data with the data-resolution matrix can provide better inversion results and to explain with the data-resolution matrix why incorporating higher-mode data in inversion can provide better results. We also calculated model-resolution matrices in these examples to show the potential of increasing model resolution with selected surface-wave data. ?? Birkhaueser 2008.

An ambiguity of information content and error in an ill-posed satellite inversion

NASA Astrophysics Data System (ADS)

Koner, Prabhat

According to Rodgers (2000, stochastic approach), the averaging kernel (AK) is the representational matrix to understand the information content in a scholastic inversion. On the other hand, in deterministic approach this is referred to as model resolution matrix (MRM, Menke 1989). The analysis of AK/MRM can only give some understanding of how much regularization is imposed on the inverse problem. The trace of the AK/MRM matrix, which is the so-called degree of freedom from signal (DFS; stochastic) or degree of freedom in retrieval (DFR; deterministic). There are no physical/mathematical explanations in the literature: why the trace of the matrix is a valid form to calculate this quantity? We will present an ambiguity between information and error using a real life problem of SST retrieval from GOES13. The stochastic information content calculation is based on the linear assumption. The validity of such mathematics in satellite inversion will be questioned because it is based on the nonlinear radiative transfer and ill-conditioned inverse problems. References: Menke, W., 1989: Geophysical data analysis: discrete inverse theory. San Diego academic press. Rodgers, C.D., 2000: Inverse methods for atmospheric soundings: theory and practice. Singapore :World Scientific.

Arikan and Alamouti matrices based on fast block-wise inverse Jacket transform

NASA Astrophysics Data System (ADS)

Lee, Moon Ho; Khan, Md Hashem Ali; Kim, Kyeong Jin

2013-12-01

Recently, Lee and Hou (IEEE Signal Process Lett 13: 461-464, 2006) proposed one-dimensional and two-dimensional fast algorithms for block-wise inverse Jacket transforms (BIJTs). Their BIJTs are not real inverse Jacket transforms from mathematical point of view because their inverses do not satisfy the usual condition, i.e., the multiplication of a matrix with its inverse matrix is not equal to the identity matrix. Therefore, we mathematically propose a fast block-wise inverse Jacket transform of orders N = 2 k , 3 k , 5 k , and 6 k , where k is a positive integer. Based on the Kronecker product of the successive lower order Jacket matrices and the basis matrix, the fast algorithms for realizing these transforms are obtained. Due to the simple inverse and fast algorithms of Arikan polar binary and Alamouti multiple-input multiple-output (MIMO) non-binary matrices, which are obtained from BIJTs, they can be applied in areas such as 3GPP physical layer for ultra mobile broadband permutation matrices design, first-order q-ary Reed-Muller code design, diagonal channel design, diagonal subchannel decompose for interference alignment, and 4G MIMO long-term evolution Alamouti precoding design.

Unbiased, scalable sampling of protein loop conformations from probabilistic priors.

PubMed

Zhang, Yajia; Hauser, Kris

2013-01-01

Protein loops are flexible structures that are intimately tied to function, but understanding loop motion and generating loop conformation ensembles remain significant computational challenges. Discrete search techniques scale poorly to large loops, optimization and molecular dynamics techniques are prone to local minima, and inverse kinematics techniques can only incorporate structural preferences in adhoc fashion. This paper presents Sub-Loop Inverse Kinematics Monte Carlo (SLIKMC), a new Markov chain Monte Carlo algorithm for generating conformations of closed loops according to experimentally available, heterogeneous structural preferences. Our simulation experiments demonstrate that the method computes high-scoring conformations of large loops (>10 residues) orders of magnitude faster than standard Monte Carlo and discrete search techniques. Two new developments contribute to the scalability of the new method. First, structural preferences are specified via a probabilistic graphical model (PGM) that links conformation variables, spatial variables (e.g., atom positions), constraints and prior information in a unified framework. The method uses a sparse PGM that exploits locality of interactions between atoms and residues. Second, a novel method for sampling sub-loops is developed to generate statistically unbiased samples of probability densities restricted by loop-closure constraints. Numerical experiments confirm that SLIKMC generates conformation ensembles that are statistically consistent with specified structural preferences. Protein conformations with 100+ residues are sampled on standard PC hardware in seconds. Application to proteins involved in ion-binding demonstrate its potential as a tool for loop ensemble generation and missing structure completion.

Unbiased, scalable sampling of protein loop conformations from probabilistic priors

PubMed Central

2013-01-01

Background Protein loops are flexible structures that are intimately tied to function, but understanding loop motion and generating loop conformation ensembles remain significant computational challenges. Discrete search techniques scale poorly to large loops, optimization and molecular dynamics techniques are prone to local minima, and inverse kinematics techniques can only incorporate structural preferences in adhoc fashion. This paper presents Sub-Loop Inverse Kinematics Monte Carlo (SLIKMC), a new Markov chain Monte Carlo algorithm for generating conformations of closed loops according to experimentally available, heterogeneous structural preferences. Results Our simulation experiments demonstrate that the method computes high-scoring conformations of large loops (>10 residues) orders of magnitude faster than standard Monte Carlo and discrete search techniques. Two new developments contribute to the scalability of the new method. First, structural preferences are specified via a probabilistic graphical model (PGM) that links conformation variables, spatial variables (e.g., atom positions), constraints and prior information in a unified framework. The method uses a sparse PGM that exploits locality of interactions between atoms and residues. Second, a novel method for sampling sub-loops is developed to generate statistically unbiased samples of probability densities restricted by loop-closure constraints. Conclusion Numerical experiments confirm that SLIKMC generates conformation ensembles that are statistically consistent with specified structural preferences. Protein conformations with 100+ residues are sampled on standard PC hardware in seconds. Application to proteins involved in ion-binding demonstrate its potential as a tool for loop ensemble generation and missing structure completion. PMID:24565175

Convex Banding of the Covariance Matrix

PubMed Central

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings. PMID:28042189

Convex Banding of the Covariance Matrix.

PubMed

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings.

Sub-basalt Imaging of Hydrocarbon-Bearing Mesozoic Sediments Using Ray-Trace Inversion of First-Arrival Seismic Data and Elastic Finite-Difference Full-Wave Modeling Along Sinor-Valod Profile of Deccan Syneclise, India

NASA Astrophysics Data System (ADS)

Talukdar, Karabi; Behera, Laxmidhar

2018-03-01

Imaging below the basalt for hydrocarbon exploration is a global problem because of poor penetration and significant loss of seismic energy due to scattering, attenuation, absorption and mode-conversion when the seismic waves encounter a highly heterogeneous and rugose basalt layer. The conventional (short offset) seismic data acquisition, processing and modeling techniques adopted by the oil industry generally fails to image hydrocarbon-bearing sub-trappean Mesozoic sediments hidden below the basalt and is considered as a serious problem for hydrocarbon exploration in the world. To overcome this difficulty of sub-basalt imaging, we have generated dense synthetic seismic data with the help of elastic finite-difference full-wave modeling using staggered-grid scheme for the model derived from ray-trace inversion using sparse wide-angle seismic data acquired along Sinor-Valod profile in the Deccan Volcanic Province of India. The full-wave synthetic seismic data generated have been processed and imaged using conventional seismic data processing technique with Kirchhoff pre-stack time and depth migrations. The seismic image obtained correlates with all the structural features of the model obtained through ray-trace inversion of wide-angle seismic data, validating the effectiveness of robust elastic finite-difference full-wave modeling approach for imaging below thick basalts. Using the full-wave modeling also allows us to decipher small-scale heterogeneities imposed in the model as a measure of the rugose basalt interfaces, which could not be dealt with ray-trace inversion. Furthermore, we were able to accurately image thin low-velocity hydrocarbon-bearing Mesozoic sediments sandwiched between and hidden below two thick sequences of high-velocity basalt layers lying above the basement.

Sparse-View Ultrasound Diffraction Tomography Using Compressed Sensing with Nonuniform FFT

PubMed Central

2014-01-01

Accurate reconstruction of the object from sparse-view sampling data is an appealing issue for ultrasound diffraction tomography (UDT). In this paper, we present a reconstruction method based on compressed sensing framework for sparse-view UDT. Due to the piecewise uniform characteristics of anatomy structures, the total variation is introduced into the cost function to find a more faithful sparse representation of the object. The inverse problem of UDT is iteratively resolved by conjugate gradient with nonuniform fast Fourier transform. Simulation results show the effectiveness of the proposed method that the main characteristics of the object can be properly presented with only 16 views. Compared to interpolation and multiband method, the proposed method can provide higher resolution and lower artifacts with the same view number. The robustness to noise and the computation complexity are also discussed. PMID:24868241

How to deal with the high condition number of the noise covariance matrix of gravity field functionals synthesised from a satellite-only global gravity field model?

NASA Astrophysics Data System (ADS)

Klees, R.; Slobbe, D. C.; Farahani, H. H.

2018-03-01

The posed question arises for instance in regional gravity field modelling using weighted least-squares techniques if the gravity field functionals are synthesised from the spherical harmonic coefficients of a satellite-only global gravity model (GGM), and are used as one of the noisy datasets. The associated noise covariance matrix, appeared to be extremely ill-conditioned with a singular value spectrum that decayed gradually to zero without any noticeable gap. We analysed three methods to deal with the ill-conditioned noise covariance matrix: Tihonov regularisation of the noise covariance matrix in combination with the standard formula for the weighted least-squares estimator, a formula of the weighted least-squares estimator, which does not involve the inverse noise covariance matrix, and an estimator based on Rao's unified theory of least-squares. Our analysis was based on a numerical experiment involving a set of height anomalies synthesised from the GGM GOCO05s, which is provided with a full noise covariance matrix. We showed that the three estimators perform similar, provided that the two regularisation parameters each method knows were chosen properly. As standard regularisation parameter choice rules do not apply here, we suggested a new parameter choice rule, and demonstrated its performance. Using this rule, we found that the differences between the three least-squares estimates were within noise. For the standard formulation of the weighted least-squares estimator with regularised noise covariance matrix, this required an exceptionally strong regularisation, much larger than one expected from the condition number of the noise covariance matrix. The preferred method is the inversion-free formulation of the weighted least-squares estimator, because of its simplicity with respect to the choice of the two regularisation parameters.

A finite element-boundary integral formulation for scattering by three-dimensional cavity-backed apertures

NASA Technical Reports Server (NTRS)

Jin, Jian-Ming; Volakis, John L.

1990-01-01

A numerical technique is proposed for the electromagnetic characterization of the scattering by a three-dimensional cavity-backed aperture in an infinite ground plane. The technique combines the finite element and boundary integral methods to formulate a system of equations for the solution of the aperture fields and those inside the cavity. Specifically, the finite element method is employed to formulate the fields in the cavity region and the boundary integral approach is used in conjunction with the equivalence principle to represent the fields above the ground plane. Unlike traditional approaches, the proposed technique does not require knowledge of the cavity's Green's function and is, therefore, applicable to arbitrary shape depressions and material fillings. Furthermore, the proposed formulation leads to a system having a partly full and partly sparse as well as symmetric and banded matrix which can be solved efficiently using special algorithms.

Task Parallel Incomplete Cholesky Factorization using 2D Partitioned-Block Layout

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Kyungjoo; Rajamanickam, Sivasankaran; Stelle, George Widgery

We introduce a task-parallel algorithm for sparse incomplete Cholesky factorization that utilizes a 2D sparse partitioned-block layout of a matrix. Our factorization algorithm follows the idea of algorithms-by-blocks by using the block layout. The algorithm-byblocks approach induces a task graph for the factorization. These tasks are inter-related to each other through their data dependences in the factorization algorithm. To process the tasks on various manycore architectures in a portable manner, we also present a portable tasking API that incorporates different tasking backends and device-specific features using an open-source framework for manycore platforms i.e., Kokkos. A performance evaluation is presented onmore » both Intel Sandybridge and Xeon Phi platforms for matrices from the University of Florida sparse matrix collection to illustrate merits of the proposed task-based factorization. Experimental results demonstrate that our task-parallel implementation delivers about 26.6x speedup (geometric mean) over single-threaded incomplete Choleskyby- blocks and 19.2x speedup over serial Cholesky performance which does not carry tasking overhead using 56 threads on the Intel Xeon Phi processor for sparse matrices arising from various application problems.« less

An efficient sparse matrix multiplication scheme for the CYBER 205 computer

NASA Technical Reports Server (NTRS)

Lambiotte, Jules J., Jr.

1988-01-01

This paper describes the development of an efficient algorithm for computing the product of a matrix and vector on a CYBER 205 vector computer. The desire to provide software which allows the user to choose between the often conflicting goals of minimizing central processing unit (CPU) time or storage requirements has led to a diagonal-based algorithm in which one of four types of storage is selected for each diagonal. The candidate storage types employed were chosen to be efficient on the CYBER 205 for diagonals which have nonzero structure which is dense, moderately sparse, very sparse and short, or very sparse and long; however, for many densities, no diagonal type is most efficient with respect to both resource requirements, and a trade-off must be made. For each diagonal, an initialization subroutine estimates the CPU time and storage required for each storage type based on results from previously performed numerical experimentation. These requirements are adjusted by weights provided by the user which reflect the relative importance the user places on the two resources. The adjusted resource requirements are then compared to select the most efficient storage and computational scheme.

Discriminative Dictionary Learning With Two-Level Low Rank and Group Sparse Decomposition for Image Classification.

PubMed

Wen, Zaidao; Hou, Zaidao; Jiao, Licheng

2017-11-01

Discriminative dictionary learning (DDL) framework has been widely used in image classification which aims to learn some class-specific feature vectors as well as a representative dictionary according to a set of labeled training samples. However, interclass similarities and intraclass variances among input samples and learned features will generally weaken the representability of dictionary and the discrimination of feature vectors so as to degrade the classification performance. Therefore, how to explicitly represent them becomes an important issue. In this paper, we present a novel DDL framework with two-level low rank and group sparse decomposition model. In the first level, we learn a class-shared and several class-specific dictionaries, where a low rank and a group sparse regularization are, respectively, imposed on the corresponding feature matrices. In the second level, the class-specific feature matrix will be further decomposed into a low rank and a sparse matrix so that intraclass variances can be separated to concentrate the corresponding feature vectors. Extensive experimental results demonstrate the effectiveness of our model. Compared with the other state-of-the-arts on several popular image databases, our model can achieve a competitive or better performance in terms of the classification accuracy.

Characterization, Microbial Community Structure, and Pathogen Occurrence in Urban Faucet Biofilms in South China

PubMed Central

Lin, Huirong; Zhang, Shuting; Gong, Song; Zhang, Shenghua; Yu, Xin

2015-01-01

The composition and microbial community structure of the drinking water system biofilms were investigated using microstructure analysis and 454 pyrosequencing technique in Xiamen city, southeast of China. SEM (scanning electron microscope) results showed different features of biofilm morphology in different fields of PVC pipe. Extracellular matrix material and sparse populations of bacteria (mainly rod-shaped and coccoid) were observed. CLSM (confocal laser scanning microscope) revealed different distributions of attached cells, extracellular proteins, α-polysaccharides, and β-polysaccharides. The biofilms had complex bacterial compositions. Differences in bacteria diversity and composition from different tap materials and ages were observed. Proteobacteria was the common and predominant group in all biofilms samples. Some potential pathogens (Legionellales, Enterobacteriales, Chromatiales, and Pseudomonadales) and corrosive microorganisms were also found in the biofilms. This study provides the information of characterization and visualization of the drinking water biofilms matrix, as well as the microbial community structure and opportunistic pathogens occurrence. PMID:26273617

A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rouet, François-Henry; Li, Xiaoye S.; Ghysels, Pieter

In this paper, we present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use Hierarchically Semi-Separable (HSS) representations. Such matrices appear in many applications, for example, finite-element methods, boundary element methods, and so on. Exploiting this structure allows for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. The compression algorithm that we use, that computes the HSS form of an input dense matrix, reliesmore » on randomized sampling with a novel adaptive sampling mechanism. We discuss the parallelization of this algorithm and also present the parallelization of structured matrix-vector product, structured factorization, and solution routines. The efficiency of the approach is demonstrated on large problems from different academic and industrial applications, on up to 8,000 cores. Finally, this work is part of a more global effort, the STRUctured Matrices PACKage (STRUMPACK) software package for computations with sparse and dense structured matrices. Hence, although useful on their own right, the routines also represent a step in the direction of a distributed-memory sparse solver.« less

A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization

DOE PAGES

Rouet, François-Henry; Li, Xiaoye S.; Ghysels, Pieter; ...

