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.

Comparison of multihardware parallel implementations for a phase unwrapping algorithm

NASA Astrophysics Data System (ADS)

Hernandez-Lopez, Francisco Javier; Rivera, Mariano; Salazar-Garibay, Adan; Legarda-Sáenz, Ricardo

2018-04-01

Phase unwrapping is an important problem in the areas of optical metrology, synthetic aperture radar (SAR) image analysis, and magnetic resonance imaging (MRI) analysis. These images are becoming larger in size and, particularly, the availability and need for processing of SAR and MRI data have increased significantly with the acquisition of remote sensing data and the popularization of magnetic resonators in clinical diagnosis. Therefore, it is important to develop faster and accurate phase unwrapping algorithms. We propose a parallel multigrid algorithm of a phase unwrapping method named accumulation of residual maps, which builds on a serial algorithm that consists of the minimization of a cost function; minimization achieved by means of a serial Gauss-Seidel kind algorithm. Our algorithm also optimizes the original cost function, but unlike the original work, our algorithm is a parallel Jacobi class with alternated minimizations. This strategy is known as the chessboard type, where red pixels can be updated in parallel at same iteration since they are independent. Similarly, black pixels can be updated in parallel in an alternating iteration. We present parallel implementations of our algorithm for different parallel multicore architecture such as CPU-multicore, Xeon Phi coprocessor, and Nvidia graphics processing unit. In all the cases, we obtain a superior performance of our parallel algorithm when compared with the original serial version. In addition, we present a detailed comparative performance of the developed parallel versions.

Efficient data communication protocols for wireless networks

NASA Astrophysics Data System (ADS)

Zeydan, Engin

In this dissertation, efficient decentralized algorithms are investigated for cost minimization problems in wireless networks. For wireless sensor networks, we investigate both the reduction in the energy consumption and throughput maximization problems separately using multi-hop data aggregation for correlated data in wireless sensor networks. The proposed algorithms exploit data redundancy using a game theoretic framework. For energy minimization, routes are chosen to minimize the total energy expended by the network using best response dynamics to local data. The cost function used in routing takes into account distance, interference and in-network data aggregation. The proposed energy-efficient correlation-aware routing algorithm significantly reduces the energy consumption in the network and converges in a finite number of steps iteratively. For throughput maximization, we consider both the interference distribution across the network and correlation between forwarded data when establishing routes. Nodes along each route are chosen to minimize the interference impact in their neighborhood and to maximize the in-network data aggregation. The resulting network topology maximizes the global network throughput and the algorithm is guaranteed to converge with a finite number of steps using best response dynamics. For multiple antenna wireless ad-hoc networks, we present distributed cooperative and regret-matching based learning schemes for joint transmit beanformer and power level selection problem for nodes operating in multi-user interference environment. Total network transmit power is minimized while ensuring a constant received signal-to-interference and noise ratio at each receiver. In cooperative and regret-matching based power minimization algorithms, transmit beanformers are selected from a predefined codebook to minimize the total power. By selecting transmit beamformers judiciously and performing power adaptation, the cooperative algorithm is shown to converge to pure strategy Nash equilibrium with high probability throughout the iterations in the interference impaired network. On the other hand, the regret-matching learning algorithm is noncooperative and requires minimum amount of overhead. The proposed cooperative and regret-matching based distributed algorithms are also compared with centralized solutions through simulation results.

Compressively sampled MR image reconstruction using generalized thresholding iterative algorithm

NASA Astrophysics Data System (ADS)

Elahi, Sana; kaleem, Muhammad; Omer, Hammad

2018-01-01

Compressed sensing (CS) is an emerging area of interest in Magnetic Resonance Imaging (MRI). CS is used for the reconstruction of the images from a very limited number of samples in k-space. This significantly reduces the MRI data acquisition time. One important requirement for signal recovery in CS is the use of an appropriate non-linear reconstruction algorithm. It is a challenging task to choose a reconstruction algorithm that would accurately reconstruct the MR images from the under-sampled k-space data. Various algorithms have been used to solve the system of non-linear equations for better image quality and reconstruction speed in CS. In the recent past, iterative soft thresholding algorithm (ISTA) has been introduced in CS-MRI. This algorithm directly cancels the incoherent artifacts produced because of the undersampling in k -space. This paper introduces an improved iterative algorithm based on p -thresholding technique for CS-MRI image reconstruction. The use of p -thresholding function promotes sparsity in the image which is a key factor for CS based image reconstruction. The p -thresholding based iterative algorithm is a modification of ISTA, and minimizes non-convex functions. It has been shown that the proposed p -thresholding iterative algorithm can be used effectively to recover fully sampled image from the under-sampled data in MRI. The performance of the proposed method is verified using simulated and actual MRI data taken at St. Mary's Hospital, London. The quality of the reconstructed images is measured in terms of peak signal-to-noise ratio (PSNR), artifact power (AP), and structural similarity index measure (SSIM). The proposed approach shows improved performance when compared to other iterative algorithms based on log thresholding, soft thresholding and hard thresholding techniques at different reduction factors.

Comparison of sorting algorithms to increase the range of Hartmann-Shack aberrometry.

PubMed

Bedggood, Phillip; Metha, Andrew

2010-01-01

Recently many software-based approaches have been suggested for improving the range and accuracy of Hartmann-Shack aberrometry. We compare the performance of four representative algorithms, with a focus on aberrometry for the human eye. Algorithms vary in complexity from the simplistic traditional approach to iterative spline extrapolation based on prior spot measurements. Range is assessed for a variety of aberration types in isolation using computer modeling, and also for complex wavefront shapes using a real adaptive optics system. The effects of common sources of error for ocular wavefront sensing are explored. The results show that the simplest possible iterative algorithm produces comparable range and robustness compared to the more complicated algorithms, while keeping processing time minimal to afford real-time analysis.

Comparison of sorting algorithms to increase the range of Hartmann-Shack aberrometry

NASA Astrophysics Data System (ADS)

Bedggood, Phillip; Metha, Andrew

2010-11-01

Recently many software-based approaches have been suggested for improving the range and accuracy of Hartmann-Shack aberrometry. We compare the performance of four representative algorithms, with a focus on aberrometry for the human eye. Algorithms vary in complexity from the simplistic traditional approach to iterative spline extrapolation based on prior spot measurements. Range is assessed for a variety of aberration types in isolation using computer modeling, and also for complex wavefront shapes using a real adaptive optics system. The effects of common sources of error for ocular wavefront sensing are explored. The results show that the simplest possible iterative algorithm produces comparable range and robustness compared to the more complicated algorithms, while keeping processing time minimal to afford real-time analysis.

RMP: Reduced-set matching pursuit approach for efficient compressed sensing signal reconstruction.

PubMed

Abdel-Sayed, Michael M; Khattab, Ahmed; Abu-Elyazeed, Mohamed F

2016-11-01

Compressed sensing enables the acquisition of sparse signals at a rate that is much lower than the Nyquist rate. Compressed sensing initially adopted [Formula: see text] minimization for signal reconstruction which is computationally expensive. Several greedy recovery algorithms have been recently proposed for signal reconstruction at a lower computational complexity compared to the optimal [Formula: see text] minimization, while maintaining a good reconstruction accuracy. In this paper, the Reduced-set Matching Pursuit (RMP) greedy recovery algorithm is proposed for compressed sensing. Unlike existing approaches which either select too many or too few values per iteration, RMP aims at selecting the most sufficient number of correlation values per iteration, which improves both the reconstruction time and error. Furthermore, RMP prunes the estimated signal, and hence, excludes the incorrectly selected values. The RMP algorithm achieves a higher reconstruction accuracy at a significantly low computational complexity compared to existing greedy recovery algorithms. It is even superior to [Formula: see text] minimization in terms of the normalized time-error product, a new metric introduced to measure the trade-off between the reconstruction time and error. RMP superior performance is illustrated with both noiseless and noisy samples.

Reconstruction of sparse-view X-ray computed tomography using adaptive iterative algorithms.

PubMed

Liu, Li; Lin, Weikai; Jin, Mingwu

2015-01-01

In this paper, we propose two reconstruction algorithms for sparse-view X-ray computed tomography (CT). Treating the reconstruction problems as data fidelity constrained total variation (TV) minimization, both algorithms adapt the alternate two-stage strategy: projection onto convex sets (POCS) for data fidelity and non-negativity constraints and steepest descent for TV minimization. The novelty of this work is to determine iterative parameters automatically from data, thus avoiding tedious manual parameter tuning. In TV minimization, the step sizes of steepest descent are adaptively adjusted according to the difference from POCS update in either the projection domain or the image domain, while the step size of algebraic reconstruction technique (ART) in POCS is determined based on the data noise level. In addition, projection errors are used to compare with the error bound to decide whether to perform ART so as to reduce computational costs. The performance of the proposed methods is studied and evaluated using both simulated and physical phantom data. Our methods with automatic parameter tuning achieve similar, if not better, reconstruction performance compared to a representative two-stage algorithm. Copyright © 2014 Elsevier Ltd. All rights reserved.

A parallel Jacobson-Oksman optimization algorithm. [parallel processing (computers)

NASA Technical Reports Server (NTRS)

Straeter, T. A.; Markos, A. T.

1975-01-01

A gradient-dependent optimization technique which exploits the vector-streaming or parallel-computing capabilities of some modern computers is presented. The algorithm, derived by assuming that the function to be minimized is homogeneous, is a modification of the Jacobson-Oksman serial minimization method. In addition to describing the algorithm, conditions insuring the convergence of the iterates of the algorithm and the results of numerical experiments on a group of sample test functions are presented. The results of these experiments indicate that this algorithm will solve optimization problems in less computing time than conventional serial methods on machines having vector-streaming or parallel-computing capabilities.

Image restoration by minimizing zero norm of wavelet frame coefficients

NASA Astrophysics Data System (ADS)

Bao, Chenglong; Dong, Bin; Hou, Likun; Shen, Zuowei; Zhang, Xiaoqun; Zhang, Xue

2016-11-01

In this paper, we propose two algorithms, namely the extrapolated proximal iterative hard thresholding (EPIHT) algorithm and the EPIHT algorithm with line-search, for solving the {{\\ell }}0-norm regularized wavelet frame balanced approach for image restoration. Under the theoretical framework of Kurdyka-Łojasiewicz property, we show that the sequences generated by the two algorithms converge to a local minimizer with linear convergence rate. Moreover, extensive numerical experiments on sparse signal reconstruction and wavelet frame based image restoration problems including CT reconstruction, image deblur, demonstrate the improvement of {{\\ell }}0-norm based regularization models over some prevailing ones, as well as the computational efficiency of the proposed algorithms.

Upwind relaxation methods for the Navier-Stokes equations using inner iterations

NASA Technical Reports Server (NTRS)

Taylor, Arthur C., III; Ng, Wing-Fai; Walters, Robert W.

1992-01-01

A subsonic and a supersonic problem are respectively treated by an upwind line-relaxation algorithm for the Navier-Stokes equations using inner iterations to accelerate steady-state solution convergence and thereby minimize CPU time. While the ability of the inner iterative procedure to mimic the quadratic convergence of the direct solver method is attested to in both test problems, some of the nonquadratic inner iterative results are noted to have been more efficient than the quadratic. In the more successful, supersonic test case, inner iteration required only about 65 percent of the line-relaxation method-entailed CPU time.

Nonconvex Nonsmooth Low Rank Minimization via Iteratively Reweighted Nuclear Norm.

PubMed

Lu, Canyi; Tang, Jinhui; Yan, Shuicheng; Lin, Zhouchen

2016-02-01

The nuclear norm is widely used as a convex surrogate of the rank function in compressive sensing for low rank matrix recovery with its applications in image recovery and signal processing. However, solving the nuclear norm-based relaxed convex problem usually leads to a suboptimal solution of the original rank minimization problem. In this paper, we propose to use a family of nonconvex surrogates of L0-norm on the singular values of a matrix to approximate the rank function. This leads to a nonconvex nonsmooth minimization problem. Then, we propose to solve the problem by an iteratively re-weighted nuclear norm (IRNN) algorithm. IRNN iteratively solves a weighted singular value thresholding problem, which has a closed form solution due to the special properties of the nonconvex surrogate functions. We also extend IRNN to solve the nonconvex problem with two or more blocks of variables. In theory, we prove that the IRNN decreases the objective function value monotonically, and any limit point is a stationary point. Extensive experiments on both synthesized data and real images demonstrate that IRNN enhances the low rank matrix recovery compared with the state-of-the-art convex algorithms.

Penalized weighted least-squares approach for low-dose x-ray computed tomography

NASA Astrophysics Data System (ADS)

Wang, Jing; Li, Tianfang; Lu, Hongbing; Liang, Zhengrong

2006-03-01

The noise of low-dose computed tomography (CT) sinogram follows approximately a Gaussian distribution with nonlinear dependence between the sample mean and variance. The noise is statistically uncorrelated among detector bins at any view angle. However the correlation coefficient matrix of data signal indicates a strong signal correlation among neighboring views. Based on above observations, Karhunen-Loeve (KL) transform can be used to de-correlate the signal among the neighboring views. In each KL component, a penalized weighted least-squares (PWLS) objective function can be constructed and optimal sinogram can be estimated by minimizing the objective function, followed by filtered backprojection (FBP) for CT image reconstruction. In this work, we compared the KL-PWLS method with an iterative image reconstruction algorithm, which uses the Gauss-Seidel iterative calculation to minimize the PWLS objective function in image domain. We also compared the KL-PWLS with an iterative sinogram smoothing algorithm, which uses the iterated conditional mode calculation to minimize the PWLS objective function in sinogram space, followed by FBP for image reconstruction. Phantom experiments show a comparable performance of these three PWLS methods in suppressing the noise-induced artifacts and preserving resolution in reconstructed images. Computer simulation concurs with the phantom experiments in terms of noise-resolution tradeoff and detectability in low contrast environment. The KL-PWLS noise reduction may have the advantage in computation for low-dose CT imaging, especially for dynamic high-resolution studies.

A look-ahead variant of the Lanczos algorithm and its application to the quasi-minimal residual method for non-Hermitian linear systems. Ph.D. Thesis - Massachusetts Inst. of Technology, Aug. 1991

NASA Technical Reports Server (NTRS)

Nachtigal, Noel M.

1991-01-01

The Lanczos algorithm can be used both for eigenvalue problems and to solve linear systems. However, when applied to non-Hermitian matrices, the classical Lanczos algorithm is susceptible to breakdowns and potential instabilities. In addition, the biconjugate gradient (BCG) algorithm, which is the natural generalization of the conjugate gradient algorithm to non-Hermitian linear systems, has a second source of breakdowns, independent of the Lanczos breakdowns. Here, we present two new results. We propose an implementation of a look-ahead variant of the Lanczos algorithm which overcomes the breakdowns by skipping over those steps where a breakdown or a near-breakdown would occur. The new algorithm can handle look-ahead steps of any length and requires the same number of matrix-vector products and inner products per step as the classical Lanczos algorithm without look-ahead. Based on the proposed look-ahead Lanczos algorithm, we then present a novel BCG-like approach, the quasi-minimal residual (QMR) method, which avoids the second source of breakdowns in the BCG algorithm. We present details of the new method and discuss some of its properties. In particular, we discuss the relationship between QMR and BCG, showing how one can recover the BCG iterates, when they exist, from the QMR iterates. We also present convergence results for QMR, showing the connection between QMR and the generalized minimal residual (GMRES) algorithm, the optimal method in this class of methods. Finally, we give some numerical examples, both for eigenvalue computations and for non-Hermitian linear systems.

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes. Part 3; The Map and Related Decoding Algirithms

NASA Technical Reports Server (NTRS)

Lin, Shu; Fossorier, Marc

1998-01-01

In a coded communication system with equiprobable signaling, MLD minimizes the word error probability and delivers the most likely codeword associated with the corresponding received sequence. This decoding has two drawbacks. First, minimization of the word error probability is not equivalent to minimization of the bit error probability. Therefore, MLD becomes suboptimum with respect to the bit error probability. Second, MLD delivers a hard-decision estimate of the received sequence, so that information is lost between the input and output of the ML decoder. This information is important in coded schemes where the decoded sequence is further processed, such as concatenated coding schemes, multi-stage and iterative decoding schemes. In this chapter, we first present a decoding algorithm which both minimizes bit error probability, and provides the corresponding soft information at the output of the decoder. This algorithm is referred to as the MAP (maximum aposteriori probability) decoding algorithm.

ANOTHER LOOK AT THE FAST ITERATIVE SHRINKAGE/THRESHOLDING ALGORITHM (FISTA)*

PubMed Central

Kim, Donghwan; Fessler, Jeffrey A.

2017-01-01

This paper provides a new way of developing the “Fast Iterative Shrinkage/Thresholding Algorithm (FISTA)” [3] that is widely used for minimizing composite convex functions with a nonsmooth term such as the ℓ1 regularizer. In particular, this paper shows that FISTA corresponds to an optimized approach to accelerating the proximal gradient method with respect to a worst-case bound of the cost function. This paper then proposes a new algorithm that is derived by instead optimizing the step coefficients of the proximal gradient method with respect to a worst-case bound of the composite gradient mapping. The proof is based on the worst-case analysis called Performance Estimation Problem in [11]. PMID:29805242

Single-snapshot DOA estimation by using Compressed Sensing

NASA Astrophysics Data System (ADS)

Fortunati, Stefano; Grasso, Raffaele; Gini, Fulvio; Greco, Maria S.; LePage, Kevin

2014-12-01

This paper deals with the problem of estimating the directions of arrival (DOA) of multiple source signals from a single observation vector of an array data. In particular, four estimation algorithms based on the theory of compressed sensing (CS), i.e., the classical ℓ 1 minimization (or Least Absolute Shrinkage and Selection Operator, LASSO), the fast smooth ℓ 0 minimization, and the Sparse Iterative Covariance-Based Estimator, SPICE and the Iterative Adaptive Approach for Amplitude and Phase Estimation, IAA-APES algorithms, are analyzed, and their statistical properties are investigated and compared with the classical Fourier beamformer (FB) in different simulated scenarios. We show that unlike the classical FB, a CS-based beamformer (CSB) has some desirable properties typical of the adaptive algorithms (e.g., Capon and MUSIC) even in the single snapshot case. Particular attention is devoted to the super-resolution property. Theoretical arguments and simulation analysis provide evidence that a CS-based beamformer can achieve resolution beyond the classical Rayleigh limit. Finally, the theoretical findings are validated by processing a real sonar dataset.

Iterative Nonlinear Tikhonov Algorithm with Constraints for Electromagnetic Tomography

NASA Technical Reports Server (NTRS)

Xu, Feng; Deshpande, Manohar

2012-01-01

Low frequency electromagnetic tomography such as the capacitance tomography (ECT) has been proposed for monitoring and mass-gauging of gas-liquid two-phase system under microgravity condition in NASA's future long-term space missions. Due to the ill-posed inverse problem of ECT, images reconstructed using conventional linear algorithms often suffer from limitations such as low resolution and blurred edges. Hence, new efficient high resolution nonlinear imaging algorithms are needed for accurate two-phase imaging. The proposed Iterative Nonlinear Tikhonov Regularized Algorithm with Constraints (INTAC) is based on an efficient finite element method (FEM) forward model of quasi-static electromagnetic problem. It iteratively minimizes the discrepancy between FEM simulated and actual measured capacitances by adjusting the reconstructed image using the Tikhonov regularized method. More importantly, it enforces the known permittivity of two phases to the unknown pixels which exceed the reasonable range of permittivity in each iteration. This strategy does not only stabilize the converging process, but also produces sharper images. Simulations show that resolution improvement of over 2 times can be achieved by INTAC with respect to conventional approaches. Strategies to further improve spatial imaging resolution are suggested, as well as techniques to accelerate nonlinear forward model and thus increase the temporal resolution.

ɛ-subgradient algorithms for bilevel convex optimization

NASA Astrophysics Data System (ADS)

Helou, Elias S.; Simões, Lucas E. A.

2017-05-01

This paper introduces and studies the convergence properties of a new class of explicit ɛ-subgradient methods for the task of minimizing a convex function over a set of minimizers of another convex minimization problem. The general algorithm specializes to some important cases, such as first-order methods applied to a varying objective function, which have computationally cheap iterations. We present numerical experimentation concerning certain applications where the theoretical framework encompasses efficient algorithmic techniques, enabling the use of the resulting methods to solve very large practical problems arising in tomographic image reconstruction. ES Helou was supported by FAPESP grants 2013/07375-0 and 2013/16508-3 and CNPq grant 311476/2014-7. LEA Simões was supported by FAPESP grants 2011/02219-4 and 2013/14615-7.

A successive overrelaxation iterative technique for an adaptive equalizer

NASA Technical Reports Server (NTRS)

Kosovych, O. S.

1973-01-01

An adaptive strategy for the equalization of pulse-amplitude-modulated signals in the presence of intersymbol interference and additive noise is reported. The successive overrelaxation iterative technique is used as the algorithm for the iterative adjustment of the equalizer coefficents during a training period for the minimization of the mean square error. With 2-cyclic and nonnegative Jacobi matrices substantial improvement is demonstrated in the rate of convergence over the commonly used gradient techniques. The Jacobi theorems are also extended to nonpositive Jacobi matrices. Numerical examples strongly indicate that the improvements obtained for the special cases are possible for general channel characteristics. The technique is analytically demonstrated to decrease the mean square error at each iteration for a large range of parameter values for light or moderate intersymbol interference and for small intervals for general channels. Analytically, convergence of the relaxation algorithm was proven in a noisy environment and the coefficient variance was demonstrated to be bounded.

Probabilistic distance-based quantizer design for distributed estimation

NASA Astrophysics Data System (ADS)

Kim, Yoon Hak

2016-12-01

We consider an iterative design of independently operating local quantizers at nodes that should cooperate without interaction to achieve application objectives for distributed estimation systems. We suggest as a new cost function a probabilistic distance between the posterior distribution and its quantized one expressed as the Kullback Leibler (KL) divergence. We first present the analysis that minimizing the KL divergence in the cyclic generalized Lloyd design framework is equivalent to maximizing the logarithmic quantized posterior distribution on the average which can be further computationally reduced in our iterative design. We propose an iterative design algorithm that seeks to maximize the simplified version of the posterior quantized distribution and discuss that our algorithm converges to a global optimum due to the convexity of the cost function and generates the most informative quantized measurements. We also provide an independent encoding technique that enables minimization of the cost function and can be efficiently simplified for a practical use of power-constrained nodes. We finally demonstrate through extensive experiments an obvious advantage of improved estimation performance as compared with the typical designs and the novel design techniques previously published.

System identification using Nuclear Norm & Tabu Search optimization

NASA Astrophysics Data System (ADS)

Ahmed, Asif A.; Schoen, Marco P.; Bosworth, Ken W.

2018-01-01

In recent years, subspace System Identification (SI) algorithms have seen increased research, stemming from advanced minimization methods being applied to the Nuclear Norm (NN) approach in system identification. These minimization algorithms are based on hard computing methodologies. To the authors’ knowledge, as of now, there has been no work reported that utilizes soft computing algorithms to address the minimization problem within the nuclear norm SI framework. A linear, time-invariant, discrete time system is used in this work as the basic model for characterizing a dynamical system to be identified. The main objective is to extract a mathematical model from collected experimental input-output data. Hankel matrices are constructed from experimental data, and the extended observability matrix is employed to define an estimated output of the system. This estimated output and the actual - measured - output are utilized to construct a minimization problem. An embedded rank measure assures minimum state realization outcomes. Current NN-SI algorithms employ hard computing algorithms for minimization. In this work, we propose a simple Tabu Search (TS) algorithm for minimization. TS algorithm based SI is compared with the iterative Alternating Direction Method of Multipliers (ADMM) line search optimization based NN-SI. For comparison, several different benchmark system identification problems are solved by both approaches. Results show improved performance of the proposed SI-TS algorithm compared to the NN-SI ADMM algorithm.