2016-06-30

In this paper, we present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use Hierarchically Semi-Separable (HSS) representations. Such matrices appear in many applications, for example, finite-element methods, boundary element methods, and so on. Exploiting this structure allows for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. The compression algorithm that we use, that computes the HSS form of an input dense matrix, reliesmore » on randomized sampling with a novel adaptive sampling mechanism. We discuss the parallelization of this algorithm and also present the parallelization of structured matrix-vector product, structured factorization, and solution routines. The efficiency of the approach is demonstrated on large problems from different academic and industrial applications, on up to 8,000 cores. Finally, this work is part of a more global effort, the STRUctured Matrices PACKage (STRUMPACK) software package for computations with sparse and dense structured matrices. Hence, although useful on their own right, the routines also represent a step in the direction of a distributed-memory sparse solver.« less

General Matrix Inversion for the Calibration of Electric Field Sensor Arrays on Aircraft Platforms

NASA Technical Reports Server (NTRS)

Mach, D. M.; Koshak, W. J.

2006-01-01

We have developed a matrix calibration procedure that uniquely relates the electric fields measured at the aircraft with the external vector electric field and net aircraft charge. Our calibration method is being used with all of our aircraft/electric field sensing combinations and can be generalized to any reasonable combination of electric field measurements and aircraft. We determine a calibration matrix that represents the individual instrument responses to the external electric field. The aircraft geometry and configuration of field mills (FMs) uniquely define the matrix. The matrix can then be inverted to determine the external electric field and net aircraft charge from the FM outputs. A distinct advantage of the method is that if one or more FMs need to be eliminated or de-emphasized (for example, due to a malfunction), it is a simple matter to reinvert the matrix without the malfunctioning FMs. To demonstrate our calibration technique, we present data from several of our aircraft programs (ER-2, DC-8, Altus, Citation).

2D Inviscid and Viscous Inverse Design Using Continuous Adjoint and Lax-Wendroff Formulation

NASA Astrophysics Data System (ADS)

Proctor, Camron Lisle

The continuous adjoint (CA) technique for optimization and/or inverse-design of aerodynamic components has seen nearly 30 years of documented success in academia. The benefits of using CA versus a direct sensitivity analysis are shown repeatedly in the literature. However, the use of CA in industry is relatively unheard-of. The sparseness of industry contributions to the field may be attributed to the tediousness of the derivation and/or to the difficulties in implementation due to the lack of well-documented adjoint numerical methods. The focus of this work has been to thoroughly document the techniques required to build a two-dimensional CA inverse-design tool. To this end, this work begins with a short background on computational fluid dynamics (CFD) and the use of optimization tools in conjunction with CFD tools to solve aerodynamic optimization problems. A thorough derivation of the continuous adjoint equations and the accompanying gradient calculations for inviscid and viscous constraining equations follows the introduction. Next, the numerical techniques used for solving the partial differential equations (PDEs) governing the flow equations and the adjoint equations are described. Numerical techniques for the supplementary equations are discussed briefly. Subsequently, a verification of the efficacy of the inverse design tool, for the inviscid adjoint equations as well as possible numerical implementation pitfalls are discussed. The NACA0012 airfoil is used as an initial airfoil and surface pressure distribution and the NACA16009 is used as the desired pressure and vice versa. Using a Savitsky-Golay gradient filter, convergence (defined as a cost function<1E-5) is reached in approximately 220 design iteration using 121 design variables. The inverse-design using inviscid adjoint equations results are followed by the discussion of the viscous inverse design results and techniques used to further the convergence of the optimizer. The relationship between limiting step-size and convergence in a line-search optimization is shown to slightly decrease the final cost function at significant computational cost. A gradient damping technique is presented and shown to increase the convergence rate for the optimization in viscous problems, at a negligible increase in computational cost, but is insufficient to converge the solution. Systematically including adjacent surface vertices in the perturbation of a design variable, also a surface vertex, is shown to affect the convergence capability of the viscous optimizer. Finally, a comparison of using inviscid adjoint equations, as opposed to viscous adjoint equations, on viscous flow is presented, and the inviscid adjoint paired with viscous flow is found to reduce the cost function further than the viscous adjoint for the presented problem.

Optimal parallel solution of sparse triangular systems

NASA Technical Reports Server (NTRS)

Alvarado, Fernando L.; Schreiber, Robert

1990-01-01

A method for the parallel solution of triangular sets of equations is described that is appropriate when there are many right-handed sides. By preprocessing, the method can reduce the number of parallel steps required to solve Lx = b compared to parallel forward or backsolve. Applications are to iterative solvers with triangular preconditioners, to structural analysis, or to power systems applications, where there may be many right-handed sides (not all available a priori). The inverse of L is represented as a product of sparse triangular factors. The problem is to find a factored representation of this inverse of L with the smallest number of factors (or partitions), subject to the requirement that no new nonzero elements be created in the formation of these inverse factors. A method from an earlier reference is shown to solve this problem. This method is improved upon by constructing a permutation of the rows and columns of L that preserves triangularity and allow for the best possible such partition. A number of practical examples and algorithmic details are presented. The parallelism attainable is illustrated by means of elimination trees and clique trees.

A Fine-Grained Pipelined Implementation for Large-Scale Matrix Inversion on FPGA

NASA Astrophysics Data System (ADS)

Zhou, Jie; Dou, Yong; Zhao, Jianxun; Xia, Fei; Lei, Yuanwu; Tang, Yuxing

Large-scale matrix inversion play an important role in many applications. However to the best of our knowledge, there is no FPGA-based implementation. In this paper, we explore the possibility of accelerating large-scale matrix inversion on FPGA. To exploit the computational potential of FPGA, we introduce a fine-grained parallel algorithm for matrix inversion. A scalable linear array processing elements (PEs), which is the core component of the FPGA accelerator, is proposed to implement this algorithm. A total of 12 PEs can be integrated into an Altera StratixII EP2S130F1020C5 FPGA on our self-designed board. Experimental results show that a factor of 2.6 speedup and the maximum power-performance of 41 can be achieved compare to Pentium Dual CPU with double SSE threads.

Easy way to determine quantitative spatial resolution distribution for a general inverse problem

NASA Astrophysics Data System (ADS)

An, M.; Feng, M.

2013-12-01

The spatial resolution computation of a solution was nontrivial and more difficult than solving an inverse problem. Most geophysical studies, except for tomographic studies, almost uniformly neglect the calculation of a practical spatial resolution. In seismic tomography studies, a qualitative resolution length can be indicatively given via visual inspection of the restoration of a synthetic structure (e.g., checkerboard tests). An effective strategy for obtaining quantitative resolution length is to calculate Backus-Gilbert resolution kernels (also referred to as a resolution matrix) by matrix operation. However, not all resolution matrices can provide resolution length information, and the computation of resolution matrix is often a difficult problem for very large inverse problems. A new class of resolution matrices, called the statistical resolution matrices (An, 2012, GJI), can be directly determined via a simple one-parameter nonlinear inversion performed based on limited pairs of random synthetic models and their inverse solutions. The total procedure were restricted to forward/inversion processes used in the real inverse problem and were independent of the degree of inverse skill used in the solution inversion. Spatial resolution lengths can be directly given during the inversion. Tests on 1D/2D/3D model inversion demonstrated that this simple method can be at least valid for a general linear inverse problem.

Joint 3D Inversion of ZTEM Airborne and Ground MT Data with Application to Geothermal Exploration

NASA Astrophysics Data System (ADS)

Wannamaker, P. E.; Maris, V.; Kordy, M. A.

2017-12-01

ZTEM is an airborne electromagnetic (EM) geophysical technique developed by Geotech Inc® where naturally propagated EM fields originating with regional and global lightning discharges (sferics) are measured as a means of inferring subsurface electrical resistivity structure. A helicopter-borne coil platform (bird) measuring the vertical component of magnetic (H) field variations along a flown profile is referenced to a pair of horizontal coils at a fixed location on the ground in order to estimate a tensor H-field transfer function. The ZTEM method is distinct from the traditional magnetotelluric (MT) method in that the electric (E) fields are not considered because of the technological challenge of measuring E-fields in the dielectric air medium. This can lend some non-uniqueness to ZTEM interpretation because a range of conductivity structures in the earth depending upon an assumed background earth resistivity model can fit ZTEM data to within tolerance. MT data do not suffer this particular problem, but they are cumbersome to acquire in their common need for land-based transport often in near-roadless areas and for laying out and digging the electrodes and H coils. The complementary nature of ZTEM and MT logistics and resolution has motivated development of schemes to acquire appropriate amounts of each data type in a single survey and to produce an earth image through joint inversion. In particular, consideration is given to surveys where only sparse MT soundings are needed to drastically reduce the non-uniqueness associated with background uncertainty while straining logistics minimally. Synthetic and field data are analysed using 2D and 3D finite element platforms developed for this purpose. Results to date suggest that indeed dense ZTEM surveys can provide detailed heterogeneous model images with large-scale averages constrained by a modest number of MT soundings. Further research is needed in determining the allowable degree of MT sparseness and the relative weighting of the two data sets in joint inversion.

Sparse and incomplete factorial matrices to screen membrane protein 2D crystallization

PubMed Central

Lasala, R.; Coudray, N.; Abdine, A.; Zhang, Z.; Lopez-Redondo, M.; Kirshenbaum, R.; Alexopoulos, J.; Zolnai, Z.; Stokes, D.L.; Ubarretxena-Belandia, I.

2014-01-01

Electron crystallography is well suited for studying the structure of membrane proteins in their native lipid bilayer environment. This technique relies on electron cryomicroscopy of two-dimensional (2D) crystals, grown generally by reconstitution of purified membrane proteins into proteoliposomes under conditions favoring the formation of well-ordered lattices. Growing these crystals presents one of the major hurdles in the application of this technique. To identify conditions favoring crystallization a wide range of factors that can lead to a vast matrix of possible reagent combinations must be screened. However, in 2D crystallization these factors have traditionally been surveyed in a relatively limited fashion. To address this problem we carried out a detailed analysis of published 2D crystallization conditions for 12 β-barrel and 138 α-helical membrane proteins. From this analysis we identified the most successful conditions and applied them in the design of new sparse and incomplete factorial matrices to screen membrane protein 2D crystallization. Using these matrices we have run 19 crystallization screens for 16 different membrane proteins totaling over 1,300 individual crystallization conditions. Six membrane proteins have yielded diffracting 2D crystals suitable for structure determination, indicating that these new matrices show promise to accelerate the success rate of membrane protein 2D crystallization. PMID:25478971

Implicit solvers for unstructured meshes

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, Dimitri J.

1991-01-01

Implicit methods for unstructured mesh computations are developed and tested. The approximate system which arises from the Newton-linearization of the nonlinear evolution operator is solved by using the preconditioned generalized minimum residual technique. These different preconditioners are investigated: the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over-relaxation (SSOR). The preconditioners have been optimized to have good vectorization properties. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also investigated. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Eigensolver for a Sparse, Large Hermitian Matrix

NASA Technical Reports Server (NTRS)

Tisdale, E. Robert; Oyafuso, Fabiano; Klimeck, Gerhard; Brown, R. Chris

2003-01-01

A parallel-processing computer program finds a few eigenvalues in a sparse Hermitian matrix that contains as many as 100 million diagonal elements. This program finds the eigenvalues faster, using less memory, than do other, comparable eigensolver programs. This program implements a Lanczos algorithm in the American National Standards Institute/ International Organization for Standardization (ANSI/ISO) C computing language, using the Message Passing Interface (MPI) standard to complement an eigensolver in PARPACK. [PARPACK (Parallel Arnoldi Package) is an extension, to parallel-processing computer architectures, of ARPACK (Arnoldi Package), which is a collection of Fortran 77 subroutines that solve large-scale eigenvalue problems.] The eigensolver runs on Beowulf clusters of computers at the Jet Propulsion Laboratory (JPL).

Sparse distributed memory and related models

NASA Technical Reports Server (NTRS)

Kanerva, Pentti

1992-01-01

Described here is sparse distributed memory (SDM) as a neural-net associative memory. It is characterized by two weight matrices and by a large internal dimension - the number of hidden units is much larger than the number of input or output units. The first matrix, A, is fixed and possibly random, and the second matrix, C, is modifiable. The SDM is compared and contrasted to (1) computer memory, (2) correlation-matrix memory, (3) feet-forward artificial neural network, (4) cortex of the cerebellum, (5) Marr and Albus models of the cerebellum, and (6) Albus' cerebellar model arithmetic computer (CMAC). Several variations of the basic SDM design are discussed: the selected-coordinate and hyperplane designs of Jaeckel, the pseudorandom associative neural memory of Hassoun, and SDM with real-valued input variables by Prager and Fallside. SDM research conducted mainly at the Research Institute for Advanced Computer Science (RIACS) in 1986-1991 is highlighted.

Integration of Sparse Multi-modality Representation and Geometrical Constraint for Isointense Infant Brain Segmentation

PubMed Central

Wang, Li; Shi, Feng; Li, Gang; Lin, Weili; Gilmore, John H.; Shen, Dinggang

2014-01-01

Segmentation of infant brain MR images is challenging due to insufficient image quality, severe partial volume effect, and ongoing maturation and myelination process. During the first year of life, the signal contrast between white matter (WM) and gray matter (GM) in MR images undergoes inverse changes. In particular, the inversion of WM/GM signal contrast appears around 6–8 months of age, where brain tissues appear isointense and hence exhibit extremely low tissue contrast, posing significant challenges for automated segmentation. In this paper, we propose a novel segmentation method to address the above-mentioned challenge based on the sparse representation of the complementary tissue distribution information from T1, T2 and diffusion-weighted images. Specifically, we first derive an initial segmentation from a library of aligned multi-modality images with ground-truth segmentations by using sparse representation in a patch-based fashion. The segmentation is further refined by the integration of the geometrical constraint information. The proposed method was evaluated on 22 6-month-old training subjects using leave-one-out cross-validation, as well as 10 additional infant testing subjects, showing superior results in comparison to other state-of-the-art methods. PMID:24505729

Integration of sparse multi-modality representation and geometrical constraint for isointense infant brain segmentation.

PubMed

Wang, Li; Shi, Feng; Li, Gang; Lin, Weili; Gilmore, John H; Shen, Dinggang

2013-01-01

Segmentation of infant brain MR images is challenging due to insufficient image quality, severe partial volume effect, and ongoing maturation and myelination process. During the first year of life, the signal contrast between white matter (WM) and gray matter (GM) in MR images undergoes inverse changes. In particular, the inversion of WM/GM signal contrast appears around 6-8 months of age, where brain tissues appear isointense and hence exhibit extremely low tissue contrast, posing significant challenges for automated segmentation. In this paper, we propose a novel segmentation method to address the above-mentioned challenge based on the sparse representation of the complementary tissue distribution information from T1, T2 and diffusion-weighted images. Specifically, we first derive an initial segmentation from a library of aligned multi-modality images with ground-truth segmentations by using sparse representation in a patch-based fashion. The segmentation is further refined by the integration of the geometrical constraint information. The proposed method was evaluated on 22 6-month-old training subjects using leave-one-out cross-validation, as well as 10 additional infant testing subjects, showing superior results in comparison to other state-of-the-art methods.

Multi-subject hierarchical inverse covariance modelling improves estimation of functional brain networks.

PubMed

Colclough, Giles L; Woolrich, Mark W; Harrison, Samuel J; Rojas López, Pedro A; Valdes-Sosa, Pedro A; Smith, Stephen M

2018-05-07

A Bayesian model for sparse, hierarchical, inver-covariance estimation is presented, and applied to multi-subject functional connectivity estimation in the human brain. It enables simultaneous inference of the strength of connectivity between brain regions at both subject and population level, and is applicable to fMRI, MEG and EEG data. Two versions of the model can encourage sparse connectivity, either using continuous priors to suppress irrelevant connections, or using an explicit description of the network structure to estimate the connection probability between each pair of regions. A large evaluation of this model, and thirteen methods that represent the state of the art of inverse covariance modelling, is conducted using both simulated and resting-state functional imaging datasets. Our novel Bayesian approach has similar performance to the best extant alternative, Ng et al.'s Sparse Group Gaussian Graphical Model algorithm, which also is based on a hierarchical structure. Using data from the Human Connectome Project, we show that these hierarchical models are able to reduce the measurement error in MEG beta-band functional networks by 10%, producing concomitant increases in estimates of the genetic influence on functional connectivity. Copyright © 2018. Published by Elsevier Inc.

Efficient Implementations of the Quadrature-Free Discontinuous Galerkin Method

NASA Technical Reports Server (NTRS)

Lockard, David P.; Atkins, Harold L.

1999-01-01

The efficiency of the quadrature-free form of the dis- continuous Galerkin method in two dimensions, and briefly in three dimensions, is examined. Most of the work for constant-coefficient, linear problems involves the volume and edge integrations, and the transformation of information from the volume to the edges. These operations can be viewed as matrix-vector multiplications. Many of the matrices are sparse as a result of symmetry, and blocking and specialized multiplication routines are used to account for the sparsity. By optimizing these operations, a 35% reduction in total CPU time is achieved. For nonlinear problems, the calculation of the flux becomes dominant because of the cost associated with polynomial products and inversion. This component of the work can be reduced by up to 75% when the products are approximated by truncating terms. Because the cost is high for nonlinear problems on general elements, it is suggested that simplified physics and the most efficient element types be used over most of the domain.