Feature Based Retention Time Alignment for Improved HDX MS Analysis

NASA Astrophysics Data System (ADS)

Venable, John D.; Scuba, William; Brock, Ansgar

2013-04-01

An algorithm for retention time alignment of mass shifted hydrogen-deuterium exchange (HDX) data based on an iterative distance minimization procedure is described. The algorithm performs pairwise comparisons in an iterative fashion between a list of features from a reference file and a file to be time aligned to calculate a retention time mapping function. Features are characterized by their charge, retention time and mass of the monoisotopic peak. The algorithm is able to align datasets with mass shifted features, which is a prerequisite for aligning hydrogen-deuterium exchange mass spectrometry datasets. Confidence assignments from the fully automated processing of a commercial HDX software package are shown to benefit significantly from retention time alignment prior to extraction of deuterium incorporation values.

Total variation iterative constraint algorithm for limited-angle tomographic reconstruction of non-piecewise-constant structures

NASA Astrophysics Data System (ADS)

Krauze, W.; Makowski, P.; Kujawińska, M.

2015-06-01

Standard tomographic algorithms applied to optical limited-angle tomography result in the reconstructions that have highly anisotropic resolution and thus special algorithms are developed. State of the art approaches utilize the Total Variation (TV) minimization technique. These methods give very good results but are applicable to piecewise constant structures only. In this paper, we propose a novel algorithm for 3D limited-angle tomography - Total Variation Iterative Constraint method (TVIC) which enhances the applicability of the TV regularization to non-piecewise constant samples, like biological cells. This approach consists of two parts. First, the TV minimization is used as a strong regularizer to create a sharp-edged image converted to a 3D binary mask which is then iteratively applied in the tomographic reconstruction as a constraint in the object domain. In the present work we test the method on a synthetic object designed to mimic basic structures of a living cell. For simplicity, the test reconstructions were performed within the straight-line propagation model (SIRT3D solver from the ASTRA Tomography Toolbox), but the strategy is general enough to supplement any algorithm for tomographic reconstruction that supports arbitrary geometries of plane-wave projection acquisition. This includes optical diffraction tomography solvers. The obtained reconstructions present resolution uniformity and general shape accuracy expected from the TV regularization based solvers, but keeping the smooth internal structures of the object at the same time. Comparison between three different patterns of object illumination arrangement show very small impact of the projection acquisition geometry on the image quality.

Development of iterative techniques for the solution of unsteady compressible viscous flows

NASA Technical Reports Server (NTRS)

Sankar, Lakshmi N.; Hixon, Duane

1991-01-01

Efficient iterative solution methods are being developed for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. Thus, the extra work required by iterative schemes can also be designed to perform efficiently on current and future generation scalable, missively parallel machines. An obvious candidate for iteratively solving the system of coupled nonlinear algebraic equations arising in CFD applications is the Newton method. Newton's method was implemented in existing finite difference and finite volume methods. Depending on the complexity of the problem, the number of Newton iterations needed per step to solve the discretized system of equations can, however, vary dramatically from a few to several hundred. Another popular approach based on the classical conjugate gradient method, known as the GMRES (Generalized Minimum Residual) algorithm is investigated. The GMRES algorithm was used in the past by a number of researchers for solving steady viscous and inviscid flow problems with considerable success. Here, the suitability of this algorithm is investigated for solving the system of nonlinear equations that arise in unsteady Navier-Stokes solvers at each time step. Unlike the Newton method which attempts to drive the error in the solution at each and every node down to zero, the GMRES algorithm only seeks to minimize the L2 norm of the error. In the GMRES algorithm the changes in the flow properties from one time step to the next are assumed to be the sum of a set of orthogonal vectors. By choosing the number of vectors to a reasonably small value N (between 5 and 20) the work required for advancing the solution from one time step to the next may be kept to (N+1) times that of a noniterative scheme. Many of the operations required by the GMRES algorithm such as matrix-vector multiplies, matrix additions and subtractions can all be vectorized and parallelized efficiently.

A Sparsity-Promoted Method Based on Majorization-Minimization for Weak Fault Feature Enhancement

PubMed Central

Hao, Yansong; Song, Liuyang; Tang, Gang; Yuan, Hongfang

2018-01-01

Fault transient impulses induced by faulty components in rotating machinery usually contain substantial interference. Fault features are comparatively weak in the initial fault stage, which renders fault diagnosis more difficult. In this case, a sparse representation method based on the Majorzation-Minimization (MM) algorithm is proposed to enhance weak fault features and extract the features from strong background noise. However, the traditional MM algorithm suffers from two issues, which are the choice of sparse basis and complicated calculations. To address these challenges, a modified MM algorithm is proposed in which a sparse optimization objective function is designed firstly. Inspired by the Basis Pursuit (BP) model, the optimization function integrates an impulsive feature-preserving factor and a penalty function factor. Second, a modified Majorization iterative method is applied to address the convex optimization problem of the designed function. A series of sparse coefficients can be achieved through iterating, which only contain transient components. It is noteworthy that there is no need to select the sparse basis in the proposed iterative method because it is fixed as a unit matrix. Then the reconstruction step is omitted, which can significantly increase detection efficiency. Eventually, envelope analysis of the sparse coefficients is performed to extract weak fault features. Simulated and experimental signals including bearings and gearboxes are employed to validate the effectiveness of the proposed method. In addition, comparisons are made to prove that the proposed method outperforms the traditional MM algorithm in terms of detection results and efficiency. PMID:29597280

A Sparsity-Promoted Method Based on Majorization-Minimization for Weak Fault Feature Enhancement.

PubMed

Ren, Bangyue; Hao, Yansong; Wang, Huaqing; Song, Liuyang; Tang, Gang; Yuan, Hongfang

2018-03-28

Fault transient impulses induced by faulty components in rotating machinery usually contain substantial interference. Fault features are comparatively weak in the initial fault stage, which renders fault diagnosis more difficult. In this case, a sparse representation method based on the Majorzation-Minimization (MM) algorithm is proposed to enhance weak fault features and extract the features from strong background noise. However, the traditional MM algorithm suffers from two issues, which are the choice of sparse basis and complicated calculations. To address these challenges, a modified MM algorithm is proposed in which a sparse optimization objective function is designed firstly. Inspired by the Basis Pursuit (BP) model, the optimization function integrates an impulsive feature-preserving factor and a penalty function factor. Second, a modified Majorization iterative method is applied to address the convex optimization problem of the designed function. A series of sparse coefficients can be achieved through iterating, which only contain transient components. It is noteworthy that there is no need to select the sparse basis in the proposed iterative method because it is fixed as a unit matrix. Then the reconstruction step is omitted, which can significantly increase detection efficiency. Eventually, envelope analysis of the sparse coefficients is performed to extract weak fault features. Simulated and experimental signals including bearings and gearboxes are employed to validate the effectiveness of the proposed method. In addition, comparisons are made to prove that the proposed method outperforms the traditional MM algorithm in terms of detection results and efficiency.

Novel aspects of plasma control in ITER

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

Humphreys, D.; Jackson, G.; Walker, M.

2015-02-15

ITER plasma control design solutions and performance requirements are strongly driven by its nuclear mission, aggressive commissioning constraints, and limited number of operational discharges. In addition, high plasma energy content, heat fluxes, neutron fluxes, and very long pulse operation place novel demands on control performance in many areas ranging from plasma boundary and divertor regulation to plasma kinetics and stability control. Both commissioning and experimental operations schedules provide limited time for tuning of control algorithms relative to operating devices. Although many aspects of the control solutions required by ITER have been well-demonstrated in present devices and even designed satisfactorily formore » ITER application, many elements unique to ITER including various crucial integration issues are presently under development. We describe selected novel aspects of plasma control in ITER, identifying unique parts of the control problem and highlighting some key areas of research remaining. Novel control areas described include control physics understanding (e.g., current profile regulation, tearing mode (TM) suppression), control mathematics (e.g., algorithmic and simulation approaches to high confidence robust performance), and integration solutions (e.g., methods for management of highly subscribed control resources). We identify unique aspects of the ITER TM suppression scheme, which will pulse gyrotrons to drive current within a magnetic island, and turn the drive off following suppression in order to minimize use of auxiliary power and maximize fusion gain. The potential role of active current profile control and approaches to design in ITER are discussed. Issues and approaches to fault handling algorithms are described, along with novel aspects of actuator sharing in ITER.« less

Novel aspects of plasma control in ITER

DOE PAGES

Humphreys, David; Ambrosino, G.; de Vries, Peter; ...

2015-02-12

ITER plasma control design solutions and performance requirements are strongly driven by its nuclear mission, aggressive commissioning constraints, and limited number of operational discharges. In addition, high plasma energy content, heat fluxes, neutron fluxes, and very long pulse operation place novel demands on control performance in many areas ranging from plasma boundary and divertor regulation to plasma kinetics and stability control. Both commissioning and experimental operations schedules provide limited time for tuning of control algorithms relative to operating devices. Although many aspects of the control solutions required by ITER have been well-demonstrated in present devices and even designed satisfactorily formore » ITER application, many elements unique to ITER including various crucial integration issues are presently under development. We describe selected novel aspects of plasma control in ITER, identifying unique parts of the control problem and highlighting some key areas of research remaining. Novel control areas described include control physics understanding (e.g. current profile regulation, tearing mode suppression (TM)), control mathematics (e.g. algorithmic and simulation approaches to high confidence robust performance), and integration solutions (e.g. methods for management of highly-subscribed control resources). We identify unique aspects of the ITER TM suppression scheme, which will pulse gyrotrons to drive current within a magnetic island, and turn the drive off following suppression in order to minimize use of auxiliary power and maximize fusion gain. The potential role of active current profile control and approaches to design in ITER are discussed. Finally, issues and approaches to fault handling algorithms are described, along with novel aspects of actuator sharing in ITER.« less

Sequential computation of elementary modes and minimal cut sets in genome-scale metabolic networks using alternate integer linear programming

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

Song, Hyun-Seob; Goldberg, Noam; Mahajan, Ashutosh

Elementary (flux) modes (EMs) have served as a valuable tool for investigating structural and functional properties of metabolic networks. Identification of the full set of EMs in genome-scale networks remains challenging due to combinatorial explosion of EMs in complex networks. It is often, however, that only a small subset of relevant EMs needs to be known, for which optimization-based sequential computation is a useful alternative. Most of the currently available methods along this line are based on the iterative use of mixed integer linear programming (MILP), the effectiveness of which significantly deteriorates as the number of iterations builds up. Tomore » alleviate the computational burden associated with the MILP implementation, we here present a novel optimization algorithm termed alternate integer linear programming (AILP). Results: Our algorithm was designed to iteratively solve a pair of integer programming (IP) and linear programming (LP) to compute EMs in a sequential manner. In each step, the IP identifies a minimal subset of reactions, the deletion of which disables all previously identified EMs. Thus, a subsequent LP solution subject to this reaction deletion constraint becomes a distinct EM. In cases where no feasible LP solution is available, IP-derived reaction deletion sets represent minimal cut sets (MCSs). Despite the additional computation of MCSs, AILP achieved significant time reduction in computing EMs by orders of magnitude. The proposed AILP algorithm not only offers a computational advantage in the EM analysis of genome-scale networks, but also improves the understanding of the linkage between EMs and MCSs.« less

A polynomial primal-dual Dikin-type algorithm for linear programming

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

Jansen, B.; Roos, R.; Terlaky, T.

1994-12-31

We present a new primal-dual affine scaling method for linear programming. The search direction is obtained by using Dikin`s original idea: minimize the objective function (which is the duality gap in a primal-dual algorithm) over a suitable ellipsoid. The search direction has no obvious relationship with the directions proposed in the literature so far. It guarantees a significant decrease in the duality gap in each iteration, and at the same time drives the iterates to the central path. The method admits a polynomial complexity bound that is better than the one for Monteiro et al.`s original primal-dual affine scaling method.

Shading correction assisted iterative cone-beam CT reconstruction

NASA Astrophysics Data System (ADS)

Yang, Chunlin; Wu, Pengwei; Gong, Shutao; Wang, Jing; Lyu, Qihui; Tang, Xiangyang; Niu, Tianye

2017-11-01

Recent advances in total variation (TV) technology enable accurate CT image reconstruction from highly under-sampled and noisy projection data. The standard iterative reconstruction algorithms, which work well in conventional CT imaging, fail to perform as expected in cone beam CT (CBCT) applications, wherein the non-ideal physics issues, including scatter and beam hardening, are more severe. These physics issues result in large areas of shading artifacts and cause deterioration to the piecewise constant property assumed in reconstructed images. To overcome this obstacle, we incorporate a shading correction scheme into low-dose CBCT reconstruction and propose a clinically acceptable and stable three-dimensional iterative reconstruction method that is referred to as the shading correction assisted iterative reconstruction. In the proposed method, we modify the TV regularization term by adding a shading compensation image to the reconstructed image to compensate for the shading artifacts while leaving the data fidelity term intact. This compensation image is generated empirically, using image segmentation and low-pass filtering, and updated in the iterative process whenever necessary. When the compensation image is determined, the objective function is minimized using the fast iterative shrinkage-thresholding algorithm accelerated on a graphic processing unit. The proposed method is evaluated using CBCT projection data of the Catphan© 600 phantom and two pelvis patients. Compared with the iterative reconstruction without shading correction, the proposed method reduces the overall CT number error from around 200 HU to be around 25 HU and increases the spatial uniformity by a factor of 20 percent, given the same number of sparsely sampled projections. A clinically acceptable and stable iterative reconstruction algorithm for CBCT is proposed in this paper. Differing from the existing algorithms, this algorithm incorporates a shading correction scheme into the low-dose CBCT reconstruction and achieves more stable optimization path and more clinically acceptable reconstructed image. The method proposed by us does not rely on prior information and thus is practically attractive to the applications of low-dose CBCT imaging in the clinic.

Optimizing convergence rates of alternating minimization reconstruction algorithms for real-time explosive detection applications

NASA Astrophysics Data System (ADS)

Bosch, Carl; Degirmenci, Soysal; Barlow, Jason; Mesika, Assaf; Politte, David G.; O'Sullivan, Joseph A.

2016-05-01

X-ray computed tomography reconstruction for medical, security and industrial applications has evolved through 40 years of experience with rotating gantry scanners using analytic reconstruction techniques such as filtered back projection (FBP). In parallel, research into statistical iterative reconstruction algorithms has evolved to apply to sparse view scanners in nuclear medicine, low data rate scanners in Positron Emission Tomography (PET) [5, 7, 10] and more recently to reduce exposure to ionizing radiation in conventional X-ray CT scanners. Multiple approaches to statistical iterative reconstruction have been developed based primarily on variations of expectation maximization (EM) algorithms. The primary benefit of EM algorithms is the guarantee of convergence that is maintained when iterative corrections are made within the limits of convergent algorithms. The primary disadvantage, however is that strict adherence to correction limits of convergent algorithms extends the number of iterations and ultimate timeline to complete a 3D volumetric reconstruction. Researchers have studied methods to accelerate convergence through more aggressive corrections [1], ordered subsets [1, 3, 4, 9] and spatially variant image updates. In this paper we describe the development of an AM reconstruction algorithm with accelerated convergence for use in a real-time explosive detection application for aviation security. By judiciously applying multiple acceleration techniques and advanced GPU processing architectures, we are able to perform 3D reconstruction of scanned passenger baggage at a rate of 75 slices per second. Analysis of the results on stream of commerce passenger bags demonstrates accelerated convergence by factors of 8 to 15, when comparing images from accelerated and strictly convergent algorithms.

Trace Norm Regularized CANDECOMP/PARAFAC Decomposition With Missing Data.

PubMed

Liu, Yuanyuan; Shang, Fanhua; Jiao, Licheng; Cheng, James; Cheng, Hong

2015-11-01

In recent years, low-rank tensor completion (LRTC) problems have received a significant amount of attention in computer vision, data mining, and signal processing. The existing trace norm minimization algorithms for iteratively solving LRTC problems involve multiple singular value decompositions of very large matrices at each iteration. Therefore, they suffer from high computational cost. In this paper, we propose a novel trace norm regularized CANDECOMP/PARAFAC decomposition (TNCP) method for simultaneous tensor decomposition and completion. We first formulate a factor matrix rank minimization model by deducing the relation between the rank of each factor matrix and the mode- n rank of a tensor. Then, we introduce a tractable relaxation of our rank function, and then achieve a convex combination problem of much smaller-scale matrix trace norm minimization. Finally, we develop an efficient algorithm based on alternating direction method of multipliers to solve our problem. The promising experimental results on synthetic and real-world data validate the effectiveness of our TNCP method. Moreover, TNCP is significantly faster than the state-of-the-art methods and scales to larger problems.

Learning Efficient Sparse and Low Rank Models.

PubMed

Sprechmann, P; Bronstein, A M; Sapiro, G

2015-09-01

Parsimony, including sparsity and low rank, has been shown to successfully model data in numerous machine learning and signal processing tasks. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an objective function with parsimony-promoting terms. The inherently sequential structure and data-dependent complexity and latency of iterative optimization constitute a major limitation in many applications requiring real-time performance or involving large-scale data. Another limitation encountered by these modeling techniques is the difficulty of their inclusion in discriminative learning scenarios. In this work, we propose to move the emphasis from the model to the pursuit algorithm, and develop a process-centric view of parsimonious modeling, in which a learned deterministic fixed-complexity pursuit process is used in lieu of iterative optimization. We show a principled way to construct learnable pursuit process architectures for structured sparse and robust low rank models, derived from the iteration of proximal descent algorithms. These architectures learn to approximate the exact parsimonious representation at a fraction of the complexity of the standard optimization methods. We also show that appropriate training regimes allow to naturally extend parsimonious models to discriminative settings. State-of-the-art results are demonstrated on several challenging problems in image and audio processing with several orders of magnitude speed-up compared to the exact optimization algorithms.

QMR: A Quasi-Minimal Residual method for non-Hermitian linear systems

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noel M.

1990-01-01

The biconjugate gradient (BCG) method is the natural generalization of the classical conjugate gradient algorithm for Hermitian positive definite matrices to general non-Hermitian linear systems. Unfortunately, the original BCG algorithm is susceptible to possible breakdowns and numerical instabilities. A novel BCG like approach is presented called the quasi-minimal residual (QMR) method, which overcomes the problems of BCG. An implementation of QMR based on a look-ahead version of the nonsymmetric Lanczos algorithm is proposed. It is shown how BCG iterates can be recovered stably from the QMR process. Some further properties of the QMR approach are given and an error bound is presented. Finally, numerical experiments are reported.

A Bee Evolutionary Guiding Nondominated Sorting Genetic Algorithm II for Multiobjective Flexible Job-Shop Scheduling.

PubMed

Deng, Qianwang; Gong, Guiliang; Gong, Xuran; Zhang, Like; Liu, Wei; Ren, Qinghua

2017-01-01

Flexible job-shop scheduling problem (FJSP) is an NP-hard puzzle which inherits the job-shop scheduling problem (JSP) characteristics. This paper presents a bee evolutionary guiding nondominated sorting genetic algorithm II (BEG-NSGA-II) for multiobjective FJSP (MO-FJSP) with the objectives to minimize the maximal completion time, the workload of the most loaded machine, and the total workload of all machines. It adopts a two-stage optimization mechanism during the optimizing process. In the first stage, the NSGA-II algorithm with T iteration times is first used to obtain the initial population N , in which a bee evolutionary guiding scheme is presented to exploit the solution space extensively. In the second stage, the NSGA-II algorithm with GEN iteration times is used again to obtain the Pareto-optimal solutions. In order to enhance the searching ability and avoid the premature convergence, an updating mechanism is employed in this stage. More specifically, its population consists of three parts, and each of them changes with the iteration times. What is more, numerical simulations are carried out which are based on some published benchmark instances. Finally, the effectiveness of the proposed BEG-NSGA-II algorithm is shown by comparing the experimental results and the results of some well-known algorithms already existed.

A Bee Evolutionary Guiding Nondominated Sorting Genetic Algorithm II for Multiobjective Flexible Job-Shop Scheduling

PubMed Central

Deng, Qianwang; Gong, Xuran; Zhang, Like; Liu, Wei; Ren, Qinghua

2017-01-01

Flexible job-shop scheduling problem (FJSP) is an NP-hard puzzle which inherits the job-shop scheduling problem (JSP) characteristics. This paper presents a bee evolutionary guiding nondominated sorting genetic algorithm II (BEG-NSGA-II) for multiobjective FJSP (MO-FJSP) with the objectives to minimize the maximal completion time, the workload of the most loaded machine, and the total workload of all machines. It adopts a two-stage optimization mechanism during the optimizing process. In the first stage, the NSGA-II algorithm with T iteration times is first used to obtain the initial population N, in which a bee evolutionary guiding scheme is presented to exploit the solution space extensively. In the second stage, the NSGA-II algorithm with GEN iteration times is used again to obtain the Pareto-optimal solutions. In order to enhance the searching ability and avoid the premature convergence, an updating mechanism is employed in this stage. More specifically, its population consists of three parts, and each of them changes with the iteration times. What is more, numerical simulations are carried out which are based on some published benchmark instances. Finally, the effectiveness of the proposed BEG-NSGA-II algorithm is shown by comparing the experimental results and the results of some well-known algorithms already existed. PMID:28458687

A Laplacian based image filtering using switching noise detector.

PubMed

Ranjbaran, Ali; Hassan, Anwar Hasni Abu; Jafarpour, Mahboobe; Ranjbaran, Bahar

2015-01-01

This paper presents a Laplacian-based image filtering method. Using a local noise estimator function in an energy functional minimizing scheme we show that Laplacian that has been known as an edge detection function can be used for noise removal applications. The algorithm can be implemented on a 3x3 window and easily tuned by number of iterations. Image denoising is simplified to the reduction of the pixels value with their related Laplacian value weighted by local noise estimator. The only parameter which controls smoothness is the number of iterations. Noise reduction quality of the introduced method is evaluated and compared with some classic algorithms like Wiener and Total Variation based filters for Gaussian noise. And also the method compared with the state-of-the-art method BM3D for some images. The algorithm appears to be easy, fast and comparable with many classic denoising algorithms for Gaussian noise.

X-ray dose reduction in abdominal computed tomography using advanced iterative reconstruction algorithms.

PubMed

Ning, Peigang; Zhu, Shaocheng; Shi, Dapeng; Guo, Ying; Sun, Minghua

2014-01-01

This work aims to explore the effects of adaptive statistical iterative reconstruction (ASiR) and model-based iterative reconstruction (MBIR) algorithms in reducing computed tomography (CT) radiation dosages in abdominal imaging. CT scans on a standard male phantom were performed at different tube currents. Images at the different tube currents were reconstructed with the filtered back-projection (FBP), 50% ASiR and MBIR algorithms and compared. The CT value, image noise and contrast-to-noise ratios (CNRs) of the reconstructed abdominal images were measured. Volumetric CT dose indexes (CTDIvol) were recorded. At different tube currents, 50% ASiR and MBIR significantly reduced image noise and increased the CNR when compared with FBP. The minimal tube current values required by FBP, 50% ASiR, and MBIR to achieve acceptable image quality using this phantom were 200, 140, and 80 mA, respectively. At the identical image quality, 50% ASiR and MBIR reduced the radiation dose by 35.9% and 59.9% respectively when compared with FBP. Advanced iterative reconstruction techniques are able to reduce image noise and increase image CNRs. Compared with FBP, 50% ASiR and MBIR reduced radiation doses by 35.9% and 59.9%, respectively.