Blind compressed sensing image reconstruction based on alternating direction method

NASA Astrophysics Data System (ADS)

Liu, Qinan; Guo, Shuxu

2018-04-01

In order to solve the problem of how to reconstruct the original image under the condition of unknown sparse basis, this paper proposes an image reconstruction method based on blind compressed sensing model. In this model, the image signal is regarded as the product of a sparse coefficient matrix and a dictionary matrix. Based on the existing blind compressed sensing theory, the optimal solution is solved by the alternative minimization method. The proposed method solves the problem that the sparse basis in compressed sensing is difficult to represent, which restrains the noise and improves the quality of reconstructed image. This method ensures that the blind compressed sensing theory has a unique solution and can recover the reconstructed original image signal from a complex environment with a stronger self-adaptability. The experimental results show that the image reconstruction algorithm based on blind compressed sensing proposed in this paper can recover high quality image signals under the condition of under-sampling.

The incomplete inverse and its applications to the linear least squares problem

NASA Technical Reports Server (NTRS)

Morduch, G. E.

1977-01-01

A modified matrix product is explained, and it is shown that this product defiles a group whose inverse is called the incomplete inverse. It was proven that the incomplete inverse of an augmented normal matrix includes all the quantities associated with the least squares solution. An answer is provided to the problem that occurs when the data residuals are too large and when insufficient data to justify augmenting the model are available.

Bayesian Orbit Computation Tools for Objects on Geocentric Orbits

NASA Astrophysics Data System (ADS)

Virtanen, J.; Granvik, M.; Muinonen, K.; Oszkiewicz, D.

2013-08-01

We consider the space-debris orbital inversion problem via the concept of Bayesian inference. The methodology has been put forward for the orbital analysis of solar system small bodies in early 1990's [7] and results in a full solution of the statistical inverse problem given in terms of a posteriori probability density function (PDF) for the orbital parameters. We demonstrate the applicability of our statistical orbital analysis software to Earth orbiting objects, both using well-established Monte Carlo (MC) techniques (for a review, see e.g. [13] as well as recently developed Markov-chain MC (MCMC) techniques (e.g., [9]). In particular, we exploit the novel virtual observation MCMC method [8], which is based on the characterization of the phase-space volume of orbital solutions before the actual MCMC sampling. Our statistical methods and the resulting PDFs immediately enable probabilistic impact predictions to be carried out. Furthermore, this can be readily done also for very sparse data sets and data sets of poor quality - providing that some a priori information on the observational uncertainty is available. For asteroids, impact probabilities with the Earth from the discovery night onwards have been provided, e.g., by [11] and [10], the latter study includes the sampling of the observational-error standard deviation as a random variable.

Mode detection in turbofan inlets from near field sensor arrays.

PubMed

Castres, Fabrice O; Joseph, Phillip F

2007-02-01

Knowledge of the modal content of the sound field radiated from a turbofan inlet is important for source characterization and for helping to determine noise generation mechanisms in the engine. An inverse technique for determining the mode amplitudes at the duct outlet is proposed using pressure measurements made in the near field. The radiated sound pressure from a duct is modeled by directivity patterns of cut-on modes in the near field using a model based on the Kirchhoff approximation for flanged ducts with no flow. The resulting system of equations is ill posed and it is shown that the presence of modes with eigenvalues close to a cutoff frequency results in a poorly conditioned directivity matrix. An analysis of the conditioning of this directivity matrix is carried out to assess the inversion robustness and accuracy. A physical interpretation of the singular value decomposition is given and allows us to understand the issues of ill conditioning as well as the detection performance of the radiated sound field by a given sensor array.

Removal of Stationary Sinusoidal Noise from Random Vibration Signals.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, Brian; Cap, Jerome S.

In random vibration environments, sinusoidal line noise may appear in the vibration signal and can affect analysis of the resulting data. We studied two methods which remove stationary sine tones from random noise: a matrix inversion algorithm and a chirp-z transform algorithm. In addition, we developed new methods to determine the frequency of the tonal noise. The results show that both of the removal methods can eliminate sine tones in prefabricated random vibration data when the sine-to-random ratio is at least 0.25. For smaller ratios down to 0.02 only the matrix inversion technique can remove the tones, but the metricsmore » to evaluate its effectiveness also degrade. We also found that using fast Fourier transforms best identified the tonal noise, and determined that band-pass-filtering the signals prior to the process improved sine removal. When applied to actual vibration test data, the methods were not as effective at removing harmonic tones, which we believe to be a result of mixed-phase sinusoidal noise.« less

Factorization in large-scale many-body calculations

DOE PAGES

Johnson, Calvin W.; Ormand, W. Erich; Krastev, Plamen G.

2013-08-07

One approach for solving interacting many-fermion systems is the configuration-interaction method, also sometimes called the interacting shell model, where one finds eigenvalues of the Hamiltonian in a many-body basis of Slater determinants (antisymmetrized products of single-particle wavefunctions). The resulting Hamiltonian matrix is typically very sparse, but for large systems the nonzero matrix elements can nonetheless require terabytes or more of storage. An alternate algorithm, applicable to a broad class of systems with symmetry, in our case rotational invariance, is to exactly factorize both the basis and the interaction using additive/multiplicative quantum numbers; such an algorithm recreates the many-body matrix elementsmore » on the fly and can reduce the storage requirements by an order of magnitude or more. Here, we discuss factorization in general and introduce a novel, generalized factorization method, essentially a ‘double-factorization’ which speeds up basis generation and set-up of required arrays. Although we emphasize techniques, we also place factorization in the context of a specific (unpublished) configuration-interaction code, BIGSTICK, which runs both on serial and parallel machines, and discuss the savings in memory due to factorization.« less

Transurethral Ultrasound Diffraction Tomography

DTIC Science & Technology

2007-03-01

the covariance matrix was derived. The covariance reduced to that of the X- ray CT under the assumptions of linear operator and real data.[5] The...the covariance matrix in the linear x- ray computed tomography is a special case of the inverse scattering matrix derived in this paper. The matrix was...is derived in Sec. IV, and its relation to that of the linear x- ray computed tomography appears in Sec. V. In Sec. VI, the inverse scattering

M-matrices with prescribed elementary divisors

NASA Astrophysics Data System (ADS)

Soto, Ricardo L.; Díaz, Roberto C.; Salas, Mario; Rojo, Oscar

2017-09-01

A real matrix A is said to be an M-matrix if it is of the form A=α I-B, where B is a nonnegative matrix with Perron eigenvalue ρ (B), and α ≥slant ρ (B) . This paper provides sufficient conditions for the existence and construction of an M-matrix A with prescribed elementary divisors, which are the characteristic polynomials of the Jordan blocks of the Jordan canonical form of A. This inverse problem on M-matrices has not been treated until now. We solve the inverse elementary divisors problem for diagonalizable M-matrices and the symmetric generalized doubly stochastic inverse M-matrix problem for lists of real numbers and for lists of complex numbers of the form Λ =\\{λ 1, a+/- bi, \\ldots, a+/- bi\\} . The constructive nature of our results allows for the computation of a solution matrix. The paper also discusses an application of M-matrices to a capacity problem in wireless communications.

Communication requirements of sparse Cholesky factorization with nested dissection ordering

NASA Technical Reports Server (NTRS)

Naik, Vijay K.; Patrick, Merrell L.

1989-01-01

Load distribution schemes for minimizing the communication requirements of the Cholesky factorization of dense and sparse, symmetric, positive definite matrices on multiprocessor systems are presented. The total data traffic in factoring an n x n sparse symmetric positive definite matrix representing an n-vertex regular two-dimensional grid graph using n exp alpha, alpha not greater than 1, processors are shown to be O(n exp 1 + alpha/2). It is O(n), when n exp alpha, alpha not smaller than 1, processors are used. Under the conditions of uniform load distribution, these results are shown to be asymptotically optimal.

GPU-accelerated element-free reverse-time migration with Gauss points partition

NASA Astrophysics Data System (ADS)

Zhou, Zhen; Jia, Xiaofeng; Qiang, Xiaodong

2018-06-01

An element-free method (EFM) has been demonstrated successfully in elasticity, heat conduction and fatigue crack growth problems. We present the theory of EFM and its numerical applications in seismic modelling and reverse time migration (RTM). Compared with the finite difference method and the finite element method, the EFM has unique advantages: (1) independence of grids in computation and (2) lower expense and more flexibility (because only the information of the nodes and the boundary of the concerned area is required). However, in EFM, due to improper computation and storage of some large sparse matrices, such as the mass matrix and the stiffness matrix, the method is difficult to apply to seismic modelling and RTM for a large velocity model. To solve the problem of storage and computation efficiency, we propose a concept of Gauss points partition and utilise the graphics processing unit to improve the computational efficiency. We employ the compressed sparse row format to compress the intermediate large sparse matrices and attempt to simplify the operations by solving the linear equations with CULA solver. To improve the computation efficiency further, we introduce the concept of the lumped mass matrix. Numerical experiments indicate that the proposed method is accurate and more efficient than the regular EFM.

A regional high-resolution carbon flux inversion of North America for 2004

NASA Astrophysics Data System (ADS)

Schuh, A. E.; Denning, A. S.; Corbin, K. D.; Baker, I. T.; Uliasz, M.; Parazoo, N.; Andrews, A. E.; Worthy, D. E. J.

2010-05-01

Resolving the discrepancies between NEE estimates based upon (1) ground studies and (2) atmospheric inversion results, demands increasingly sophisticated techniques. In this paper we present a high-resolution inversion based upon a regional meteorology model (RAMS) and an underlying biosphere (SiB3) model, both running on an identical 40 km grid over most of North America. Current operational systems like CarbonTracker as well as many previous global inversions including the Transcom suite of inversions have utilized inversion regions formed by collapsing biome-similar grid cells into larger aggregated regions. An extreme example of this might be where corrections to NEE imposed on forested regions on the east coast of the United States might be the same as that imposed on forests on the west coast of the United States while, in reality, there likely exist subtle differences in the two areas, both natural and anthropogenic. Our current inversion framework utilizes a combination of previously employed inversion techniques while allowing carbon flux corrections to be biome independent. Temporally and spatially high-resolution results utilizing biome-independent corrections provide insight into carbon dynamics in North America. In particular, we analyze hourly CO2 mixing ratio data from a sparse network of eight towers in North America for 2004. A prior estimate of carbon fluxes due to Gross Primary Productivity (GPP) and Ecosystem Respiration (ER) is constructed from the SiB3 biosphere model on a 40 km grid. A combination of transport from the RAMS and the Parameterized Chemical Transport Model (PCTM) models is used to forge a connection between upwind biosphere fluxes and downwind observed CO2 mixing ratio data. A Kalman filter procedure is used to estimate weekly corrections to biosphere fluxes based upon observed CO2. RMSE-weighted annual NEE estimates, over an ensemble of potential inversion parameter sets, show a mean estimate 0.57 Pg/yr sink in North America. We perform the inversion with two independently derived boundary inflow conditions and calculate jackknife-based statistics to test the robustness of the model results. We then compare final results to estimates obtained from the CarbonTracker inversion system and at the Southern Great Plains flux site. Results are promising, showing the ability to correct carbon fluxes from the biosphere models over annual and seasonal time scales, as well as over the different GPP and ER components. Additionally, the correlation of an estimated sink of carbon in the South Central United States with regional anomalously high precipitation in an area of managed agricultural and forest lands provides interesting hypotheses for future work.

Development and characterization of polyethersulfone/TiO2 mixed matrix membranes for CO2/CH4 separation

NASA Astrophysics Data System (ADS)

Galaleldin, S.; Mannan, H. A.; Mukhtar, H.

2017-12-01

In this study, mixed matrix membranes comprised of polyethersulfone as the bulk polymer phase and titanium dioxide (TiO2) nanoparticles as the inorganic discontinuous phase were prepared for CO2/CH4 separation. Membranes were synthesized at filler loading of 0, 5, 10 and 15 wt % via dry phase inversion method. Morphology, chemical bonding and thermal characteristics of membranes were scrutinized utilizing different techniques, namely: Field Emission Scanning Electron Microscopy (FESEM), Fourier Transform InfraRed (FTIR) spectra and Thermogravimetric analysis (TGA) respectively. Membranes gas separation performance was evaluated for CO2 and CH4 gases at 4 bar feed pressure. The highest separation performance was achieved by mixed matrix membrane (MMM) at 5 % loading of TiO2.

An overview of NSPCG: A nonsymmetric preconditioned conjugate gradient package

NASA Astrophysics Data System (ADS)

Oppe, Thomas C.; Joubert, Wayne D.; Kincaid, David R.

1989-05-01

The most recent research-oriented software package developed as part of the ITPACK Project is called "NSPCG" since it contains many nonsymmetric preconditioned conjugate gradient procedures. It is designed to solve large sparse systems of linear algebraic equations by a variety of different iterative methods. One of the main purposes for the development of the package is to provide a common modular structure for research on iterative methods for nonsymmetric matrices. Another purpose for the development of the package is to investigate the suitability of several iterative methods for vector computers. Since the vectorizability of an iterative method depends greatly on the matrix structure, NSPCG allows great flexibility in the operator representation. The coefficient matrix can be passed in one of several different matrix data storage schemes. These sparse data formats allow matrices with a wide range of structures from highly structured ones such as those with all nonzeros along a relatively small number of diagonals to completely unstructured sparse matrices. Alternatively, the package allows the user to call the accelerators directly with user-supplied routines for performing certain matrix operations. In this case, one can use the data format from an application program and not be required to copy the matrix into one of the package formats. This is particularly advantageous when memory space is limited. Some of the basic preconditioners that are available are point methods such as Jacobi, Incomplete LU Decomposition and Symmetric Successive Overrelaxation as well as block and multicolor preconditioners. The user can select from a large collection of accelerators such as Conjugate Gradient (CG), Chebyshev (SI, for semi-iterative), Generalized Minimal Residual (GMRES), Biconjugate Gradient Squared (BCGS) and many others. The package is modular so that almost any accelerator can be used with almost any preconditioner.

Color normalization of histology slides using graph regularized sparse NMF

NASA Astrophysics Data System (ADS)

Sha, Lingdao; Schonfeld, Dan; Sethi, Amit

2017-03-01

Computer based automatic medical image processing and quantification are becoming popular in digital pathology. However, preparation of histology slides can vary widely due to differences in staining equipment, procedures and reagents, which can reduce the accuracy of algorithms that analyze their color and texture information. To re- duce the unwanted color variations, various supervised and unsupervised color normalization methods have been proposed. Compared with supervised color normalization methods, unsupervised color normalization methods have advantages of time and cost efficient and universal applicability. Most of the unsupervised color normaliza- tion methods for histology are based on stain separation. Based on the fact that stain concentration cannot be negative and different parts of the tissue absorb different stains, nonnegative matrix factorization (NMF), and particular its sparse version (SNMF), are good candidates for stain separation. However, most of the existing unsupervised color normalization method like PCA, ICA, NMF and SNMF fail to consider important information about sparse manifolds that its pixels occupy, which could potentially result in loss of texture information during color normalization. Manifold learning methods like Graph Laplacian have proven to be very effective in interpreting high-dimensional data. In this paper, we propose a novel unsupervised stain separation method called graph regularized sparse nonnegative matrix factorization (GSNMF). By considering the sparse prior of stain concentration together with manifold information from high-dimensional image data, our method shows better performance in stain color deconvolution than existing unsupervised color deconvolution methods, especially in keeping connected texture information. To utilized the texture information, we construct a nearest neighbor graph between pixels within a spatial area of an image based on their distances using heat kernal in lαβ space. The representation of a pixel in the stain density space is constrained to follow the feature distance of the pixel to pixels in the neighborhood graph. Utilizing color matrix transfer method with the stain concentrations found using our GSNMF method, the color normalization performance was also better than existing methods.