A shifted hyperbolic augmented Lagrangian-based artificial fish two-swarm algorithm with guaranteed convergence for constrained global optimization

NASA Astrophysics Data System (ADS)

Rocha, Ana Maria A. C.; Costa, M. Fernanda P.; Fernandes, Edite M. G. P.

2016-12-01

This article presents a shifted hyperbolic penalty function and proposes an augmented Lagrangian-based algorithm for non-convex constrained global optimization problems. Convergence to an ?-global minimizer is proved. At each iteration k, the algorithm requires the ?-global minimization of a bound constrained optimization subproblem, where ?. The subproblems are solved by a stochastic population-based metaheuristic that relies on the artificial fish swarm paradigm and a two-swarm strategy. To enhance the speed of convergence, the algorithm invokes the Nelder-Mead local search with a dynamically defined probability. Numerical experiments with benchmark functions and engineering design problems are presented. The results show that the proposed shifted hyperbolic augmented Lagrangian compares favorably with other deterministic and stochastic penalty-based methods.

HPC-NMF: A High-Performance Parallel Algorithm for Nonnegative Matrix Factorization

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

Kannan, Ramakrishnan; Sukumar, Sreenivas R.; Ballard, Grey M.

NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient distributed algorithms to solve the problem for big data sets. We propose a high-performance distributed-memory parallel algorithm that computes the factorization by iteratively solving alternating non-negative least squares (NLS) subproblems formore » $$\\WW$$ and $$\\HH$$. It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). As opposed to previous implementation, our algorithm is also flexible: It performs well for both dense and sparse matrices, and allows the user to choose any one of the multiple algorithms for solving the updates to low rank factors $$\\WW$$ and $$\\HH$$ within the alternating iterations.« less

An efficient parallel algorithm: Poststack and prestack Kirchhoff 3D depth migration using flexi-depth iterations

NASA Astrophysics Data System (ADS)

Rastogi, Richa; Srivastava, Abhishek; Khonde, Kiran; Sirasala, Kirannmayi M.; Londhe, Ashutosh; Chavhan, Hitesh

2015-07-01

This paper presents an efficient parallel 3D Kirchhoff depth migration algorithm suitable for current class of multicore architecture. The fundamental Kirchhoff depth migration algorithm exhibits inherent parallelism however, when it comes to 3D data migration, as the data size increases the resource requirement of the algorithm also increases. This challenges its practical implementation even on current generation high performance computing systems. Therefore a smart parallelization approach is essential to handle 3D data for migration. The most compute intensive part of Kirchhoff depth migration algorithm is the calculation of traveltime tables due to its resource requirements such as memory/storage and I/O. In the current research work, we target this area and develop a competent parallel algorithm for post and prestack 3D Kirchhoff depth migration, using hybrid MPI+OpenMP programming techniques. We introduce a concept of flexi-depth iterations while depth migrating data in parallel imaging space, using optimized traveltime table computations. This concept provides flexibility to the algorithm by migrating data in a number of depth iterations, which depends upon the available node memory and the size of data to be migrated during runtime. Furthermore, it minimizes the requirements of storage, I/O and inter-node communication, thus making it advantageous over the conventional parallelization approaches. The developed parallel algorithm is demonstrated and analysed on Yuva II, a PARAM series of supercomputers. Optimization, performance and scalability experiment results along with the migration outcome show the effectiveness of the parallel algorithm.

Iterative quantization: a Procrustean approach to learning binary codes for large-scale image retrieval.

PubMed

Gong, Yunchao; Lazebnik, Svetlana; Gordo, Albert; Perronnin, Florent

2013-12-01

This paper addresses the problem of learning similarity-preserving binary codes for efficient similarity search in large-scale image collections. We formulate this problem in terms of finding a rotation of zero-centered data so as to minimize the quantization error of mapping this data to the vertices of a zero-centered binary hypercube, and propose a simple and efficient alternating minimization algorithm to accomplish this task. This algorithm, dubbed iterative quantization (ITQ), has connections to multiclass spectral clustering and to the orthogonal Procrustes problem, and it can be used both with unsupervised data embeddings such as PCA and supervised embeddings such as canonical correlation analysis (CCA). The resulting binary codes significantly outperform several other state-of-the-art methods. We also show that further performance improvements can result from transforming the data with a nonlinear kernel mapping prior to PCA or CCA. Finally, we demonstrate an application of ITQ to learning binary attributes or "classemes" on the ImageNet data set.

Iterated greedy algorithms to minimize the total family flow time for job-shop scheduling with job families and sequence-dependent set-ups

NASA Astrophysics Data System (ADS)

Kim, Ji-Su; Park, Jung-Hyeon; Lee, Dong-Ho

2017-10-01

This study addresses a variant of job-shop scheduling in which jobs are grouped into job families, but they are processed individually. The problem can be found in various industrial systems, especially in reprocessing shops of remanufacturing systems. If the reprocessing shop is a job-shop type and has the component-matching requirements, it can be regarded as a job shop with job families since the components of a product constitute a job family. In particular, sequence-dependent set-ups in which set-up time depends on the job just completed and the next job to be processed are also considered. The objective is to minimize the total family flow time, i.e. the maximum among the completion times of the jobs within a job family. A mixed-integer programming model is developed and two iterated greedy algorithms with different local search methods are proposed. Computational experiments were conducted on modified benchmark instances and the results are reported.

Evaluation of hybrid SART  +  OS  +  TV iterative reconstruction algorithm for optical-CT gel dosimeter imaging

NASA Astrophysics Data System (ADS)

Du, Yi; Wang, Xiangang; Xiang, Xincheng; Wei, Zhouping

2016-12-01

Optical computed tomography (optical-CT) is a high-resolution, fast, and easily accessible readout modality for gel dosimeters. This paper evaluates a hybrid iterative image reconstruction algorithm for optical-CT gel dosimeter imaging, namely, the simultaneous algebraic reconstruction technique (SART) integrated with ordered subsets (OS) iteration and total variation (TV) minimization regularization. The mathematical theory and implementation workflow of the algorithm are detailed. Experiments on two different optical-CT scanners were performed for cross-platform validation. For algorithm evaluation, the iterative convergence is first shown, and peak-to-noise-ratio (PNR) and contrast-to-noise ratio (CNR) results are given with the cone-beam filtered backprojection (FDK) algorithm and the FDK results followed by median filtering (mFDK) as reference. The effect on spatial gradients and reconstruction artefacts is also investigated. The PNR curve illustrates that the results of SART  +  OS  +  TV finally converges to that of FDK but with less noise, which implies that the dose-OD calibration method for FDK is also applicable to the proposed algorithm. The CNR in selected regions-of-interest (ROIs) of SART  +  OS  +  TV results is almost double that of FDK and 50% higher than that of mFDK. The artefacts in SART  +  OS  +  TV results are still visible, but have been much suppressed with little spatial gradient loss. Based on the assessment, we can conclude that this hybrid SART  +  OS  +  TV algorithm outperforms both FDK and mFDK in denoising, preserving spatial dose gradients and reducing artefacts, and its effectiveness and efficiency are platform independent.

Near-optimal matrix recovery from random linear measurements.

PubMed

Romanov, Elad; Gavish, Matan

2018-06-25

In matrix recovery from random linear measurements, one is interested in recovering an unknown M-by-N matrix [Formula: see text] from [Formula: see text] measurements [Formula: see text], where each [Formula: see text] is an M-by-N measurement matrix with i.i.d. random entries, [Formula: see text] We present a matrix recovery algorithm, based on approximate message passing, which iteratively applies an optimal singular-value shrinker-a nonconvex nonlinearity tailored specifically for matrix estimation. Our algorithm typically converges exponentially fast, offering a significant speedup over previously suggested matrix recovery algorithms, such as iterative solvers for nuclear norm minimization (NNM). It is well known that there is a recovery tradeoff between the information content of the object [Formula: see text] to be recovered (specifically, its matrix rank r) and the number of linear measurements n from which recovery is to be attempted. The precise tradeoff between r and n, beyond which recovery by a given algorithm becomes possible, traces the so-called phase transition curve of that algorithm in the [Formula: see text] plane. The phase transition curve of our algorithm is noticeably better than that of NNM. Interestingly, it is close to the information-theoretic lower bound for the minimal number of measurements needed for matrix recovery, making it not only state of the art in terms of convergence rate, but also near optimal in terms of the matrices it successfully recovers. Copyright © 2018 the Author(s). Published by PNAS.

Joint Transmit Power Allocation and Splitting for SWIPT Aided OFDM-IDMA in Wireless Sensor Networks

PubMed Central

Li, Shanshan; Zhou, Xiaotian; Wang, Cheng-Xiang; Yuan, Dongfeng; Zhang, Wensheng

2017-01-01

In this paper, we propose to combine Orthogonal Frequency Division Multiplexing-Interleave Division Multiple Access (OFDM-IDMA) with Simultaneous Wireless Information and Power Transfer (SWIPT), resulting in SWIPT aided OFDM-IDMA scheme for power-limited sensor networks. In the proposed system, the Receive Node (RN) applies Power Splitting (PS) to coordinate the Energy Harvesting (EH) and Information Decoding (ID) process, where the harvested energy is utilized to guarantee the iterative Multi-User Detection (MUD) of IDMA to work under sufficient number of iterations. Our objective is to minimize the total transmit power of Source Node (SN), while satisfying the requirements of both minimum harvested energy and Bit Error Rate (BER) performance from individual receive nodes. We formulate such a problem as a joint power allocation and splitting one, where the iteration number of MUD is also taken into consideration as the key parameter to affect both EH and ID constraints. To solve it, a sub-optimal algorithm is proposed to determine the power profile, PS ratio and iteration number of MUD in an iterative manner. Simulation results verify that the proposed algorithm can provide significant performance improvement. PMID:28677636

Joint Transmit Power Allocation and Splitting for SWIPT Aided OFDM-IDMA in Wireless Sensor Networks.

PubMed

Li, Shanshan; Zhou, Xiaotian; Wang, Cheng-Xiang; Yuan, Dongfeng; Zhang, Wensheng

2017-07-04

In this paper, we propose to combine Orthogonal Frequency Division Multiplexing-Interleave Division Multiple Access (OFDM-IDMA) with Simultaneous Wireless Information and Power Transfer (SWIPT), resulting in SWIPT aided OFDM-IDMA scheme for power-limited sensor networks. In the proposed system, the Receive Node (RN) applies Power Splitting (PS) to coordinate the Energy Harvesting (EH) and Information Decoding (ID) process, where the harvested energy is utilized to guarantee the iterative Multi-User Detection (MUD) of IDMA to work under sufficient number of iterations. Our objective is to minimize the total transmit power of Source Node (SN), while satisfying the requirements of both minimum harvested energy and Bit Error Rate (BER) performance from individual receive nodes. We formulate such a problem as a joint power allocation and splitting one, where the iteration number of MUD is also taken into consideration as the key parameter to affect both EH and ID constraints. To solve it, a sub-optimal algorithm is proposed to determine the power profile, PS ratio and iteration number of MUD in an iterative manner. Simulation results verify that the proposed algorithm can provide significant performance improvement.

Computing Maximum Likelihood Estimates of Loglinear Models from Marginal Sums with Special Attention to Loglinear Item Response Theory. [Project Psychometric Aspects of Item Banking No. 53.] Research Report 91-1.

ERIC Educational Resources Information Center

Kelderman, Henk

In this paper, algorithms are described for obtaining the maximum likelihood estimates of the parameters in log-linear models. Modified versions of the iterative proportional fitting and Newton-Raphson algorithms are described that work on the minimal sufficient statistics rather than on the usual counts in the full contingency table. This is…

An Efficient Augmented Lagrangian Method for Statistical X-Ray CT Image Reconstruction.

PubMed

Li, Jiaojiao; Niu, Shanzhou; Huang, Jing; Bian, Zhaoying; Feng, Qianjin; Yu, Gaohang; Liang, Zhengrong; Chen, Wufan; Ma, Jianhua

2015-01-01

Statistical iterative reconstruction (SIR) for X-ray computed tomography (CT) under the penalized weighted least-squares criteria can yield significant gains over conventional analytical reconstruction from the noisy measurement. However, due to the nonlinear expression of the objective function, most exiting algorithms related to the SIR unavoidably suffer from heavy computation load and slow convergence rate, especially when an edge-preserving or sparsity-based penalty or regularization is incorporated. In this work, to address abovementioned issues of the general algorithms related to the SIR, we propose an adaptive nonmonotone alternating direction algorithm in the framework of augmented Lagrangian multiplier method, which is termed as "ALM-ANAD". The algorithm effectively combines an alternating direction technique with an adaptive nonmonotone line search to minimize the augmented Lagrangian function at each iteration. To evaluate the present ALM-ANAD algorithm, both qualitative and quantitative studies were conducted by using digital and physical phantoms. Experimental results show that the present ALM-ANAD algorithm can achieve noticeable gains over the classical nonlinear conjugate gradient algorithm and state-of-the-art split Bregman algorithm in terms of noise reduction, contrast-to-noise ratio, convergence rate, and universal quality index metrics.

A Matrix Pencil Algorithm Based Multiband Iterative Fusion Imaging Method

NASA Astrophysics Data System (ADS)

Zou, Yong Qiang; Gao, Xun Zhang; Li, Xiang; Liu, Yong Xiang

2016-01-01

Multiband signal fusion technique is a practicable and efficient way to improve the range resolution of ISAR image. The classical fusion method estimates the poles of each subband signal by the root-MUSIC method, and some good results were get in several experiments. However, this method is fragile in noise for the proper poles could not easy to get in low signal to noise ratio (SNR). In order to eliminate the influence of noise, this paper propose a matrix pencil algorithm based method to estimate the multiband signal poles. And to deal with mutual incoherent between subband signals, the incoherent parameters (ICP) are predicted through the relation of corresponding poles of each subband. Then, an iterative algorithm which aimed to minimize the 2-norm of signal difference is introduced to reduce signal fusion error. Applications to simulate dada verify that the proposed method get better fusion results at low SNR.

A Matrix Pencil Algorithm Based Multiband Iterative Fusion Imaging Method

PubMed Central

Zou, Yong Qiang; Gao, Xun Zhang; Li, Xiang; Liu, Yong Xiang

2016-01-01

Multiband signal fusion technique is a practicable and efficient way to improve the range resolution of ISAR image. The classical fusion method estimates the poles of each subband signal by the root-MUSIC method, and some good results were get in several experiments. However, this method is fragile in noise for the proper poles could not easy to get in low signal to noise ratio (SNR). In order to eliminate the influence of noise, this paper propose a matrix pencil algorithm based method to estimate the multiband signal poles. And to deal with mutual incoherent between subband signals, the incoherent parameters (ICP) are predicted through the relation of corresponding poles of each subband. Then, an iterative algorithm which aimed to minimize the 2-norm of signal difference is introduced to reduce signal fusion error. Applications to simulate dada verify that the proposed method get better fusion results at low SNR. PMID:26781194

DQM: Decentralized Quadratically Approximated Alternating Direction Method of Multipliers

NASA Astrophysics Data System (ADS)

Mokhtari, Aryan; Shi, Wei; Ling, Qing; Ribeiro, Alejandro

2016-10-01

This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with neighbors only. A decentralized version of the alternating directions method of multipliers (DADMM) is a common method for solving this category of problems. DADMM exhibits linear convergence rate to the optimal objective but its implementation requires solving a convex optimization problem at each iteration. This can be computationally costly and may result in large overall convergence times. The decentralized quadratically approximated ADMM algorithm (DQM), which minimizes a quadratic approximation of the objective function that DADMM minimizes at each iteration, is proposed here. The consequent reduction in computational time is shown to have minimal effect on convergence properties. Convergence still proceeds at a linear rate with a guaranteed constant that is asymptotically equivalent to the DADMM linear convergence rate constant. Numerical results demonstrate advantages of DQM relative to DADMM and other alternatives in a logistic regression problem.

Discrete-Time Local Value Iteration Adaptive Dynamic Programming: Admissibility and Termination Analysis.

PubMed

Wei, Qinglai; Liu, Derong; Lin, Qiao

In this paper, a novel local value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon optimal control problems for discrete-time nonlinear systems. The focuses of this paper are to study admissibility properties and the termination criteria of discrete-time local value iteration ADP algorithms. In the discrete-time local value iteration ADP algorithm, the iterative value functions and the iterative control laws are both updated in a given subset of the state space in each iteration, instead of the whole state space. For the first time, admissibility properties of iterative control laws are analyzed for the local value iteration ADP algorithm. New termination criteria are established, which terminate the iterative local ADP algorithm with an admissible approximate optimal control law. Finally, simulation results are given to illustrate the performance of the developed algorithm.In this paper, a novel local value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon optimal control problems for discrete-time nonlinear systems. The focuses of this paper are to study admissibility properties and the termination criteria of discrete-time local value iteration ADP algorithms. In the discrete-time local value iteration ADP algorithm, the iterative value functions and the iterative control laws are both updated in a given subset of the state space in each iteration, instead of the whole state space. For the first time, admissibility properties of iterative control laws are analyzed for the local value iteration ADP algorithm. New termination criteria are established, which terminate the iterative local ADP algorithm with an admissible approximate optimal control law. Finally, simulation results are given to illustrate the performance of the developed algorithm.

On the convergence of nonconvex minimization methods for image recovery.

PubMed

Xiao, Jin; Ng, Michael Kwok-Po; Yang, Yu-Fei

2015-05-01

Nonconvex nonsmooth regularization method has been shown to be effective for restoring images with neat edges. Fast alternating minimization schemes have also been proposed and developed to solve the nonconvex nonsmooth minimization problem. The main contribution of this paper is to show the convergence of these alternating minimization schemes, based on the Kurdyka-Łojasiewicz property. In particular, we show that the iterates generated by the alternating minimization scheme, converges to a critical point of this nonconvex nonsmooth objective function. We also extend the analysis to nonconvex nonsmooth regularization model with box constraints, and obtain similar convergence results of the related minimization algorithm. Numerical examples are given to illustrate our convergence analysis.

On global optimization using an estimate of Lipschitz constant and simplicial partition

NASA Astrophysics Data System (ADS)

Gimbutas, Albertas; Žilinskas, Antanas

2016-10-01

A new algorithm is proposed for finding the global minimum of a multi-variate black-box Lipschitz function with an unknown Lipschitz constant. The feasible region is initially partitioned into simplices; in the subsequent iteration, the most suitable simplices are selected and bisected via the middle point of the longest edge. The suitability of a simplex for bisection is evaluated by minimizing of a surrogate function which mimics the lower bound for the considered objective function over that simplex. The surrogate function is defined using an estimate of the Lipschitz constant and the objective function values at the vertices of a simplex. The novelty of the algorithm is the sophisticated method of estimating the Lipschitz constant, and the appropriate method to minimize the surrogate function. The proposed algorithm was tested using 600 random test problems of different complexity, showing competitive results with two popular advanced algorithms which are based on similar assumptions.

An implementation of the QMR method based on coupled two-term recurrences

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noeel M.

1992-01-01

The authors have proposed a new Krylov subspace iteration, the quasi-minimal residual algorithm (QMR), for solving non-Hermitian linear systems. In the original implementation of the QMR method, the Lanczos process with look-ahead is used to generate basis vectors for the underlying Krylov subspaces. In the Lanczos algorithm, these basis vectors are computed by means of three-term recurrences. It has been observed that, in finite precision arithmetic, vector iterations based on three-term recursions are usually less robust than mathematically equivalent coupled two-term vector recurrences. This paper presents a look-ahead algorithm that constructs the Lanczos basis vectors by means of coupled two-term recursions. Implementation details are given, and the look-ahead strategy is described. A new implementation of the QMR method, based on this coupled two-term algorithm, is described. A simplified version of the QMR algorithm without look-ahead is also presented, and the special case of QMR for complex symmetric linear systems is considered. Results of numerical experiments comparing the original and the new implementations of the QMR method are reported.

Concurrent optimization of material spatial distribution and material anisotropy repartition for two-dimensional structures

NASA Astrophysics Data System (ADS)

Ranaivomiarana, Narindra; Irisarri, François-Xavier; Bettebghor, Dimitri; Desmorat, Boris

2018-04-01

An optimization methodology to find concurrently material spatial distribution and material anisotropy repartition is proposed for orthotropic, linear and elastic two-dimensional membrane structures. The shape of the structure is parameterized by a density variable that determines the presence or absence of material. The polar method is used to parameterize a general orthotropic material by its elasticity tensor invariants by change of frame. A global structural stiffness maximization problem written as a compliance minimization problem is treated, and a volume constraint is applied. The compliance minimization can be put into a double minimization of complementary energy. An extension of the alternate directions algorithm is proposed to solve the double minimization problem. The algorithm iterates between local minimizations in each element of the structure and global minimizations. Thanks to the polar method, the local minimizations are solved explicitly providing analytical solutions. The global minimizations are performed with finite element calculations. The method is shown to be straightforward and efficient. Concurrent optimization of density and anisotropy distribution of a cantilever beam and a bridge are presented.

Low dose CT reconstruction via L1 norm dictionary learning using alternating minimization algorithm and balancing principle.

PubMed

Wu, Junfeng; Dai, Fang; Hu, Gang; Mou, Xuanqin

2018-04-18

Excessive radiation exposure in computed tomography (CT) scans increases the chance of developing cancer and has become a major clinical concern. Recently, statistical iterative reconstruction (SIR) with l0-norm dictionary learning regularization has been developed to reconstruct CT images from the low dose and few-view dataset in order to reduce radiation dose. Nonetheless, the sparse regularization term adopted in this approach is l0-norm, which cannot guarantee the global convergence of the proposed algorithm. To address this problem, in this study we introduced the l1-norm dictionary learning penalty into SIR framework for low dose CT image reconstruction, and developed an alternating minimization algorithm to minimize the associated objective function, which transforms CT image reconstruction problem into a sparse coding subproblem and an image updating subproblem. During the image updating process, an efficient model function approach based on balancing principle is applied to choose the regularization parameters. The proposed alternating minimization algorithm was evaluated first using real projection data of a sheep lung CT perfusion and then using numerical simulation based on sheep lung CT image and chest image. Both visual assessment and quantitative comparison using terms of root mean square error (RMSE) and structural similarity (SSIM) index demonstrated that the new image reconstruction algorithm yielded similar performance with l0-norm dictionary learning penalty and outperformed the conventional filtered backprojection (FBP) and total variation (TV) minimization algorithms.

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).

Iterative-Transform Phase Retrieval Using Adaptive Diversity

NASA Technical Reports Server (NTRS)

Dean, Bruce H.