Guidance of Nonlinear Nonminimum-Phase Dynamic Systems

NASA Technical Reports Server (NTRS)

Devasia, Santosh

1996-01-01

The research work has advanced the inversion-based guidance theory for: systems with non-hyperbolic internal dynamics; systems with parameter jumps; and systems where a redesign of the output trajectory is desired. A technique to achieve output tracking for nonminimum phase linear systems with non-hyperbolic and near non-hyperbolic internal dynamics was developed. This approach integrated stable inversion techniques, that achieve exact-tracking, with approximation techniques, that modify the internal dynamics to achieve desirable performance. Such modification of the internal dynamics was used (a) to remove non-hyperbolicity which is an obstruction to applying stable inversion techniques and (b) to reduce large preactuation times needed to apply stable inversion for near non-hyperbolic cases. The method was applied to an example helicopter hover control problem with near non-hyperbolic internal dynamics for illustrating the trade-off between exact tracking and reduction of preactuation time. Future work will extend these results to guidance of nonlinear non-hyperbolic systems. The exact output tracking problem for systems with parameter jumps was considered. Necessary and sufficient conditions were derived for the elimination of switching-introduced output transient. While previous works had studied this problem by developing a regulator that maintains exact tracking through parameter jumps (switches), such techniques are, however, only applicable to minimum-phase systems. In contrast, our approach is also applicable to nonminimum-phase systems and leads to bounded but possibly non-causal solutions. In addition, for the case when the reference trajectories are generated by an exosystem, we developed an exact-tracking controller which could be written in a feedback form. As in standard regulator theory, we also obtained a linear map from the states of the exosystem to the desired system state, which was defined via a matrix differential equation.

Efficient parallel linear scaling construction of the density matrix for Born-Oppenheimer molecular dynamics.

PubMed

Mniszewski, S M; Cawkwell, M J; Wall, M E; Mohd-Yusof, J; Bock, N; Germann, T C; Niklasson, A M N

2015-10-13

We present an algorithm for the calculation of the density matrix that for insulators scales linearly with system size and parallelizes efficiently on multicore, shared memory platforms with small and controllable numerical errors. The algorithm is based on an implementation of the second-order spectral projection (SP2) algorithm [ Niklasson, A. M. N. Phys. Rev. B 2002 , 66 , 155115 ] in sparse matrix algebra with the ELLPACK-R data format. We illustrate the performance of the algorithm within self-consistent tight binding theory by total energy calculations of gas phase poly(ethylene) molecules and periodic liquid water systems containing up to 15,000 atoms on up to 16 CPU cores. We consider algorithm-specific performance aspects, such as local vs nonlocal memory access and the degree of matrix sparsity. Comparisons to sparse matrix algebra implementations using off-the-shelf libraries on multicore CPUs, graphics processing units (GPUs), and the Intel many integrated core (MIC) architecture are also presented. The accuracy and stability of the algorithm are illustrated with long duration Born-Oppenheimer molecular dynamics simulations of 1000 water molecules and a 303 atom Trp cage protein solvated by 2682 water molecules.

Parallel three-dimensional magnetotelluric inversion using adaptive finite-element method. Part I: theory and synthetic study

NASA Astrophysics Data System (ADS)

Grayver, Alexander V.

2015-07-01

This paper presents a distributed magnetotelluric inversion scheme based on adaptive finite-element method (FEM). The key novel aspect of the introduced algorithm is the use of automatic mesh refinement techniques for both forward and inverse modelling. These techniques alleviate tedious and subjective procedure of choosing a suitable model parametrization. To avoid overparametrization, meshes for forward and inverse problems were decoupled. For calculation of accurate electromagnetic (EM) responses, automatic mesh refinement algorithm based on a goal-oriented error estimator has been adopted. For further efficiency gain, EM fields for each frequency were calculated using independent meshes in order to account for substantially different spatial behaviour of the fields over a wide range of frequencies. An automatic approach for efficient initial mesh design in inverse problems based on linearized model resolution matrix was developed. To make this algorithm suitable for large-scale problems, it was proposed to use a low-rank approximation of the linearized model resolution matrix. In order to fill a gap between initial and true model complexities and resolve emerging 3-D structures better, an algorithm for adaptive inverse mesh refinement was derived. Within this algorithm, spatial variations of the imaged parameter are calculated and mesh is refined in the neighborhoods of points with the largest variations. A series of numerical tests were performed to demonstrate the utility of the presented algorithms. Adaptive mesh refinement based on the model resolution estimates provides an efficient tool to derive initial meshes which account for arbitrary survey layouts, data types, frequency content and measurement uncertainties. Furthermore, the algorithm is capable to deliver meshes suitable to resolve features on multiple scales while keeping number of unknowns low. However, such meshes exhibit dependency on an initial model guess. Additionally, it is demonstrated that the adaptive mesh refinement can be particularly efficient in resolving complex shapes. The implemented inversion scheme was able to resolve a hemisphere object with sufficient resolution starting from a coarse discretization and refining mesh adaptively in a fully automatic process. The code is able to harness the computational power of modern distributed platforms and is shown to work with models consisting of millions of degrees of freedom. Significant computational savings were achieved by using locally refined decoupled meshes.

spammpack, Version 2013-06-18

DOE Office of Scientific and Technical Information (OSTI.GOV)

2014-01-17

This library is an implementation of the Sparse Approximate Matrix Multiplication (SpAMM) algorithm introduced. It provides a matrix data type, and an approximate matrix product, which exhibits linear scaling computational complexity for matrices with decay. The product error and the performance of the multiply can be tuned by choosing an appropriate tolerance. The library can be compiled for serial execution or parallel execution on shared memory systems with an OpenMP capable compiler

Bit error rate tester using fast parallel generation of linear recurring sequences

DOEpatents

Pierson, Lyndon G.; Witzke, Edward L.; Maestas, Joseph H.

2003-05-06

A fast method for generating linear recurring sequences by parallel linear recurring sequence generators (LRSGs) with a feedback circuit optimized to balance minimum propagation delay against maximal sequence period. Parallel generation of linear recurring sequences requires decimating the sequence (creating small contiguous sections of the sequence in each LRSG). A companion matrix form is selected depending on whether the LFSR is right-shifting or left-shifting. The companion matrix is completed by selecting a primitive irreducible polynomial with 1's most closely grouped in a corner of the companion matrix. A decimation matrix is created by raising the companion matrix to the (n*k).sup.th power, where k is the number of parallel LRSGs and n is the number of bits to be generated at a time by each LRSG. Companion matrices with 1's closely grouped in a corner will yield sparse decimation matrices. A feedback circuit comprised of XOR logic gates implements the decimation matrix in hardware. Sparse decimation matrices can be implemented with minimum number of XOR gates, and therefore a minimum propagation delay through the feedback circuit. The LRSG of the invention is particularly well suited to use as a bit error rate tester on high speed communication lines because it permits the receiver to synchronize to the transmitted pattern within 2n bits.

Accelerating non-contrast-enhanced MR angiography with inflow inversion recovery imaging by skipped phase encoding and edge deghosting (SPEED).

PubMed

Chang, Zheng; Xiang, Qing-San; Shen, Hao; Yin, Fang-Fang

2010-03-01

To accelerate non-contrast-enhanced MR angiography (MRA) with inflow inversion recovery (IFIR) with a fast imaging method, Skipped Phase Encoding and Edge Deghosting (SPEED). IFIR imaging uses a preparatory inversion pulse to reduce signals from static tissue, while leaving inflow arterial blood unaffected, resulting in sparse arterial vasculature on modest tissue background. By taking advantage of vascular sparsity, SPEED can be simplified with a single-layer model to achieve higher efficiency in both scan time reduction and image reconstruction. SPEED can also make use of information available in multiple coils for further acceleration. The techniques are demonstrated with a three-dimensional renal non-contrast-enhanced IFIR MRA study. Images are reconstructed by SPEED based on a single-layer model to achieve an undersampling factor of up to 2.5 using one skipped phase encoding direction. By making use of information available in multiple coils, SPEED can achieve an undersampling factor of up to 8.3 with four receiver coils. The reconstructed images generally have comparable quality as that of the reference images reconstructed from full k-space data. As demonstrated with a three-dimensional renal IFIR scan, SPEED based on a single-layer model is able to reduce scan time further and achieve higher computational efficiency than the original SPEED.

Electrical source imaging of interictal spikes using multiple sparse volumetric priors for presurgical epileptogenic focus localization

PubMed Central

Strobbe, Gregor; Carrette, Evelien; López, José David; Montes Restrepo, Victoria; Van Roost, Dirk; Meurs, Alfred; Vonck, Kristl; Boon, Paul; Vandenberghe, Stefaan; van Mierlo, Pieter

2016-01-01

Electrical source imaging of interictal spikes observed in EEG recordings of patients with refractory epilepsy provides useful information to localize the epileptogenic focus during the presurgical evaluation. However, the selection of the time points or time epochs of the spikes in order to estimate the origin of the activity remains a challenge. In this study, we consider a Bayesian EEG source imaging technique for distributed sources, i.e. the multiple volumetric sparse priors (MSVP) approach. The approach allows to estimate the time courses of the intensity of the sources corresponding with a specific time epoch of the spike. Based on presurgical averaged interictal spikes in six patients who were successfully treated with surgery, we estimated the time courses of the source intensities for three different time epochs: (i) an epoch starting 50 ms before the spike peak and ending at 50% of the spike peak during the rising phase of the spike, (ii) an epoch starting 50 ms before the spike peak and ending at the spike peak and (iii) an epoch containing the full spike time period starting 50 ms before the spike peak and ending 230 ms after the spike peak. To identify the primary source of the spike activity, the source with the maximum energy from 50 ms before the spike peak till 50% of the spike peak was subsequently selected for each of the time windows. For comparison, the activity at the spike peaks and at 50% of the peaks was localized using the LORETA inversion technique and an ECD approach. Both patient-specific spherical forward models and patient-specific 5-layered finite difference models were considered to evaluate the influence of the forward model. Based on the resected zones in each of the patients, extracted from post-operative MR images, we compared the distances to the resection border of the estimated activity. Using the spherical models, the distances to the resection border for the MSVP approach and each of the different time epochs were in the same range as the LORETA and ECD techniques. We found distances smaller than 23 mm, with robust results for all the patients. For the finite difference models, we found that the distances to the resection border for the MSVP inversions of the full spike time epochs were generally smaller compared to the MSVP inversions of the time epochs before the spike peak. The results also suggest that the inversions using the finite difference models resulted in slightly smaller distances to the resection border compared to the spherical models. The results we obtained are promising because the MSVP approach allows to study the network of the estimated source-intensities and allows to characterize the spatial extent of the underlying sources. PMID:26958464

SPAR reference manual

NASA Technical Reports Server (NTRS)

Whetstone, W. D.

1976-01-01

The functions and operating rules of the SPAR system, which is a group of computer programs used primarily to perform stress, buckling, and vibrational analyses of linear finite element systems, were given. The following subject areas were discussed: basic information, structure definition, format system matrix processors, utility programs, static solutions, stresses, sparse matrix eigensolver, dynamic response, graphics, and substructure processors.

Matrix Recipes for Hard Thresholding Methods

DTIC Science & Technology

2012-11-07

have been proposed to approximate the solution. In [11], Donoho et al . demonstrate that, in the sparse approximation problem, under basic incoherence...inducing convex surrogate ‖ · ‖1 with provable guarantees for unique signal recovery. In the ARM problem, Fazel et al . [12] identified the nuclear norm...sparse recovery for all. Technical report, EPFL, 2011 . [25] N. Halko , P. G. Martinsson, and J. A. Tropp. Finding structure with randomness: Probabilistic

Efficient Computation of Sparse Matrix Functions for Large-Scale Electronic Structure Calculations: The CheSS Library.

PubMed

Mohr, Stephan; Dawson, William; Wagner, Michael; Caliste, Damien; Nakajima, Takahito; Genovese, Luigi

2017-10-10

We present CheSS, the "Chebyshev Sparse Solvers" library, which has been designed to solve typical problems arising in large-scale electronic structure calculations using localized basis sets. The library is based on a flexible and efficient expansion in terms of Chebyshev polynomials and presently features the calculation of the density matrix, the calculation of matrix powers for arbitrary powers, and the extraction of eigenvalues in a selected interval. CheSS is able to exploit the sparsity of the matrices and scales linearly with respect to the number of nonzero entries, making it well-suited for large-scale calculations. The approach is particularly adapted for setups leading to small spectral widths of the involved matrices and outperforms alternative methods in this regime. By coupling CheSS to the DFT code BigDFT, we show that such a favorable setup is indeed possible in practice. In addition, the approach based on Chebyshev polynomials can be massively parallelized, and CheSS exhibits excellent scaling up to thousands of cores even for relatively small matrix sizes.

Round-off errors in cutting plane algorithms based on the revised simplex procedure

NASA Technical Reports Server (NTRS)

Moore, J. E.

1973-01-01

This report statistically analyzes computational round-off errors associated with the cutting plane approach to solving linear integer programming problems. Cutting plane methods require that the inverse of a sequence of matrices be computed. The problem basically reduces to one of minimizing round-off errors in the sequence of inverses. Two procedures for minimizing this problem are presented, and their influence on error accumulation is statistically analyzed. One procedure employs a very small tolerance factor to round computed values to zero. The other procedure is a numerical analysis technique for reinverting or improving the approximate inverse of a matrix. The results indicated that round-off accumulation can be effectively minimized by employing a tolerance factor which reflects the number of significant digits carried for each calculation and by applying the reinversion procedure once to each computed inverse. If 18 significant digits plus an exponent are carried for each variable during computations, then a tolerance value of 0.1 x 10 to the minus 12th power is reasonable.

Spherical earth gravity and magnetic anomaly analysis by equivalent point source inversion

NASA Technical Reports Server (NTRS)

Von Frese, R. R. B.; Hinze, W. J.; Braile, L. W.

1981-01-01

To facilitate geologic interpretation of satellite elevation potential field data, analysis techniques are developed and verified in the spherical domain that are commensurate with conventional flat earth methods of potential field interpretation. A powerful approach to the spherical earth problem relates potential field anomalies to a distribution of equivalent point sources by least squares matrix inversion. Linear transformations of the equivalent source field lead to corresponding geoidal anomalies, pseudo-anomalies, vector anomaly components, spatial derivatives, continuations, and differential magnetic pole reductions. A number of examples using 1 deg-averaged surface free-air gravity anomalies of POGO satellite magnetometer data for the United States, Mexico, and Central America illustrate the capabilities of the method.

Bypassing the Limits of Ll Regularization: Convex Sparse Signal Processing Using Non-Convex Regularization

NASA Astrophysics Data System (ADS)

Parekh, Ankit

Sparsity has become the basis of some important signal processing methods over the last ten years. Many signal processing problems (e.g., denoising, deconvolution, non-linear component analysis) can be expressed as inverse problems. Sparsity is invoked through the formulation of an inverse problem with suitably designed regularization terms. The regularization terms alone encode sparsity into the problem formulation. Often, the ℓ1 norm is used to induce sparsity, so much so that ℓ1 regularization is considered to be `modern least-squares'. The use of ℓ1 norm, as a sparsity-inducing regularizer, leads to a convex optimization problem, which has several benefits: the absence of extraneous local minima, well developed theory of globally convergent algorithms, even for large-scale problems. Convex regularization via the ℓ1 norm, however, tends to under-estimate the non-zero values of sparse signals. In order to estimate the non-zero values more accurately, non-convex regularization is often favored over convex regularization. However, non-convex regularization generally leads to non-convex optimization, which suffers from numerous issues: convergence may be guaranteed to only a stationary point, problem specific parameters may be difficult to set, and the solution is sensitive to the initialization of the algorithm. The first part of this thesis is aimed toward combining the benefits of non-convex regularization and convex optimization to estimate sparse signals more effectively. To this end, we propose to use parameterized non-convex regularizers with designated non-convexity and provide a range for the non-convex parameter so as to ensure that the objective function is strictly convex. By ensuring convexity of the objective function (sum of data-fidelity and non-convex regularizer), we can make use of a wide variety of convex optimization algorithms to obtain the unique global minimum reliably. The second part of this thesis proposes a non-linear signal decomposition technique for an important biomedical signal processing problem: the detection of sleep spindles and K-complexes in human sleep electroencephalography (EEG). We propose a non-linear model for the EEG consisting of three components: (1) a transient (sparse piecewise constant) component, (2) a low-frequency component, and (3) an oscillatory component. The oscillatory component admits a sparse time-frequency representation. Using a convex objective function, we propose a fast non-linear optimization algorithm to estimate the three components in the proposed signal model. The low-frequency and oscillatory components are then used to estimate the K-complexes and sleep spindles respectively. The proposed detection method is shown to outperform several state-of-the-art automated sleep spindles detection methods.

Thermomechanical Fatigue Damage/Failure Mechanisms in SCS-6/Timetal 21S [0/90](Sub S) Composite

NASA Technical Reports Server (NTRS)

Castelli, Michael G.