2007-01-01

A phase-diverse iterative-transform phase-retrieval algorithm enables high spatial-frequency, high-dynamic-range, image-based wavefront sensing. [The terms phase-diverse, phase retrieval, image-based, and wavefront sensing are defined in the first of the two immediately preceding articles, Broadband Phase Retrieval for Image-Based Wavefront Sensing (GSC-14899-1).] As described below, no prior phase-retrieval algorithm has offered both high dynamic range and the capability to recover high spatial-frequency components. Each of the previously developed image-based phase-retrieval techniques can be classified into one of two categories: iterative transform or parametric. Among the modifications of the original iterative-transform approach has been the introduction of a defocus diversity function (also defined in the cited companion article). Modifications of the original parametric approach have included minimizing alternative objective functions as well as implementing a variety of nonlinear optimization methods. The iterative-transform approach offers the advantage of ability to recover low, middle, and high spatial frequencies, but has disadvantage of having a limited dynamic range to one wavelength or less. In contrast, parametric phase retrieval offers the advantage of high dynamic range, but is poorly suited for recovering higher spatial frequency aberrations. The present phase-diverse iterative transform phase-retrieval algorithm offers both the high-spatial-frequency capability of the iterative-transform approach and the high dynamic range of parametric phase-recovery techniques. In implementation, this is a focus-diverse iterative-transform phaseretrieval algorithm that incorporates an adaptive diversity function, which makes it possible to avoid phase unwrapping while preserving high-spatial-frequency recovery. The algorithm includes an inner and an outer loop (see figure). An initial estimate of phase is used to start the algorithm on the inner loop, wherein multiple intensity images are processed, each using a different defocus value. The processing is done by an iterative-transform method, yielding individual phase estimates corresponding to each image of the defocus-diversity data set. These individual phase estimates are combined in a weighted average to form a new phase estimate, which serves as the initial phase estimate for either the next iteration of the iterative-transform method or, if the maximum number of iterations has been reached, for the next several steps, which constitute the outerloop portion of the algorithm. The details of the next several steps must be omitted here for the sake of brevity. The overall effect of these steps is to adaptively update the diversity defocus values according to recovery of global defocus in the phase estimate. Aberration recovery varies with differing amounts as the amount of diversity defocus is updated in each image; thus, feedback is incorporated into the recovery process. This process is iterated until the global defocus error is driven to zero during the recovery process. The amplitude of aberration may far exceed one wavelength after completion of the inner-loop portion of the algorithm, and the classical iterative transform method does not, by itself, enable recovery of multi-wavelength aberrations. Hence, in the absence of a means of off-loading the multi-wavelength portion of the aberration, the algorithm would produce a wrapped phase map. However, a special aberration-fitting procedure can be applied to the wrapped phase data to transfer at least some portion of the multi-wavelength aberration to the diversity function, wherein the data are treated as known phase values. In this way, a multiwavelength aberration can be recovered incrementally by successively applying the aberration-fitting procedure to intermediate wrapped phase maps. During recovery, as more of the aberration is transferred to the diversity function following successive iterations around the ter loop, the estimated phase ceases to wrap in places where the aberration values become incorporated as part of the diversity function. As a result, as the aberration content is transferred to the diversity function, the phase estimate resembles that of a reference flat.

Sequentially reweighted TV minimization for CT metal artifact reduction.

PubMed

Zhang, Xiaomeng; Xing, Lei

2013-07-01

Metal artifact reduction has long been an important topic in x-ray CT image reconstruction. In this work, the authors propose an iterative method that sequentially minimizes a reweighted total variation (TV) of the image and produces substantially artifact-reduced reconstructions. A sequentially reweighted TV minimization algorithm is proposed to fully exploit the sparseness of image gradients (IG). The authors first formulate a constrained optimization model that minimizes a weighted TV of the image, subject to the constraint that the estimated projection data are within a specified tolerance of the available projection measurements, with image non-negativity enforced. The authors then solve a sequence of weighted TV minimization problems where weights used for the next iteration are computed from the current solution. Using the complete projection data, the algorithm first reconstructs an image from which a binary metal image can be extracted. Forward projection of the binary image identifies metal traces in the projection space. The metal-free background image is then reconstructed from the metal-trace-excluded projection data by employing a different set of weights. Each minimization problem is solved using a gradient method that alternates projection-onto-convex-sets and steepest descent. A series of simulation and experimental studies are performed to evaluate the proposed approach. Our study shows that the sequentially reweighted scheme, by altering a single parameter in the weighting function, flexibly controls the sparsity of the IG and reconstructs artifacts-free images in a two-stage process. It successfully produces images with significantly reduced streak artifacts, suppressed noise and well-preserved contrast and edge properties. The sequentially reweighed TV minimization provides a systematic approach for suppressing CT metal artifacts. The technique can also be generalized to other "missing data" problems in CT image reconstruction.

Adaptively Tuned Iterative Low Dose CT Image Denoising

PubMed Central

Hashemi, SayedMasoud; Paul, Narinder S.; Beheshti, Soosan; Cobbold, Richard S. C.

2015-01-01

Improving image quality is a critical objective in low dose computed tomography (CT) imaging and is the primary focus of CT image denoising. State-of-the-art CT denoising algorithms are mainly based on iterative minimization of an objective function, in which the performance is controlled by regularization parameters. To achieve the best results, these should be chosen carefully. However, the parameter selection is typically performed in an ad hoc manner, which can cause the algorithms to converge slowly or become trapped in a local minimum. To overcome these issues a noise confidence region evaluation (NCRE) method is used, which evaluates the denoising residuals iteratively and compares their statistics with those produced by additive noise. It then updates the parameters at the end of each iteration to achieve a better match to the noise statistics. By combining NCRE with the fundamentals of block matching and 3D filtering (BM3D) approach, a new iterative CT image denoising method is proposed. It is shown that this new denoising method improves the BM3D performance in terms of both the mean square error and a structural similarity index. Moreover, simulations and patient results show that this method preserves the clinically important details of low dose CT images together with a substantial noise reduction. PMID:26089972

Sequential computation of elementary modes and minimal cut sets in genome-scale metabolic networks using alternate integer linear programming.

PubMed

Song, Hyun-Seob; Goldberg, Noam; Mahajan, Ashutosh; Ramkrishna, Doraiswami

2017-08-01

Elementary (flux) modes (EMs) have served as a valuable tool for investigating structural and functional properties of metabolic networks. Identification of the full set of EMs in genome-scale networks remains challenging due to combinatorial explosion of EMs in complex networks. It is often, however, that only a small subset of relevant EMs needs to be known, for which optimization-based sequential computation is a useful alternative. Most of the currently available methods along this line are based on the iterative use of mixed integer linear programming (MILP), the effectiveness of which significantly deteriorates as the number of iterations builds up. To alleviate the computational burden associated with the MILP implementation, we here present a novel optimization algorithm termed alternate integer linear programming (AILP). Our algorithm was designed to iteratively solve a pair of integer programming (IP) and linear programming (LP) to compute EMs in a sequential manner. In each step, the IP identifies a minimal subset of reactions, the deletion of which disables all previously identified EMs. Thus, a subsequent LP solution subject to this reaction deletion constraint becomes a distinct EM. In cases where no feasible LP solution is available, IP-derived reaction deletion sets represent minimal cut sets (MCSs). Despite the additional computation of MCSs, AILP achieved significant time reduction in computing EMs by orders of magnitude. The proposed AILP algorithm not only offers a computational advantage in the EM analysis of genome-scale networks, but also improves the understanding of the linkage between EMs and MCSs. The software is implemented in Matlab, and is provided as supplementary information . hyunseob.song@pnnl.gov. Supplementary data are available at Bioinformatics online. Published by Oxford University Press 2017. This work is written by US Government employees and are in the public domain in the US.

Enhancing Sparsity by Reweighted l(1) Minimization

DTIC Science & Technology

2008-07-01

recovery depends on the sparsity level k. The dashed curves represent a reweighted ℓ1 algorithm that outperforms the traditional unweighted ℓ1...approach (solid curve ). (a) Performance after 4 reweighting iterations as a function of ǫ. (b) Performance with fixed ǫ = 0.1 as a function of the number of...signal recovery (declared when ‖x0 − x‖ℓ∞ ≤ 10−3) for the unweighted ℓ1 algorithm as a function of the sparsity level k. The dashed curves represent the

Accelerating the weighted histogram analysis method by direct inversion in the iterative subspace.

PubMed

Zhang, Cheng; Lai, Chun-Liang; Pettitt, B Montgomery

The weighted histogram analysis method (WHAM) for free energy calculations is a valuable tool to produce free energy differences with the minimal errors. Given multiple simulations, WHAM obtains from the distribution overlaps the optimal statistical estimator of the density of states, from which the free energy differences can be computed. The WHAM equations are often solved by an iterative procedure. In this work, we use a well-known linear algebra algorithm which allows for more rapid convergence to the solution. We find that the computational complexity of the iterative solution to WHAM and the closely-related multiple Bennett acceptance ratio (MBAR) method can be improved by using the method of direct inversion in the iterative subspace. We give examples from a lattice model, a simple liquid and an aqueous protein solution.

Feature-based three-dimensional registration for repetitive geometry in machine vision

PubMed Central

Gong, Yuanzheng; Seibel, Eric J.

2016-01-01

As an important step in three-dimensional (3D) machine vision, 3D registration is a process of aligning two or multiple 3D point clouds that are collected from different perspectives together into a complete one. The most popular approach to register point clouds is to minimize the difference between these point clouds iteratively by Iterative Closest Point (ICP) algorithm. However, ICP does not work well for repetitive geometries. To solve this problem, a feature-based 3D registration algorithm is proposed to align the point clouds that are generated by vision-based 3D reconstruction. By utilizing texture information of the object and the robustness of image features, 3D correspondences can be retrieved so that the 3D registration of two point clouds is to solve a rigid transformation. The comparison of our method and different ICP algorithms demonstrates that our proposed algorithm is more accurate, efficient and robust for repetitive geometry registration. Moreover, this method can also be used to solve high depth uncertainty problem caused by little camera baseline in vision-based 3D reconstruction. PMID:28286703

SU-E-I-01: Iterative CBCT Reconstruction with a Feature-Preserving Penalty

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

Lyu, Q; Li, B; Southern Medical University, Guangzhou

2015-06-15

Purpose: Low-dose CBCT is desired in various clinical applications. Iterative image reconstruction algorithms have shown advantages in suppressing noise in low-dose CBCT. However, due to the smoothness constraint enforced during the reconstruction process, edges may be blurred and image features may lose in the reconstructed image. In this work, we proposed a new penalty design to preserve image features in the image reconstructed by iterative algorithms. Methods: Low-dose CBCT is reconstructed by minimizing the penalized weighted least-squares (PWLS) objective function. Binary Robust Independent Elementary Features (BRIEF) of the image were integrated into the penalty of PWLS. BRIEF is a generalmore » purpose point descriptor that can be used to identify important features of an image. In this work, BRIEF distance of two neighboring pixels was used to weigh the smoothing parameter in PWLS. For pixels of large BRIEF distance, weaker smooth constraint will be enforced. Image features will be better preserved through such a design. The performance of the PWLS algorithm with BRIEF penalty was evaluated by a CatPhan 600 phantom. Results: The image quality reconstructed by the proposed PWLS-BRIEF algorithm is superior to that by the conventional PWLS method and the standard FDK method. At matched noise level, edges in PWLS-BRIEF reconstructed image are better preserved. Conclusion: This study demonstrated that the proposed PWLS-BRIEF algorithm has great potential on preserving image features in low-dose CBCT.« less

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Jothiprasad, Giridhar; Mavriplis, Dimitri J.; Caughey, David A.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The efficiency gains obtained using higher-order implicit Runge-Kutta schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each timestep are presented. The first algorithm (NMG) is a pseudo-time-stepping scheme which employs a non-linear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on Inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the Generalized Minimal Residual method. Results demonstrating the relative superiority of these Newton's methods based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes with the more efficient nonlinear solvers.