1994-01-01

The thermomechanical fatigue (TMF) deformation, damage, and life behaviors of SCS6/Timetal 21S (0/90)s were investigated under zero-tension conditions. In-phase (IP) and out-of-phase (OP) loadings were investigated with a temperature cycle from 150 to 650 deg C. An advanced TMF test technique was used to quantify mechanically damage progression. The technique incorporated explicit measurements of the macroscopic (1) isothermal static moduli at the temperature extremes of the TMF cycle and (2) coefficient of thermal expansion (CTE) as functions of the TMF cycles. The importance of thermal property degradation and its relevance to accurate post-test data analysis and interpretation is briefly addressed. Extensive fractography and metallography were conducted on specimens from failed and interrupted tests to characterize the extent of damage at the microstructure level. Fatigue life results indicated trends analogous to those established for similar unidirectional(0) reinforced titanium matrix composite systems. High stress IP and mid to low stress OP loading conditions were life-limiting in comparison to maximum temperature isothermal conditions. Dominant damage mechanisms changed with cycle type. Damage resulting from IP TMF conditions produced measurable decreases in static moduli but only minimal changes in the CTE. Metallography on interrupted and failed specimens revealed extensive (0) fiber cracking with sparse matrix damage. No surface initiated matrix cracks were present. Comparable OP TMF conditions initiated environment enhanced surface cracking and matrix cracking initiated at (90) fiber/matrix (F/M) interfaces. Notable static moduli and CTE degradations were measured. Fractography and metallography revealed that the transverse cracks originating from the surface and (90) F/M interfaces tended to converge and coalesce at the (0) fibers.

An efficient classification method based on principal component and sparse representation.

PubMed

Zhai, Lin; Fu, Shujun; Zhang, Caiming; Liu, Yunxian; Wang, Lu; Liu, Guohua; Yang, Mingqiang

2016-01-01

As an important application in optical imaging, palmprint recognition is interfered by many unfavorable factors. An effective fusion of blockwise bi-directional two-dimensional principal component analysis and grouping sparse classification is presented. The dimension reduction and normalizing are implemented by the blockwise bi-directional two-dimensional principal component analysis for palmprint images to extract feature matrixes, which are assembled into an overcomplete dictionary in sparse classification. A subspace orthogonal matching pursuit algorithm is designed to solve the grouping sparse representation. Finally, the classification result is gained by comparing the residual between testing and reconstructed images. Experiments are carried out on a palmprint database, and the results show that this method has better robustness against position and illumination changes of palmprint images, and can get higher rate of palmprint recognition.

Contribution of non-negative matrix factorization to the classification of remote sensing images

NASA Astrophysics Data System (ADS)

Karoui, M. S.; Deville, Y.; Hosseini, S.; Ouamri, A.; Ducrot, D.

2008-10-01

Remote sensing has become an unavoidable tool for better managing our environment, generally by realizing maps of land cover using classification techniques. The classification process requires some pre-processing, especially for data size reduction. The most usual technique is Principal Component Analysis. Another approach consists in regarding each pixel of the multispectral image as a mixture of pure elements contained in the observed area. Using Blind Source Separation (BSS) methods, one can hope to unmix each pixel and to perform the recognition of the classes constituting the observed scene. Our contribution consists in using Non-negative Matrix Factorization (NMF) combined with sparse coding as a solution to BSS, in order to generate new images (which are at least partly separated images) using HRV SPOT images from Oran area, Algeria). These images are then used as inputs of a supervised classifier integrating textural information. The results of classifications of these "separated" images show a clear improvement (correct pixel classification rate improved by more than 20%) compared to classification of initial (i.e. non separated) images. These results show the contribution of NMF as an attractive pre-processing for classification of multispectral remote sensing imagery.

A Novel 2D Image Compression Algorithm Based on Two Levels DWT and DCT Transforms with Enhanced Minimize-Matrix-Size Algorithm for High Resolution Structured Light 3D Surface Reconstruction

NASA Astrophysics Data System (ADS)

Siddeq, M. M.; Rodrigues, M. A.

2015-09-01

Image compression techniques are widely used on 2D image 2D video 3D images and 3D video. There are many types of compression techniques and among the most popular are JPEG and JPEG2000. In this research, we introduce a new compression method based on applying a two level discrete cosine transform (DCT) and a two level discrete wavelet transform (DWT) in connection with novel compression steps for high-resolution images. The proposed image compression algorithm consists of four steps. (1) Transform an image by a two level DWT followed by a DCT to produce two matrices: DC- and AC-Matrix, or low and high frequency matrix, respectively, (2) apply a second level DCT on the DC-Matrix to generate two arrays, namely nonzero-array and zero-array, (3) apply the Minimize-Matrix-Size algorithm to the AC-Matrix and to the other high-frequencies generated by the second level DWT, (4) apply arithmetic coding to the output of previous steps. A novel decompression algorithm, Fast-Match-Search algorithm (FMS), is used to reconstruct all high-frequency matrices. The FMS-algorithm computes all compressed data probabilities by using a table of data, and then using a binary search algorithm for finding decompressed data inside the table. Thereafter, all decoded DC-values with the decoded AC-coefficients are combined in one matrix followed by inverse two levels DCT with two levels DWT. The technique is tested by compression and reconstruction of 3D surface patches. Additionally, this technique is compared with JPEG and JPEG2000 algorithm through 2D and 3D root-mean-square-error following reconstruction. The results demonstrate that the proposed compression method has better visual properties than JPEG and JPEG2000 and is able to more accurately reconstruct surface patches in 3D.

Joint analysis of multiple high-dimensional data types using sparse matrix approximations of rank-1 with applications to ovarian and liver cancer.

PubMed

Okimoto, Gordon; Zeinalzadeh, Ashkan; Wenska, Tom; Loomis, Michael; Nation, James B; Fabre, Tiphaine; Tiirikainen, Maarit; Hernandez, Brenda; Chan, Owen; Wong, Linda; Kwee, Sandi

2016-01-01

Technological advances enable the cost-effective acquisition of Multi-Modal Data Sets (MMDS) composed of measurements for multiple, high-dimensional data types obtained from a common set of bio-samples. The joint analysis of the data matrices associated with the different data types of a MMDS should provide a more focused view of the biology underlying complex diseases such as cancer that would not be apparent from the analysis of a single data type alone. As multi-modal data rapidly accumulate in research laboratories and public databases such as The Cancer Genome Atlas (TCGA), the translation of such data into clinically actionable knowledge has been slowed by the lack of computational tools capable of analyzing MMDSs. Here, we describe the Joint Analysis of Many Matrices by ITeration (JAMMIT) algorithm that jointly analyzes the data matrices of a MMDS using sparse matrix approximations of rank-1. The JAMMIT algorithm jointly approximates an arbitrary number of data matrices by rank-1 outer-products composed of "sparse" left-singular vectors (eigen-arrays) that are unique to each matrix and a right-singular vector (eigen-signal) that is common to all the matrices. The non-zero coefficients of the eigen-arrays identify small subsets of variables for each data type (i.e., signatures) that in aggregate, or individually, best explain a dominant eigen-signal defined on the columns of the data matrices. The approximation is specified by a single "sparsity" parameter that is selected based on false discovery rate estimated by permutation testing. Multiple signals of interest in a given MDDS are sequentially detected and modeled by iterating JAMMIT on "residual" data matrices that result from a given sparse approximation. We show that JAMMIT outperforms other joint analysis algorithms in the detection of multiple signatures embedded in simulated MDDS. On real multimodal data for ovarian and liver cancer we show that JAMMIT identified multi-modal signatures that were clinically informative and enriched for cancer-related biology. Sparse matrix approximations of rank-1 provide a simple yet effective means of jointly reducing multiple, big data types to a small subset of variables that characterize important clinical and/or biological attributes of the bio-samples from which the data were acquired.

Decomposed direct matrix inversion for fast non-cartesian SENSE reconstructions.

PubMed

Qian, Yongxian; Zhang, Zhenghui; Wang, Yi; Boada, Fernando E

2006-08-01

A new k-space direct matrix inversion (DMI) method is proposed here to accelerate non-Cartesian SENSE reconstructions. In this method a global k-space matrix equation is established on basic MRI principles, and the inverse of the global encoding matrix is found from a set of local matrix equations by taking advantage of the small extension of k-space coil maps. The DMI algorithm's efficiency is achieved by reloading the precalculated global inverse when the coil maps and trajectories remain unchanged, such as in dynamic studies. Phantom and human subject experiments were performed on a 1.5T scanner with a standard four-channel phased-array cardiac coil. Interleaved spiral trajectories were used to collect fully sampled and undersampled 3D raw data. The equivalence of the global k-space matrix equation to its image-space version, was verified via conjugate gradient (CG) iterative algorithms on a 2x undersampled phantom and numerical-model data sets. When applied to the 2x undersampled phantom and human-subject raw data, the decomposed DMI method produced images with small errors (< or = 3.9%) relative to the reference images obtained from the fully-sampled data, at a rate of 2 s per slice (excluding 4 min for precalculating the global inverse at an image size of 256 x 256). The DMI method may be useful for noise evaluations in parallel coil designs, dynamic MRI, and 3D sodium MRI with fixed coils and trajectories. Copyright 2006 Wiley-Liss, Inc.

Sensitivity computation of the ell1 minimization problem and its application to dictionary design of ill-posed problems

NASA Astrophysics Data System (ADS)

Horesh, L.; Haber, E.

2009-09-01

The ell1 minimization problem has been studied extensively in the past few years. Recently, there has been a growing interest in its application for inverse problems. Most studies have concentrated in devising ways for sparse representation of a solution using a given prototype dictionary. Very few studies have addressed the more challenging problem of optimal dictionary construction, and even these were primarily devoted to the simplistic sparse coding application. In this paper, sensitivity analysis of the inverse solution with respect to the dictionary is presented. This analysis reveals some of the salient features and intrinsic difficulties which are associated with the dictionary design problem. Equipped with these insights, we propose an optimization strategy that alleviates these hurdles while utilizing the derived sensitivity relations for the design of a locally optimal dictionary. Our optimality criterion is based on local minimization of the Bayesian risk, given a set of training models. We present a mathematical formulation and an algorithmic framework to achieve this goal. The proposed framework offers the design of dictionaries for inverse problems that incorporate non-trivial, non-injective observation operators, where the data and the recovered parameters may reside in different spaces. We test our algorithm and show that it yields improved dictionaries for a diverse set of inverse problems in geophysics and medical imaging.

AZTEC. Parallel Iterative method Software for Solving Linear Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hutchinson, S.; Shadid, J.; Tuminaro, R.

1995-07-01

AZTEC is an interactive library that greatly simplifies the parrallelization process when solving the linear systems of equations Ax=b where A is a user supplied n X n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. AZTEC is intended as a software tool for users who want to avoid cumbersome parallel programming details but who have large sparse linear systems which require an efficiently utilized parallel processing system. A collection of data transformation tools are provided that allow for easy creation of distributed sparse unstructured matricesmore » for parallel solutions.« less

Efficient Implementation of an Optimal Interpolator for Large Spatial Data Sets

NASA Technical Reports Server (NTRS)

Memarsadeghi, Nargess; Mount, David M.

2007-01-01

Scattered data interpolation is a problem of interest in numerous areas such as electronic imaging, smooth surface modeling, and computational geometry. Our motivation arises from applications in geology and mining, which often involve large scattered data sets and a demand for high accuracy. The method of choice is ordinary kriging. This is because it is a best unbiased estimator. Unfortunately, this interpolant is computationally very expensive to compute exactly. For n scattered data points, computing the value of a single interpolant involves solving a dense linear system of size roughly n x n. This is infeasible for large n. In practice, kriging is solved approximately by local approaches that are based on considering only a relatively small'number of points that lie close to the query point. There are many problems with this local approach, however. The first is that determining the proper neighborhood size is tricky, and is usually solved by ad hoc methods such as selecting a fixed number of nearest neighbors or all the points lying within a fixed radius. Such fixed neighborhood sizes may not work well for all query points, depending on local density of the point distribution. Local methods also suffer from the problem that the resulting interpolant is not continuous. Meyer showed that while kriging produces smooth continues surfaces, it has zero order continuity along its borders. Thus, at interface boundaries where the neighborhood changes, the interpolant behaves discontinuously. Therefore, it is important to consider and solve the global system for each interpolant. However, solving such large dense systems for each query point is impractical. Recently a more principled approach to approximating kriging has been proposed based on a technique called covariance tapering. The problems arise from the fact that the covariance functions that are used in kriging have global support. Our implementations combine, utilize, and enhance a number of different approaches that have been introduced in literature for solving large linear systems for interpolation of scattered data points. For very large systems, exact methods such as Gaussian elimination are impractical since they require 0(n(exp 3)) time and 0(n(exp 2)) storage. As Billings et al. suggested, we use an iterative approach. In particular, we use the SYMMLQ method, for solving the large but sparse ordinary kriging systems that result from tapering. The main technical issue that need to be overcome in our algorithmic solution is that the points' covariance matrix for kriging should be symmetric positive definite. The goal of tapering is to obtain a sparse approximate representation of the covariance matrix while maintaining its positive definiteness. Furrer et al. used tapering to obtain a sparse linear system of the form Ax = b, where A is the tapered symmetric positive definite covariance matrix. Thus, Cholesky factorization could be used to solve their linear systems. They implemented an efficient sparse Cholesky decomposition method. They also showed if these tapers are used for a limited class of covariance models, the solution of the system converges to the solution of the original system. Matrix A in the ordinary kriging system, while symmetric, is not positive definite. Thus, their approach is not applicable to the ordinary kriging system. Therefore, we use tapering only to obtain a sparse linear system. Then, we use SYMMLQ to solve the ordinary kriging system. We show that solving large kriging systems becomes practical via tapering and iterative methods, and results in lower estimation errors compared to traditional local approaches, and significant memory savings compared to the original global system. We also developed a more efficient variant of the sparse SYMMLQ method for large ordinary kriging systems. This approach adaptively finds the correct local neighborhood for each query point in the interpolation process.

The Use of Sparse Direct Solver in Vector Finite Element Modeling for Calculating Two Dimensional (2-D) Magnetotelluric Responses in Transverse Electric (TE) Mode

NASA Astrophysics Data System (ADS)

Yihaa Roodhiyah, Lisa’; Tjong, Tiffany; Nurhasan; Sutarno, D.

2018-04-01

The late research, linear matrices of vector finite element in two dimensional(2-D) magnetotelluric (MT) responses modeling was solved by non-sparse direct solver in TE mode. Nevertheless, there is some weakness which have to be improved especially accuracy in the low frequency (10-3 Hz-10-5 Hz) which is not achieved yet and high cost computation in dense mesh. In this work, the solver which is used is sparse direct solver instead of non-sparse direct solverto overcome the weaknesses of solving linear matrices of vector finite element metod using non-sparse direct solver. Sparse direct solver will be advantageous in solving linear matrices of vector finite element method because of the matrix properties which is symmetrical and sparse. The validation of sparse direct solver in solving linear matrices of vector finite element has been done for a homogen half-space model and vertical contact model by analytical solution. Thevalidation result of sparse direct solver in solving linear matrices of vector finite element shows that sparse direct solver is more stable than non-sparse direct solver in computing linear problem of vector finite element method especially in low frequency. In the end, the accuracy of 2D MT responses modelling in low frequency (10-3 Hz-10-5 Hz) has been reached out under the efficient allocation memory of array and less computational time consuming.

Efficient Sum of Outer Products Dictionary Learning (SOUP-DIL) and Its Application to Inverse Problems.

PubMed

Ravishankar, Saiprasad; Nadakuditi, Raj Rao; Fessler, Jeffrey A

2017-12-01

The sparsity of signals in a transform domain or dictionary has been exploited in applications such as compression, denoising and inverse problems. More recently, data-driven adaptation of synthesis dictionaries has shown promise compared to analytical dictionary models. However, dictionary learning problems are typically non-convex and NP-hard, and the usual alternating minimization approaches for these problems are often computationally expensive, with the computations dominated by the NP-hard synthesis sparse coding step. This paper exploits the ideas that drive algorithms such as K-SVD, and investigates in detail efficient methods for aggregate sparsity penalized dictionary learning by first approximating the data with a sum of sparse rank-one matrices (outer products) and then using a block coordinate descent approach to estimate the unknowns. The resulting block coordinate descent algorithms involve efficient closed-form solutions. Furthermore, we consider the problem of dictionary-blind image reconstruction, and propose novel and efficient algorithms for adaptive image reconstruction using block coordinate descent and sum of outer products methodologies. We provide a convergence study of the algorithms for dictionary learning and dictionary-blind image reconstruction. Our numerical experiments show the promising performance and speedups provided by the proposed methods over previous schemes in sparse data representation and compressed sensing-based image reconstruction.

Efficient Sum of Outer Products Dictionary Learning (SOUP-DIL) and Its Application to Inverse Problems

PubMed Central

Ravishankar, Saiprasad; Nadakuditi, Raj Rao; Fessler, Jeffrey A.

2017-01-01

The sparsity of signals in a transform domain or dictionary has been exploited in applications such as compression, denoising and inverse problems. More recently, data-driven adaptation of synthesis dictionaries has shown promise compared to analytical dictionary models. However, dictionary learning problems are typically non-convex and NP-hard, and the usual alternating minimization approaches for these problems are often computationally expensive, with the computations dominated by the NP-hard synthesis sparse coding step. This paper exploits the ideas that drive algorithms such as K-SVD, and investigates in detail efficient methods for aggregate sparsity penalized dictionary learning by first approximating the data with a sum of sparse rank-one matrices (outer products) and then using a block coordinate descent approach to estimate the unknowns. The resulting block coordinate descent algorithms involve efficient closed-form solutions. Furthermore, we consider the problem of dictionary-blind image reconstruction, and propose novel and efficient algorithms for adaptive image reconstruction using block coordinate descent and sum of outer products methodologies. We provide a convergence study of the algorithms for dictionary learning and dictionary-blind image reconstruction. Our numerical experiments show the promising performance and speedups provided by the proposed methods over previous schemes in sparse data representation and compressed sensing-based image reconstruction. PMID:29376111

Saliency Detection via Absorbing Markov Chain With Learnt Transition Probability.

PubMed

Lihe Zhang; Jianwu Ai; Bowen Jiang; Huchuan Lu; Xiukui Li

2018-02-01

In this paper, we propose a bottom-up saliency model based on absorbing Markov chain (AMC). First, a sparsely connected graph is constructed to capture the local context information of each node. All image boundary nodes and other nodes are, respectively, treated as the absorbing nodes and transient nodes in the absorbing Markov chain. Then, the expected number of times from each transient node to all other transient nodes can be used to represent the saliency value of this node. The absorbed time depends on the weights on the path and their spatial coordinates, which are completely encoded in the transition probability matrix. Considering the importance of this matrix, we adopt different hierarchies of deep features extracted from fully convolutional networks and learn a transition probability matrix, which is called learnt transition probability matrix. Although the performance is significantly promoted, salient objects are not uniformly highlighted very well. To solve this problem, an angular embedding technique is investigated to refine the saliency results. Based on pairwise local orderings, which are produced by the saliency maps of AMC and boundary maps, we rearrange the global orderings (saliency value) of all nodes. Extensive experiments demonstrate that the proposed algorithm outperforms the state-of-the-art methods on six publicly available benchmark data sets.

Covariance specification and estimation to improve top-down Green House Gas emission estimates

NASA Astrophysics Data System (ADS)

Ghosh, S.; Lopez-Coto, I.; Prasad, K.; Whetstone, J. R.

2015-12-01

The National Institute of Standards and Technology (NIST) operates the North-East Corridor (NEC) project and the Indianapolis Flux Experiment (INFLUX) in order to develop measurement methods to quantify sources of Greenhouse Gas (GHG) emissions as well as their uncertainties in urban domains using a top down inversion method. Top down inversion updates prior knowledge using observations in a Bayesian way. One primary consideration in a Bayesian inversion framework is the covariance structure of (1) the emission prior residuals and (2) the observation residuals (i.e. the difference between observations and model predicted observations). These covariance matrices are respectively referred to as the prior covariance matrix and the model-data mismatch covariance matrix. It is known that the choice of these covariances can have large effect on estimates. The main objective of this work is to determine the impact of different covariance models on inversion estimates and their associated uncertainties in urban domains. We use a pseudo-data Bayesian inversion framework using footprints (i.e. sensitivities of tower measurements of GHGs to surface emissions) and emission priors (based on Hestia project to quantify fossil-fuel emissions) to estimate posterior emissions using different covariance schemes. The posterior emission estimates and uncertainties are compared to the hypothetical truth. We find that, if we correctly specify spatial variability and spatio-temporal variability in prior and model-data mismatch covariances respectively, then we can compute more accurate posterior estimates. We discuss few covariance models to introduce space-time interacting mismatches along with estimation of the involved parameters. We then compare several candidate prior spatial covariance models from the Matern covariance class and estimate their parameters with specified mismatches. We find that best-fitted prior covariances are not always best in recovering the truth. To achieve accuracy, we perform a sensitivity study to further tune covariance parameters. Finally, we introduce a shrinkage based sample covariance estimation technique for both prior and mismatch covariances. This technique allows us to achieve similar accuracy nonparametrically in a more efficient and automated way.

Turbo-SMT: Parallel Coupled Sparse Matrix-Tensor Factorizations and Applications

PubMed Central

Papalexakis, Evangelos E.; Faloutsos, Christos; Mitchell, Tom M.; Talukdar, Partha Pratim; Sidiropoulos, Nicholas D.; Murphy, Brian

2016-01-01

How can we correlate the neural activity in the human brain as it responds to typed words, with properties of these terms (like ’edible’, ’fits in hand’)? In short, we want to find latent variables, that jointly explain both the brain activity, as well as the behavioral responses. This is one of many settings of the Coupled Matrix-Tensor Factorization (CMTF) problem. Can we enhance any CMTF solver, so that it can operate on potentially very large datasets that may not fit in main memory? We introduce Turbo-SMT, a meta-method capable of doing exactly that: it boosts the performance of any CMTF algorithm, produces sparse and interpretable solutions, and parallelizes any CMTF algorithm, producing sparse and interpretable solutions (up to 65 fold). Additionally, we improve upon ALS, the work-horse algorithm for CMTF, with respect to efficiency and robustness to missing values. We apply Turbo-SMT to BrainQ, a dataset consisting of a (nouns, brain voxels, human subjects) tensor and a (nouns, properties) matrix, with coupling along the nouns dimension. Turbo-SMT is able to find meaningful latent variables, as well as to predict brain activity with competitive accuracy. Finally, we demonstrate the generality of Turbo-SMT, by applying it on a Facebook dataset (users, ’friends’, wall-postings); there, Turbo-SMT spots spammer-like anomalies. PMID:27672406

Performance analysis of distributed symmetric sparse matrix vector multiplication algorithm for multi-core architectures

DOE PAGES

Oryspayev, Dossay; Aktulga, Hasan Metin; Sosonkina, Masha; ...

2015-07-14

In this article, sparse matrix vector multiply (SpMVM) is an important kernel that frequently arises in high performance computing applications. Due to its low arithmetic intensity, several approaches have been proposed in literature to improve its scalability and efficiency in large scale computations. In this paper, our target systems are high end multi-core architectures and we use messaging passing interface + open multiprocessing hybrid programming model for parallelism. We analyze the performance of recently proposed implementation of the distributed symmetric SpMVM, originally developed for large sparse symmetric matrices arising in ab initio nuclear structure calculations. We also study important featuresmore » of this implementation and compare with previously reported implementations that do not exploit underlying symmetry. Our SpMVM implementations leverage the hybrid paradigm to efficiently overlap expensive communications with computations. Our main comparison criterion is the "CPU core hours" metric, which is the main measure of resource usage on supercomputers. We analyze the effects of topology-aware mapping heuristic using simplified network load model. Furthermore, we have tested the different SpMVM implementations on two large clusters with 3D Torus and Dragonfly topology. Our results show that the distributed SpMVM implementation that exploits matrix symmetry and hides communication yields the best value for the "CPU core hours" metric and significantly reduces data movement overheads.« less

Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method.

PubMed

He, Xiaowei; Liang, Jimin; Wang, Xiaorui; Yu, Jingjing; Qu, Xiaochao; Wang, Xiaodong; Hou, Yanbin; Chen, Duofang; Liu, Fang; Tian, Jie

2010-11-22

In this paper, we present an incomplete variables truncated conjugate gradient (IVTCG) method for bioluminescence tomography (BLT). Considering the sparse characteristic of the light source and insufficient surface measurement in the BLT scenarios, we combine a sparseness-inducing (ℓ1 norm) regularization term with a quadratic error term in the IVTCG-based framework for solving the inverse problem. By limiting the number of variables updated at each iterative and combining a variable splitting strategy to find the search direction more efficiently, it obtains fast and stable source reconstruction, even without a priori information of the permissible source region and multispectral measurements. Numerical experiments on a mouse atlas validate the effectiveness of the method. In vivo mouse experimental results further indicate its potential for a practical BLT system.

Using Fisher Information Criteria for Chemical Sensor Selection via Convex Optimization Methods

DTIC Science & Technology

2016-11-16

determinant of the inverse Fisher information matrix which is proportional to the global error volume. If a practitioner has a suitable...pro- ceeds from the determinant of the inverse Fisher information matrix which is proportional to the global error volume. If a practitioner has a...design of statistical estimators (i.e. sensors) as their respective inverses act as lower bounds to the (co)variances of the subject estimator, a property

STRONG ORACLE OPTIMALITY OF FOLDED CONCAVE PENALIZED ESTIMATION.

PubMed

Fan, Jianqing; Xue, Lingzhou; Zou, Hui

2014-06-01

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local linear approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local linear approximation. In addition, once the oracle estimator is obtained, the local linear approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, i.e., sparse linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression.

STRONG ORACLE OPTIMALITY OF FOLDED CONCAVE PENALIZED ESTIMATION

PubMed Central

Fan, Jianqing; Xue, Lingzhou; Zou, Hui

2014-01-01

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local linear approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local linear approximation. In addition, once the oracle estimator is obtained, the local linear approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, i.e., sparse linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression. PMID:25598560

Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems

DOE PAGES

Bavier, Eric; Hoemmen, Mark; Rajamanickam, Sivasankaran; ...

2012-01-01

Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples themore » algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.« less

Matrix computations in MACSYMA

NASA Technical Reports Server (NTRS)

Wang, P. S.

1977-01-01

Facilities built into MACSYMA for manipulating matrices with numeric or symbolic entries are described. Computations will be done exactly, keeping symbols as symbols. Topics discussed include how to form a matrix and create other matrices by transforming existing matrices within MACSYMA; arithmetic and other computation with matrices; and user control of computational processes through the use of optional variables. Two algorithms designed for sparse matrices are given. The computing times of several different ways to compute the determinant of a matrix are compared.

Fabric defect detection based on visual saliency using deep feature and low-rank recovery

NASA Astrophysics Data System (ADS)

Liu, Zhoufeng; Wang, Baorui; Li, Chunlei; Li, Bicao; Dong, Yan

2018-04-01

Fabric defect detection plays an important role in improving the quality of fabric product. In this paper, a novel fabric defect detection method based on visual saliency using deep feature and low-rank recovery was proposed. First, unsupervised training is carried out by the initial network parameters based on MNIST large datasets. The supervised fine-tuning of fabric image library based on Convolutional Neural Networks (CNNs) is implemented, and then more accurate deep neural network model is generated. Second, the fabric images are uniformly divided into the image block with the same size, then we extract their multi-layer deep features using the trained deep network. Thereafter, all the extracted features are concentrated into a feature matrix. Third, low-rank matrix recovery is adopted to divide the feature matrix into the low-rank matrix which indicates the background and the sparse matrix which indicates the salient defect. In the end, the iterative optimal threshold segmentation algorithm is utilized to segment the saliency maps generated by the sparse matrix to locate the fabric defect area. Experimental results demonstrate that the feature extracted by CNN is more suitable for characterizing the fabric texture than the traditional LBP, HOG and other hand-crafted features extraction method, and the proposed method can accurately detect the defect regions of various fabric defects, even for the image with complex texture.

Photon-efficient super-resolution laser radar

NASA Astrophysics Data System (ADS)

Shin, Dongeek; Shapiro, Jeffrey H.; Goyal, Vivek K.

2017-08-01

The resolution achieved in photon-efficient active optical range imaging systems can be low due to non-idealities such as propagation through a diffuse scattering medium. We propose a constrained optimization-based frame- work to address extremes in scarcity of photons and blurring by a forward imaging kernel. We provide two algorithms for the resulting inverse problem: a greedy algorithm, inspired by sparse pursuit algorithms; and a convex optimization heuristic that incorporates image total variation regularization. We demonstrate that our framework outperforms existing deconvolution imaging techniques in terms of peak signal-to-noise ratio. Since our proposed method is able to super-resolve depth features using small numbers of photon counts, it can be useful for observing fine-scale phenomena in remote sensing through a scattering medium and through-the-skin biomedical imaging applications.

Civil Engineering Applications of Ground Penetrating Radar Recent Advances @ the ELEDIA Research Center

NASA Astrophysics Data System (ADS)

Salucci, Marco; Tenuti, Lorenza; Nardin, Cristina; Oliveri, Giacomo; Viani, Federico; Rocca, Paolo; Massa, Andrea

2014-05-01

The application of non-destructive testing and evaluation (NDT/NDE) methodologies in civil engineering has raised a growing interest during the last years because of its potential impact in several different scenarios. As a consequence, Ground Penetrating Radar (GPR) technologies have been widely adopted as an instrument for the inspection of the structural stability of buildings and for the detection of cracks and voids. In this framework, the development and validation of GPR algorithms and methodologies represents one of the most active research areas within the ELEDIA Research Center of the University of Trento. More in detail, great efforts have been devoted towards the development of inversion techniques based on the integration of deterministic and stochastic search algorithms with multi-focusing strategies. These approaches proved to be effective in mitigating the effects of both nonlinearity and ill-posedness of microwave imaging problems, which represent the well-known issues arising in GPR inverse scattering formulations. More in detail, a regularized multi-resolution approach based on the Inexact Newton Method (INM) has been recently applied to subsurface prospecting, showing a remarkable advantage over a single-resolution implementation [1]. Moreover, the use of multi-frequency or frequency-hopping strategies to exploit the information coming from GPR data collected in time domain and transformed into its frequency components has been proposed as well. In this framework, the effectiveness of the multi-resolution multi-frequency techniques has been proven on synthetic data generated with numerical models such as GprMax [2]. The application of inversion algorithms based on Bayesian Compressive Sampling (BCS) [3][4] to GPR is currently under investigation, as well, in order to exploit their capability to provide satisfactory reconstructions in presence of single and multiple sparse scatterers [3][4]. Furthermore, multi-scaling approaches exploiting level-set-based optimization have been developed for the qualitative reconstruction of multiple and disconnected homogeneous scatterers [5]. Finally, the real-time detection and classification of subsurface scatterers has been investigated by means of learning-by-examples (LBE) techniques, such as Support Vector Machines (SVM) [6]. Acknowledgment - This work was partially supported by COST Action TU1208 'Civil Engineering Applications of Ground Penetrating Radar' References [1] M. Salucci, D. Sartori, N. Anselmi, A. Randazzo, G. Oliveri, and A. Massa, 'Imaging Buried Objects within the Second-Order Born Approximation through a Multiresolution Regularized Inexact-Newton Method', 2013 International Symposium on Electromagnetic Theory (EMTS), (Hiroshima, Japan), May 20-24 2013 (invited). [2] A. Giannopoulos, 'Modelling ground penetrating radar by GprMax', Construct. Build. Mater., vol. 19, no. 10, pp.755 -762 2005 [3] L. Poli, G. Oliveri, P. Rocca, and A. Massa, "Bayesian compressive sensing approaches for the reconstruction of two-dimensional sparse scatterers under TE illumination," IEEE Trans. Geosci. Remote Sensing, vol. 51, no. 5, pp. 2920-2936, May. 2013. [4] L. Poli, G. Oliveri, and A. Massa, "Imaging sparse metallic cylinders through a Local Shape Function Bayesian Compressive Sensing approach," Journal of Optical Society of America A, vol. 30, no. 6, pp. 1261-1272, 2013. [5] M. Benedetti, D. Lesselier, M. Lambert, and A. Massa, "Multiple shapes reconstruction by means of multi-region level sets," IEEE Trans. Geosci. Remote Sensing, vol. 48, no. 5, pp. 2330-2342, May 2010. [6] L. Lizzi, F. Viani, P. Rocca, G. Oliveri, M. Benedetti and A. Massa, "Three-dimensional real-time localization of subsurface objects - From theory to experimental validation," 2009 IEEE International Geoscience and Remote Sensing Symposium, vol. 2, pp. II-121-II-124, 12-17 July 2009.

Using absolute gravimeter data to determine vertical gravity gradients

USGS Publications Warehouse

Robertson, D.S.

2001-01-01

The position versus time data from a free-fall absolute gravimeter can be used to estimate the vertical gravity gradient in addition to the gravity value itself. Hipkin has reported success in estimating the vertical gradient value using a data set of unusually good quality. This paper explores techniques that may be applicable to a broader class of data that may be contaminated with "system response" errors of larger magnitude than were evident in the data used by Hipkin. This system response function is usually modelled as a sum of exponentially decaying sinusoidal components. The technique employed here involves combining the x0, v0 and g parameters from all the drops made during a site occupation into a single least-squares solution, and including the value of the vertical gradient and the coefficients of system response function in the same solution. The resulting non-linear equations must be solved iteratively and convergence presents some difficulties. Sparse matrix techniques are used to make the least-squares problem computationally tractable.

Neutron Multiplicity: LANL W Covariance Matrix for Curve Fitting

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wendelberger, James G.

2016-12-08

In neutron multiplicity counting one may fit a curve by minimizing an objective function, χmore » $$2\\atop{n}$$. The objective function includes the inverse of an n by n matrix of covariances, W. The inverse of the W matrix has a closed form solution. In addition W -1 is a tri-diagonal matrix. The closed form and tridiagonal nature allows for a simpler expression of the objective function χ$$2\\atop{n}$$. Minimization of this simpler expression will provide the optimal parameters for the fitted curve.« less

A robust bi-orthogonal/dynamically-orthogonal method using the covariance pseudo-inverse with application to stochastic flow problems

NASA Astrophysics Data System (ADS)

Babaee, Hessam; Choi, Minseok; Sapsis, Themistoklis P.; Karniadakis, George Em

2017-09-01

We develop a new robust methodology for the stochastic Navier-Stokes equations based on the dynamically-orthogonal (DO) and bi-orthogonal (BO) methods [1-3]. Both approaches are variants of a generalized Karhunen-Loève (KL) expansion in which both the stochastic coefficients and the spatial basis evolve according to system dynamics, hence, capturing the low-dimensional structure of the solution. The DO and BO formulations are mathematically equivalent [3], but they exhibit computationally complimentary properties. Specifically, the BO formulation may fail due to crossing of the eigenvalues of the covariance matrix, while both BO and DO become unstable when there is a high condition number of the covariance matrix or zero eigenvalues. To this end, we combine the two methods into a robust hybrid framework and in addition we employ a pseudo-inverse technique to invert the covariance matrix. The robustness of the proposed method stems from addressing the following issues in the DO/BO formulation: (i) eigenvalue crossing: we resolve the issue of eigenvalue crossing in the BO formulation by switching to the DO near eigenvalue crossing using the equivalence theorem and switching back to BO when the distance between eigenvalues is larger than a threshold value; (ii) ill-conditioned covariance matrix: we utilize a pseudo-inverse strategy to invert the covariance matrix; (iii) adaptivity: we utilize an adaptive strategy to add/remove modes to resolve the covariance matrix up to a threshold value. In particular, we introduce a soft-threshold criterion to allow the system to adapt to the newly added/removed mode and therefore avoid repetitive and unnecessary mode addition/removal. When the total variance approaches zero, we show that the DO/BO formulation becomes equivalent to the evolution equation of the Optimally Time-Dependent modes [4]. We demonstrate the capability of the proposed methodology with several numerical examples, namely (i) stochastic Burgers equation: we analyze the performance of the method in the presence of eigenvalue crossing and zero eigenvalues; (ii) stochastic Kovasznay flow: we examine the method in the presence of a singular covariance matrix; and (iii) we examine the adaptivity of the method for an incompressible flow over a cylinder where for large stochastic forcing thirteen DO/BO modes are active.

A path-oriented knowledge representation system: Defusing the combinatorial system

NASA Technical Reports Server (NTRS)

Karamouzis, Stamos T.; Barry, John S.; Smith, Steven L.; Feyock, Stefan

1995-01-01

LIMAP is a programming system oriented toward efficient information manipulation over fixed finite domains, and quantification over paths and predicates. A generalization of Warshall's Algorithm to precompute paths in a sparse matrix representation of semantic nets is employed to allow questions involving paths between components to be posed and answered easily. LIMAP's ability to cache all paths between two components in a matrix cell proved to be a computational obstacle, however, when the semantic net grew to realistic size. The present paper describes a means of mitigating this combinatorial explosion to an extent that makes the use of the LIMAP representation feasible for problems of significant size. The technique we describe radically reduces the size of the search space in which LIMAP must operate; semantic nets of more than 500 nodes have been attacked successfully. Furthermore, it appears that the procedure described is applicable not only to LIMAP, but to a number of other combinatorially explosive search space problems found in AI as well.

Lanczos eigensolution method for high-performance computers

NASA Technical Reports Server (NTRS)

Bostic, Susan W.

1991-01-01

The theory, computational analysis, and applications are presented of a Lanczos algorithm on high performance computers. The computationally intensive steps of the algorithm are identified as: the matrix factorization, the forward/backward equation solution, and the matrix vector multiples. These computational steps are optimized to exploit the vector and parallel capabilities of high performance computers. The savings in computational time from applying optimization techniques such as: variable band and sparse data storage and access, loop unrolling, use of local memory, and compiler directives are presented. Two large scale structural analysis applications are described: the buckling of a composite blade stiffened panel with a cutout, and the vibration analysis of a high speed civil transport. The sequential computational time for the panel problem executed on a CONVEX computer of 181.6 seconds was decreased to 14.1 seconds with the optimized vector algorithm. The best computational time of 23 seconds for the transport problem with 17,000 degs of freedom was on the the Cray-YMP using an average of 3.63 processors.

Optimal sparse approximation with integrate and fire neurons.

PubMed

Shapero, Samuel; Zhu, Mengchen; Hasler, Jennifer; Rozell, Christopher

2014-08-01

Sparse approximation is a hypothesized coding strategy where a population of sensory neurons (e.g. V1) encodes a stimulus using as few active neurons as possible. We present the Spiking LCA (locally competitive algorithm), a rate encoded Spiking Neural Network (SNN) of integrate and fire neurons that calculate sparse approximations. The Spiking LCA is designed to be equivalent to the nonspiking LCA, an analog dynamical system that converges on a ℓ(1)-norm sparse approximations exponentially. We show that the firing rate of the Spiking LCA converges on the same solution as the analog LCA, with an error inversely proportional to the sampling time. We simulate in NEURON a network of 128 neuron pairs that encode 8 × 8 pixel image patches, demonstrating that the network converges to nearly optimal encodings within 20 ms of biological time. We also show that when using more biophysically realistic parameters in the neurons, the gain function encourages additional ℓ(0)-norm sparsity in the encoding, relative both to ideal neurons and digital solvers.

Simultaneous inversion of intrinsic and scattering attenuation parameters incorporating multiple scattering effect

NASA Astrophysics Data System (ADS)

Ogiso, M.

2017-12-01

Heterogeneous attenuation structure is important for not only understanding the earth structure and seismotectonics, but also ground motion prediction. Attenuation of ground motion in high frequency range is often characterized by the distribution of intrinsic and scattering attenuation parameters (intrinsic Q and scattering coefficient). From the viewpoint of ground motion prediction, both intrinsic and scattering attenuation affect the maximum amplitude of ground motion while scattering attenuation also affect the duration time of ground motion. Hence, estimation of both attenuation parameters will lead to sophisticate the ground motion prediction. In this study, we try to estimate both parameters in southwestern Japan in a tomographic manner. We will conduct envelope fitting of seismic coda since coda has sensitivity to both intrinsic attenuation and scattering coefficients. Recently, Takeuchi (2016) successfully calculated differential envelope when these parameters have fluctuations. We adopted his equations to calculate partial derivatives of these parameters since we did not need to assume homogeneous velocity structure. Matrix for inversion of structural parameters would become too huge to solve in a straightforward manner. Hence, we adopted ART-type Bayesian Reconstruction Method (Hirahara, 1998) to project the difference of envelopes to structural parameters iteratively. We conducted checkerboard reconstruction test. We assumed checkerboard pattern of 0.4 degree interval in horizontal direction and 20 km in depth direction. Reconstructed structures well reproduced the assumed pattern in shallower part while not in deeper part. Since the inversion kernel has large sensitivity around source and stations, resolution in deeper part would be limited due to the sparse distribution of earthquakes. To apply the inversion method which described above to actual waveforms, we have to correct the effects of source and site amplification term. We consider these issues to estimate the actual intrinsic and scattering structures of the target region.Acknowledgment We used the waveforms of Hi-net, NIED. This study was supported by the Earthquake Research Institute of the University of Tokyo cooperative research program.

Parallel O(log n) algorithms for open- and closed-chain rigid multibody systems based on a new mass matrix factorization technique

NASA Technical Reports Server (NTRS)

Fijany, Amir

1993-01-01

In this paper, parallel O(log n) algorithms for computation of rigid multibody dynamics are developed. These parallel algorithms are derived by parallelization of new O(n) algorithms for the problem. The underlying feature of these O(n) algorithms is a drastically different strategy for decomposition of interbody force which leads to a new factorization of the mass matrix (M). Specifically, it is shown that a factorization of the inverse of the mass matrix in the form of the Schur Complement is derived as M(exp -1) = C - B(exp *)A(exp -1)B, wherein matrices C, A, and B are block tridiagonal matrices. The new O(n) algorithm is then derived as a recursive implementation of this factorization of M(exp -1). For the closed-chain systems, similar factorizations and O(n) algorithms for computation of Operational Space Mass Matrix lambda and its inverse lambda(exp -1) are also derived. It is shown that these O(n) algorithms are strictly parallel, that is, they are less efficient than other algorithms for serial computation of the problem. But, to our knowledge, they are the only known algorithms that can be parallelized and that lead to both time- and processor-optimal parallel algorithms for the problem, i.e., parallel O(log n) algorithms with O(n) processors. The developed parallel algorithms, in addition to their theoretical significance, are also practical from an implementation point of view due to their simple architectural requirements.

Convergence Speed of a Dynamical System for Sparse Recovery

NASA Astrophysics Data System (ADS)

Balavoine, Aurele; Rozell, Christopher J.; Romberg, Justin

2013-09-01

This paper studies the convergence rate of a continuous-time dynamical system for L1-minimization, known as the Locally Competitive Algorithm (LCA). Solving L1-minimization} problems efficiently and rapidly is of great interest to the signal processing community, as these programs have been shown to recover sparse solutions to underdetermined systems of linear equations and come with strong performance guarantees. The LCA under study differs from the typical L1 solver in that it operates in continuous time: instead of being specified by discrete iterations, it evolves according to a system of nonlinear ordinary differential equations. The LCA is constructed from simple components, giving it the potential to be implemented as a large-scale analog circuit. The goal of this paper is to give guarantees on the convergence time of the LCA system. To do so, we analyze how the LCA evolves as it is recovering a sparse signal from underdetermined measurements. We show that under appropriate conditions on the measurement matrix and the problem parameters, the path the LCA follows can be described as a sequence of linear differential equations, each with a small number of active variables. This allows us to relate the convergence time of the system to the restricted isometry constant of the matrix. Interesting parallels to sparse-recovery digital solvers emerge from this study. Our analysis covers both the noisy and noiseless settings and is supported by simulation results.

On determining important aspects of mathematical models: Application to problems in physics and chemistry

NASA Technical Reports Server (NTRS)

Rabitz, Herschel

1987-01-01

The use of parametric and functional gradient sensitivity analysis techniques is considered for models described by partial differential equations. By interchanging appropriate dependent and independent variables, questions of inverse sensitivity may be addressed to gain insight into the inversion of observational data for parameter and function identification in mathematical models. It may be argued that the presence of a subset of dominantly strong coupled dependent variables will result in the overall system sensitivity behavior collapsing into a simple set of scaling and self similarity relations amongst elements of the entire matrix of sensitivity coefficients. These general tools are generic in nature, but herein their application to problems arising in selected areas of physics and chemistry is presented.

Effects of multiple scattering and surface albedo on the photochemistry of the troposphere

NASA Technical Reports Server (NTRS)

Augustsson, T. R.; Tiwari, S. N.

1981-01-01

The effect of treatment of incoming solar radiation on the photochemistry of the troposphere is discussed. A one dimensional photochemical model of the troposphere containing the species of the nitrogen, oxygen, carbon, hydrogen, and sulfur families was developed. The vertical flux is simulated by use of the parameterized eddy diffusion coefficients. The photochemical model is coupled to a radiative transfer model that calculates the radiation field due to the incoming solar radiation which initiates much of the photochemistry of the troposphere. Vertical profiles of tropospheric species were compared with the Leighton approximation, radiative transfer, matrix inversion model. The radiative transfer code includes the effects of multiple scattering due to molecules and aerosols, pure absorption, and surface albedo on the transfer of incoming solar radiation. It is indicated that significant differences exist for several key photolysis frequencies and species number density profiles between the Leighton approximation and the profiles generated with, radiative transfer, matrix inversion technique. Most species show enhanced vertical profiles when the more realistic treatment of the incoming solar radiation field is included

Effects of multiple scattering and surface albedo on the photochemistry of the troposphere. Final report, period ending 30 Nov 1981

DOE Office of Scientific and Technical Information (OSTI.GOV)

Augustsson, T.R.; Tiwari, S.N.

The effect of treatment of incoming solar radiation on the photochemistry of the troposphere is discussed. A one dimensional photochemical model of the troposphere containing the species of the nitrogen, oxygen, carbon, hydrogen, and sulfur families was developed. The vertical flux is simulated by use of the parameterized eddy diffusion coefficients. The photochemical model is coupled to a radiative transfer model that calculates the radiation field due to the incoming solar radiation which initiates much of the photochemistry of the troposphere. Vertical profiles of tropospheric species were compared with the Leighton approximation, radiative transfer, matrix inversion model. The radiative transfermore » code includes the effects of multiple scattering due to molecules and aerosols, pure absorption, and surface albedo on the transfer of incoming solar radiation. It is indicated that significant differences exist for several key photolysis frequencies and species number density profiles between the Leighton approximation and the profiles generated with, radiative transfer, matrix inversion technique. Most species show enhanced vertical profiles when the more realistic treatment of the incoming solar radiation field is included« less

Efficient retrieval of landscape Hessian: Forced optimal covariance adaptive learning

NASA Astrophysics Data System (ADS)

Shir, Ofer M.; Roslund, Jonathan; Whitley, Darrell; Rabitz, Herschel

2014-06-01

Knowledge of the Hessian matrix at the landscape optimum of a controlled physical observable offers valuable information about the system robustness to control noise. The Hessian can also assist in physical landscape characterization, which is of particular interest in quantum system control experiments. The recently developed landscape theoretical analysis motivated the compilation of an automated method to learn the Hessian matrix about the global optimum without derivative measurements from noisy data. The current study introduces the forced optimal covariance adaptive learning (FOCAL) technique for this purpose. FOCAL relies on the covariance matrix adaptation evolution strategy (CMA-ES) that exploits covariance information amongst the control variables by means of principal component analysis. The FOCAL technique is designed to operate with experimental optimization, generally involving continuous high-dimensional search landscapes (≳30) with large Hessian condition numbers (≳104). This paper introduces the theoretical foundations of the inverse relationship between the covariance learned by the evolution strategy and the actual Hessian matrix of the landscape. FOCAL is presented and demonstrated to retrieve the Hessian matrix with high fidelity on both model landscapes and quantum control experiments, which are observed to possess nonseparable, nonquadratic search landscapes. The recovered Hessian forms were corroborated by physical knowledge of the systems. The implications of FOCAL extend beyond the investigated studies to potentially cover other physically motivated multivariate landscapes.

Hybrid reconstruction of quantum density matrix: when low-rank meets sparsity

NASA Astrophysics Data System (ADS)

Li, Kezhi; Zheng, Kai; Yang, Jingbei; Cong, Shuang; Liu, Xiaomei; Li, Zhaokai

2017-12-01

Both the mathematical theory and experiments have verified that the quantum state tomography based on compressive sensing is an efficient framework for the reconstruction of quantum density states. In recent physical experiments, we found that many unknown density matrices in which people are interested in are low-rank as well as sparse. Bearing this information in mind, in this paper we propose a reconstruction algorithm that combines the low-rank and the sparsity property of density matrices and further theoretically prove that the solution of the optimization function can be, and only be, the true density matrix satisfying the model with overwhelming probability, as long as a necessary number of measurements are allowed. The solver leverages the fixed-point equation technique in which a step-by-step strategy is developed by utilizing an extended soft threshold operator that copes with complex values. Numerical experiments of the density matrix estimation for real nuclear magnetic resonance devices reveal that the proposed method achieves a better accuracy compared to some existing methods. We believe that the proposed method could be leveraged as a generalized approach and widely implemented in the quantum state estimation.

Subspace aware recovery of low rank and jointly sparse signals

PubMed Central

Biswas, Sampurna; Dasgupta, Soura; Mudumbai, Raghuraman; Jacob, Mathews

2017-01-01

We consider the recovery of a matrix X, which is simultaneously low rank and joint sparse, from few measurements of its columns using a two-step algorithm. Each column of X is measured using a combination of two measurement matrices; one which is the same for every column, while the the second measurement matrix varies from column to column. The recovery proceeds by first estimating the row subspace vectors from the measurements corresponding to the common matrix. The estimated row subspace vectors are then used to recover X from all the measurements using a convex program of joint sparsity minimization. Our main contribution is to provide sufficient conditions on the measurement matrices that guarantee the recovery of such a matrix using the above two-step algorithm. The results demonstrate quite significant savings in number of measurements when compared to the standard multiple measurement vector (MMV) scheme, which assumes same time invariant measurement pattern for all the time frames. We illustrate the impact of the sampling pattern on reconstruction quality using breath held cardiac cine MRI and cardiac perfusion MRI data, while the utility of the algorithm to accelerate the acquisition is demonstrated on MR parameter mapping. PMID:28630889

Two variants of minimum discarded fill ordering

DOE Office of Scientific and Technical Information (OSTI.GOV)

D'Azevedo, E.F.; Forsyth, P.A.; Tang, Wei-Pai

1991-01-01

It is well known that the ordering of the unknowns can have a significant effect on the convergence of Preconditioned Conjugate Gradient (PCG) methods. There has been considerable experimental work on the effects of ordering for regular finite difference problems. In many cases, good results have been obtained with preconditioners based on diagonal, spiral or natural row orderings. However, for finite element problems having unstructured grids or grids generated by a local refinement approach, it is difficult to define many of the orderings for more regular problems. A recently proposed Minimum Discarded Fill (MDF) ordering technique is effective in findingmore » high quality Incomplete LU (ILU) preconditioners, especially for problems arising from unstructured finite element grids. Testing indicates this algorithm can identify a rather complicated physical structure in an anisotropic problem and orders the unknowns in the preferred'' direction. The MDF technique may be viewed as the numerical analogue of the minimum deficiency algorithm in sparse matrix technology. At any stage of the partial elimination, the MDF technique chooses the next pivot node so as to minimize the amount of discarded fill. In this work, two efficient variants of the MDF technique are explored to produce cost-effective high-order ILU preconditioners. The Threshold MDF orderings combine MDF ideas with drop tolerance techniques to identify the sparsity pattern in the ILU preconditioners. These techniques identify an ordering that encourages fast decay of the entries in the ILU factorization. The Minimum Update Matrix (MUM) ordering technique is a simplification of the MDF ordering and is closely related to the minimum degree algorithm. The MUM ordering is especially for large problems arising from Navier-Stokes problems. Some interesting pictures of the orderings are presented using a visualization tool. 22 refs., 4 figs., 7 tabs.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ray, Jaideep; Lee, Jina; Lefantzi, Sophia

The estimation of fossil-fuel CO2 emissions (ffCO2) from limited ground-based and satellite measurements of CO2 concentrations will form a key component of the monitoring of treaties aimed at the abatement of greenhouse gas emissions. To that end, we construct a multiresolution spatial parametrization for fossil-fuel CO2 emissions (ffCO2), to be used in atmospheric inversions. Such a parametrization does not currently exist. The parametrization uses wavelets to accurately capture the multiscale, nonstationary nature of ffCO2 emissions and employs proxies of human habitation, e.g., images of lights at night and maps of built-up areas to reduce the dimensionality of the multiresolution parametrization.more » The parametrization is used in a synthetic data inversion to test its suitability for use in atmospheric inverse problem. This linear inverse problem is predicated on observations of ffCO2 concentrations collected at measurement towers. We adapt a convex optimization technique, commonly used in the reconstruction of compressively sensed images, to perform sparse reconstruction of the time-variant ffCO2 emission field. We also borrow concepts from compressive sensing to impose boundary conditions i.e., to limit ffCO2 emissions within an irregularly shaped region (the United States, in our case). We find that the optimization algorithm performs a data-driven sparsification of the spatial parametrization and retains only of those wavelets whose weights could be estimated from the observations. Further, our method for the imposition of boundary conditions leads to a 10computational saving over conventional means of doing so. We conclude with a discussion of the accuracy of the estimated emissions and the suitability of the spatial parametrization for use in inverse problems with a significant degree of regularization.« less

Bayesian Approach to the Joint Inversion of Gravity and Magnetic Data, with Application to the Ismenius Area of Mars

NASA Technical Reports Server (NTRS)

Jewell, Jeffrey B.; Raymond, C.; Smrekar, S.; Millbury, C.

2004-01-01

This viewgraph presentation reviews a Bayesian approach to the inversion of gravity and magnetic data with specific application to the Ismenius Area of Mars. Many inverse problems encountered in geophysics and planetary science are well known to be non-unique (i.e. inversion of gravity the density structure of a body). In hopes of reducing the non-uniqueness of solutions, there has been interest in the joint analysis of data. An example is the joint inversion of gravity and magnetic data, with the assumption that the same physical anomalies generate both the observed magnetic and gravitational anomalies. In this talk, we formulate the joint analysis of different types of data in a Bayesian framework and apply the formalism to the inference of the density and remanent magnetization structure for a local region in the Ismenius area of Mars. The Bayesian approach allows prior information or constraints in the solutions to be incorporated in the inversion, with the "best" solutions those whose forward predictions most closely match the data while remaining consistent with assumed constraints. The application of this framework to the inversion of gravity and magnetic data on Mars reveals two typical challenges - the forward predictions of the data have a linear dependence on some of the quantities of interest, and non-linear dependence on others (termed the "linear" and "non-linear" variables, respectively). For observations with Gaussian noise, a Bayesian approach to inversion for "linear" variables reduces to a linear filtering problem, with an explicitly computable "error" matrix. However, for models whose forward predictions have non-linear dependencies, inference is no longer given by such a simple linear problem, and moreover, the uncertainty in the solution is no longer completely specified by a computable "error matrix". It is therefore important to develop methods for sampling from the full Bayesian posterior to provide a complete and statistically consistent picture of model uncertainty, and what has been learned from observations. We will discuss advanced numerical techniques, including Monte Carlo Markov

Computationally efficient modeling and simulation of large scale systems

NASA Technical Reports Server (NTRS)

Jain, Jitesh (Inventor); Cauley, Stephen F. (Inventor); Li, Hong (Inventor); Koh, Cheng-Kok (Inventor); Balakrishnan, Venkataramanan (Inventor)

2010-01-01

A method of simulating operation of a VLSI interconnect structure having capacitive and inductive coupling between nodes thereof. A matrix X and a matrix Y containing different combinations of passive circuit element values for the interconnect structure are obtained where the element values for each matrix include inductance L and inverse capacitance P. An adjacency matrix A associated with the interconnect structure is obtained. Numerical integration is used to solve first and second equations, each including as a factor the product of the inverse matrix X.sup.1 and at least one other matrix, with first equation including X.sup.1Y, X.sup.1A, and X.sup.1P, and the second equation including X.sup.1A and X.sup.1P.

Total-variation based velocity inversion with Bregmanized operator splitting algorithm

NASA Astrophysics Data System (ADS)

Zand, Toktam; Gholami, Ali

2018-04-01

Many problems in applied geophysics can be formulated as a linear inverse problem. The associated problems, however, are large-scale and ill-conditioned. Therefore, regularization techniques are needed to be employed for solving them and generating a stable and acceptable solution. We consider numerical methods for solving such problems in this paper. In order to tackle the ill-conditioning of the problem we use blockiness as a prior information of the subsurface parameters and formulate the problem as a constrained total variation (TV) regularization. The Bregmanized operator splitting (BOS) algorithm as a combination of the Bregman iteration and the proximal forward backward operator splitting method is developed to solve the arranged problem. Two main advantages of this new algorithm are that no matrix inversion is required and that a discrepancy stopping criterion is used to stop the iterations, which allow efficient solution of large-scale problems. The high performance of the proposed TV regularization method is demonstrated using two different experiments: 1) velocity inversion from (synthetic) seismic data which is based on Born approximation, 2) computing interval velocities from RMS velocities via Dix formula. Numerical examples are presented to verify the feasibility of the proposed method for high-resolution velocity inversion.

On the recovery of missing low and high frequency information from bandlimited reflectivity data

NASA Astrophysics Data System (ADS)

Sacchi, M. D.; Ulrych, T. J.

2007-12-01

During the last two decades, an important effort in the seismic exploration community has been made to retrieve broad-band seismic data by means of deconvolution and inversion. In general, the problem can be stated as a spectral reconstruction problem. In other words, given limited spectral information about the earth's reflectivity sequence, one attempts to create a broadband estimate of the Fourier spectra of the unknown reflectivity. Techniques based on the principle of parsimony can be effectively used to retrieve a sparse spike sequence and, consequently, a broad band signal. Alternatively, continuation methods, e.g., autoregressive modeling, can be used to extrapolate the recorded bandwidth of the seismic signal. The goal of this paper is to examine under what conditions the recovery of low and high frequencies from band-limited and noisy signals is possible. At the heart of the methods we discuss, is the celebrated non-Gaussian assumption so important in many modern signal processing methods, such as ICA, for example. Spectral recovery from limited information tends to work when the reflectivity consist of a few well isolated events. Results degrade with the number of reflectors, decreasing SNR and decreasing bandwidth of the source wavelet. Constrains and information-based priors can be used to stabilize the recovery but, as in all inverse problems, the solution is nonunique and effort is required to understand the level of recovery that is achievable, always keeping the physics of the problem in mind. We provide in this paper, a survey of methods to recover broad-band reflectivity sequences and examine the role that these techniques can play in the processing and inversion as applied to exploration and global seismology.

Hyperspherical Sparse Approximation Techniques for High-Dimensional Discontinuity Detection

DOE PAGES

Zhang, Guannan; Webster, Clayton G.; Gunzburger, Max; ...

2016-08-04

This work proposes a hyperspherical sparse approximation framework for detecting jump discontinuities in functions in high-dimensional spaces. The need for a novel approach results from the theoretical and computational inefficiencies of well-known approaches, such as adaptive sparse grids, for discontinuity detection. Our approach constructs the hyperspherical coordinate representation of the discontinuity surface of a function. Then sparse approximations of the transformed function are built in the hyperspherical coordinate system, with values at each point estimated by solving a one-dimensional discontinuity detection problem. Due to the smoothness of the hypersurface, the new technique can identify jump discontinuities with significantly reduced computationalmore » cost, compared to existing methods. Several approaches are used to approximate the transformed discontinuity surface in the hyperspherical system, including adaptive sparse grid and radial basis function interpolation, discrete least squares projection, and compressed sensing approximation. Moreover, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. In conclusion, rigorous complexity analyses of the new methods are provided, as are several numerical examples that illustrate the effectiveness of our approach.« less

TRANSPOSABLE REGULARIZED COVARIANCE MODELS WITH AN APPLICATION TO MISSING DATA IMPUTATION

PubMed Central

Allen, Genevera I.; Tibshirani, Robert

2015-01-01

Missing data estimation is an important challenge with high-dimensional data arranged in the form of a matrix. Typically this data matrix is transposable, meaning that either the rows, columns or both can be treated as features. To model transposable data, we present a modification of the matrix-variate normal, the mean-restricted matrix-variate normal, in which the rows and columns each have a separate mean vector and covariance matrix. By placing additive penalties on the inverse covariance matrices of the rows and columns, these so called transposable regularized covariance models allow for maximum likelihood estimation of the mean and non-singular covariance matrices. Using these models, we formulate EM-type algorithms for missing data imputation in both the multivariate and transposable frameworks. We present theoretical results exploiting the structure of our transposable models that allow these models and imputation methods to be applied to high-dimensional data. Simulations and results on microarray data and the Netflix data show that these imputation techniques often outperform existing methods and offer a greater degree of flexibility. PMID:26877823

TRANSPOSABLE REGULARIZED COVARIANCE MODELS WITH AN APPLICATION TO MISSING DATA IMPUTATION.

PubMed

Allen, Genevera I; Tibshirani, Robert

2010-06-01

Missing data estimation is an important challenge with high-dimensional data arranged in the form of a matrix. Typically this data matrix is transposable , meaning that either the rows, columns or both can be treated as features. To model transposable data, we present a modification of the matrix-variate normal, the mean-restricted matrix-variate normal , in which the rows and columns each have a separate mean vector and covariance matrix. By placing additive penalties on the inverse covariance matrices of the rows and columns, these so called transposable regularized covariance models allow for maximum likelihood estimation of the mean and non-singular covariance matrices. Using these models, we formulate EM-type algorithms for missing data imputation in both the multivariate and transposable frameworks. We present theoretical results exploiting the structure of our transposable models that allow these models and imputation methods to be applied to high-dimensional data. Simulations and results on microarray data and the Netflix data show that these imputation techniques often outperform existing methods and offer a greater degree of flexibility.

Development of a spectroscopic Mueller matrix imaging ellipsometer for nanostructure metrology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Xiuguo; Du, Weichao; Yuan, Kui

2016-05-15

In this paper, we describe the development of a spectroscopic Mueller matrix imaging ellipsometer (MMIE), which combines the great power of Mueller matrix ellipsometry with the high spatial resolution of optical microscopy. A dual rotating-compensator configuration is adopted to collect the full 4 × 4 imaging Mueller matrix in a single measurement. The light wavelengths are scanned in the range of 400–700 nm by a monochromator. The instrument has measurement accuracy and precision better than 0.01 for all the Mueller matrix elements in both the whole image and the whole spectral range. The instrument was then applied for the measurementmore » of nanostructures combined with an inverse diffraction problem solving technique. The experiment performed on a photoresist grating sample has demonstrated the great potential of MMIE for accurate grating reconstruction from spectral data collected by a single pixel of the camera and for efficient quantification of geometrical profile of the grating structure over a large area with pixel resolution. It is expected that MMIE will be a powerful tool for nanostructure metrology in future high-volume nanomanufacturing.« less

Random matrix theory and fund of funds portfolio optimisation

NASA Astrophysics Data System (ADS)

Conlon, T.; Ruskin, H. J.; Crane, M.

2007-08-01

The proprietary nature of Hedge Fund investing means that it is common practise for managers to release minimal information about their returns. The construction of a fund of hedge funds portfolio requires a correlation matrix which often has to be estimated using a relatively small sample of monthly returns data which induces noise. In this paper, random matrix theory (RMT) is applied to a cross-correlation matrix C, constructed using hedge fund returns data. The analysis reveals a number of eigenvalues that deviate from the spectrum suggested by RMT. The components of the deviating eigenvectors are found to correspond to distinct groups of strategies that are applied by hedge fund managers. The inverse participation ratio is used to quantify the number of components that participate in each eigenvector. Finally, the correlation matrix is cleaned by separating the noisy part from the non-noisy part of C. This technique is found to greatly reduce the difference between the predicted and realised risk of a portfolio, leading to an improved risk profile for a fund of hedge funds.

Using seismic derived lithology parameters for hydrocarbon indication

DOE Office of Scientific and Technical Information (OSTI.GOV)

Van Riel, P.; Sisk, M.

1996-08-01

The last two decades have shown a strong increase in the use of seismic amplitude information for direct hydrocarbon indication. However, working with seismic amplitudes (and seismic attributes) has several drawbacks: tuning effects must be handled; quantitative analysis is difficult because seismic amplitudes are not directly related to lithology; and seismic amplitudes are reflection events, making it is unclear if amplitude changes relate to lithology variations above or below the interface. These drawbacks are overcome by working directly on seismic derived lithology data, lithology being a layer property rather than an interface property. Technology to extract lithology from seismic datamore » has made great strides, and a large range of methods are now available to users including: (1) Bandlimited acoustic impedance (AI) inversion; (2) Reconstruction of the low AI frequencies from seismic velocities, from spatial well log interpolation, and using constrained sparse spike inversion techniques; (3) Full bandwidth reconstruction of multiple lithology properties (porosity, sand fraction, density etc.,) in time and depth using inverse modeling. For these technologies to be fully leveraged, accessibility by end users is critical. All these technologies are available as interactive 2D and 3D workstation applications, integrated with seismic interpretation functionality. Using field data examples, we will demonstrate the impact of these different approaches on deriving lithology, and in particular show how accuracy and resolution is increased as more geologic and well information is added.« less

Sensitivity of a Bayesian atmospheric-transport inversion model to spatio-temporal sensor resolution applied to the 2006 North Korean nuclear test

NASA Astrophysics Data System (ADS)

Lundquist, K. A.; Jensen, D. D.; Lucas, D. D.

2017-12-01

Atmospheric source reconstruction allows for the probabilistic estimate of source characteristics of an atmospheric release using observations of the release. Performance of the inversion depends partially on the temporal frequency and spatial scale of the observations. The objective of this study is to quantify the sensitivity of the source reconstruction method to sparse spatial and temporal observations. To this end, simulations of atmospheric transport of noble gasses are created for the 2006 nuclear test at the Punggye-ri nuclear test site. Synthetic observations are collected from the simulation, and are taken as "ground truth". Data denial techniques are used to progressively coarsen the temporal and spatial resolution of the synthetic observations, while the source reconstruction model seeks to recover the true input parameters from the synthetic observations. Reconstructed parameters considered here are source location, source timing and source quantity. Reconstruction is achieved by running an ensemble of thousands of dispersion model runs that sample from a uniform distribution of the input parameters. Machine learning is used to train a computationally-efficient surrogate model from the ensemble simulations. Monte Carlo sampling and Bayesian inversion are then used in conjunction with the surrogate model to quantify the posterior probability density functions of source input parameters. This research seeks to inform decision makers of the tradeoffs between more expensive, high frequency observations and less expensive, low frequency observations.