Accelerating an Ordered-Subset Low-Dose X-Ray Cone Beam Computed Tomography Image Reconstruction with a Power Factor and Total Variation Minimization.

PubMed

Huang, Hsuan-Ming; Hsiao, Ing-Tsung

2016-01-01

In recent years, there has been increased interest in low-dose X-ray cone beam computed tomography (CBCT) in many fields, including dentistry, guided radiotherapy and small animal imaging. Despite reducing the radiation dose, low-dose CBCT has not gained widespread acceptance in routine clinical practice. In addition to performing more evaluation studies, developing a fast and high-quality reconstruction algorithm is required. In this work, we propose an iterative reconstruction method that accelerates ordered-subsets (OS) reconstruction using a power factor. Furthermore, we combine it with the total-variation (TV) minimization method. Both simulation and phantom studies were conducted to evaluate the performance of the proposed method. Results show that the proposed method can accelerate conventional OS methods, greatly increase the convergence speed in early iterations. Moreover, applying the TV minimization to the power acceleration scheme can further improve the image quality while preserving the fast convergence rate.

Accelerating an Ordered-Subset Low-Dose X-Ray Cone Beam Computed Tomography Image Reconstruction with a Power Factor and Total Variation Minimization

PubMed Central

Huang, Hsuan-Ming; Hsiao, Ing-Tsung

2016-01-01

In recent years, there has been increased interest in low-dose X-ray cone beam computed tomography (CBCT) in many fields, including dentistry, guided radiotherapy and small animal imaging. Despite reducing the radiation dose, low-dose CBCT has not gained widespread acceptance in routine clinical practice. In addition to performing more evaluation studies, developing a fast and high-quality reconstruction algorithm is required. In this work, we propose an iterative reconstruction method that accelerates ordered-subsets (OS) reconstruction using a power factor. Furthermore, we combine it with the total-variation (TV) minimization method. Both simulation and phantom studies were conducted to evaluate the performance of the proposed method. Results show that the proposed method can accelerate conventional OS methods, greatly increase the convergence speed in early iterations. Moreover, applying the TV minimization to the power acceleration scheme can further improve the image quality while preserving the fast convergence rate. PMID:27073853

Penalized Weighted Least-Squares Approach to Sinogram Noise Reduction and Image Reconstruction for Low-Dose X-Ray Computed Tomography

PubMed Central

Wang, Jing; Li, Tianfang; Lu, Hongbing; Liang, Zhengrong

2006-01-01

Reconstructing low-dose X-ray CT (computed tomography) images is a noise problem. This work investigated a penalized weighted least-squares (PWLS) approach to address this problem in two dimensions, where the WLS considers first- and second-order noise moments and the penalty models signal spatial correlations. Three different implementations were studied for the PWLS minimization. One utilizes a MRF (Markov random field) Gibbs functional to consider spatial correlations among nearby detector bins and projection views in sinogram space and minimizes the PWLS cost function by iterative Gauss-Seidel algorithm. Another employs Karhunen-Loève (KL) transform to de-correlate data signals among nearby views and minimizes the PWLS adaptively to each KL component by analytical calculation, where the spatial correlation among nearby bins is modeled by the same Gibbs functional. The third one models the spatial correlations among image pixels in image domain also by a MRF Gibbs functional and minimizes the PWLS by iterative successive over-relaxation algorithm. In these three implementations, a quadratic functional regularization was chosen for the MRF model. Phantom experiments showed a comparable performance of these three PWLS-based methods in terms of suppressing noise-induced streak artifacts and preserving resolution in the reconstructed images. Computer simulations concurred with the phantom experiments in terms of noise-resolution tradeoff and detectability in low contrast environment. The KL-PWLS implementation may have the advantage in terms of computation for high-resolution dynamic low-dose CT imaging. PMID:17024831

Regularized minimum I-divergence methods for the inverse blackbody radiation problem

NASA Astrophysics Data System (ADS)

Choi, Kerkil; Lanterman, Aaron D.; Shin, Jaemin

2006-08-01

This paper proposes iterative methods for estimating the area temperature distribution of a blackbody from its total radiated power spectrum measurements. This is called the inverse blackbody radiation problem. This problem is inherently ill-posed due to the characteristics of the kernel in the underlying integral equation given by Planck's law. The functions involved in the problem are all non-negative. Csiszár's I-divergence is an information-theoretic discrepancy measure between two non-negative functions. We derive iterative methods for minimizing Csiszár's I-divergence between the measured power spectrum and the power spectrum arising from the estimate according to the integral equation. Due to the ill-posedness of the problem, unconstrained algorithms often produce poor estimates, especially when the measurements are corrupted by noise. To alleviate this difficulty, we apply regularization methods to our algorithms. Penalties based on Shannon's entropy, the L1-norm and Good's roughness are chosen to suppress the undesirable artefacts. When a penalty is applied, the pertinent optimization that needs to be performed at each iteration is no longer trivial. In particular, Good's roughness causes couplings between estimate components. To handle this issue, we adapt Green's one-step-late method. This choice is based on the important fact that our minimum I-divergence algorithms can be interpreted as asymptotic forms of certain expectation-maximization algorithms. The effectiveness of our methods is illustrated via various numerical experiments.

TH-E-17A-06: Anatomical-Adaptive Compressed Sensing (AACS) Reconstruction for Thoracic 4-Dimensional Cone-Beam CT

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

Shieh, C; Kipritidis, J; OBrien, R

2014-06-15

Purpose: The Feldkamp-Davis-Kress (FDK) algorithm currently used for clinical thoracic 4-dimensional (4D) cone-beam CT (CBCT) reconstruction suffers from noise and streaking artifacts due to projection under-sampling. Compressed sensing theory enables reconstruction of under-sampled datasets via total-variation (TV) minimization, but TV-minimization algorithms such as adaptive-steepest-descent-projection-onto-convex-sets (ASD-POCS) often converge slowly and are prone to over-smoothing anatomical details. These disadvantages can be overcome by incorporating general anatomical knowledge via anatomy segmentation. Based on this concept, we have developed an anatomical-adaptive compressed sensing (AACS) algorithm for thoracic 4D-CBCT reconstruction. Methods: AACS is based on the ASD-POCS framework, where each iteration consists of a TV-minimizationmore » step and a data fidelity constraint step. Prior to every AACS iteration, four major thoracic anatomical structures - soft tissue, lungs, bony anatomy, and pulmonary details - were segmented from the updated solution image. Based on the segmentation, an anatomical-adaptive weighting was applied to the TV-minimization step, so that TV-minimization was enhanced at noisy/streaky regions and suppressed at anatomical structures of interest. The image quality and convergence speed of AACS was compared to conventional ASD-POCS using an XCAT digital phantom and a patient scan. Results: For the XCAT phantom, the AACS image represented the ground truth better than the ASD-POCS image, giving a higher structural similarity index (0.93 vs. 0.84) and lower absolute difference (1.1*10{sup 4} vs. 1.4*10{sup 4}). For the patient case, while both algorithms resulted in much less noise and streaking than FDK, the AACS image showed considerably better contrast and sharpness of the vessels, tumor, and fiducial marker than the ASD-POCS image. In addition, AACS converged over 50% faster than ASD-POCS in both cases. Conclusions: The proposed AACS algorithm was shown to reconstruct thoracic 4D-CBCT images more accurately and with faster convergence compared to ASD-POCS. The superior image quality and rapid convergence makes AACS promising for future clinical use.« less

Sequential and parallel image restoration: neural network implementations.

PubMed

Figueiredo, M T; Leitao, J N

1994-01-01

Sequential and parallel image restoration algorithms and their implementations on neural networks are proposed. For images degraded by linear blur and contaminated by additive white Gaussian noise, maximum a posteriori (MAP) estimation and regularization theory lead to the same high dimension convex optimization problem. The commonly adopted strategy (in using neural networks for image restoration) is to map the objective function of the optimization problem into the energy of a predefined network, taking advantage of its energy minimization properties. Departing from this approach, we propose neural implementations of iterative minimization algorithms which are first proved to converge. The developed schemes are based on modified Hopfield (1985) networks of graded elements, with both sequential and parallel updating schedules. An algorithm supported on a fully standard Hopfield network (binary elements and zero autoconnections) is also considered. Robustness with respect to finite numerical precision is studied, and examples with real images are presented.

A general framework for regularized, similarity-based image restoration.

PubMed

Kheradmand, Amin; Milanfar, Peyman

2014-12-01

Any image can be represented as a function defined on a weighted graph, in which the underlying structure of the image is encoded in kernel similarity and associated Laplacian matrices. In this paper, we develop an iterative graph-based framework for image restoration based on a new definition of the normalized graph Laplacian. We propose a cost function, which consists of a new data fidelity term and regularization term derived from the specific definition of the normalized graph Laplacian. The normalizing coefficients used in the definition of the Laplacian and associated regularization term are obtained using fast symmetry preserving matrix balancing. This results in some desired spectral properties for the normalized Laplacian such as being symmetric, positive semidefinite, and returning zero vector when applied to a constant image. Our algorithm comprises of outer and inner iterations, where in each outer iteration, the similarity weights are recomputed using the previous estimate and the updated objective function is minimized using inner conjugate gradient iterations. This procedure improves the performance of the algorithm for image deblurring, where we do not have access to a good initial estimate of the underlying image. In addition, the specific form of the cost function allows us to render the spectral analysis for the solutions of the corresponding linear equations. In addition, the proposed approach is general in the sense that we have shown its effectiveness for different restoration problems, including deblurring, denoising, and sharpening. Experimental results verify the effectiveness of the proposed algorithm on both synthetic and real examples.

Modified conjugate gradient method for diagonalizing large matrices.

PubMed

Jie, Quanlin; Liu, Dunhuan

2003-11-01

We present an iterative method to diagonalize large matrices. The basic idea is the same as the conjugate gradient (CG) method, i.e, minimizing the Rayleigh quotient via its gradient and avoiding reintroducing errors to the directions of previous gradients. Each iteration step is to find lowest eigenvector of the matrix in a subspace spanned by the current trial vector and the corresponding gradient of the Rayleigh quotient, as well as some previous trial vectors. The gradient, together with the previous trial vectors, play a similar role as the conjugate gradient of the original CG algorithm. Our numeric tests indicate that this method converges significantly faster than the original CG method. And the computational cost of one iteration step is about the same as the original CG method. It is suitable for first principle calculations.

Low Dose CT Reconstruction via Edge-preserving Total Variation Regularization

PubMed Central

Tian, Zhen; Jia, Xun; Yuan, Kehong; Pan, Tinsu; Jiang, Steve B.

2014-01-01

High radiation dose in CT scans increases a lifetime risk of cancer and has become a major clinical concern. Recently, iterative reconstruction algorithms with Total Variation (TV) regularization have been developed to reconstruct CT images from highly undersampled data acquired at low mAs levels in order to reduce the imaging dose. Nonetheless, the low contrast structures tend to be smoothed out by the TV regularization, posing a great challenge for the TV method. To solve this problem, in this work we develop an iterative CT reconstruction algorithm with edge-preserving TV regularization to reconstruct CT images from highly undersampled data obtained at low mAs levels. The CT image is reconstructed by minimizing an energy consisting of an edge-preserving TV norm and a data fidelity term posed by the x-ray projections. The edge-preserving TV term is proposed to preferentially perform smoothing only on non-edge part of the image in order to better preserve the edges, which is realized by introducing a penalty weight to the original total variation norm. During the reconstruction process, the pixels at edges would be gradually identified and given small penalty weight. Our iterative algorithm is implemented on GPU to improve its speed. We test our reconstruction algorithm on a digital NCAT phantom, a physical chest phantom, and a Catphan phantom. Reconstruction results from a conventional FBP algorithm and a TV regularization method without edge preserving penalty are also presented for comparison purpose. The experimental results illustrate that both TV-based algorithm and our edge-preserving TV algorithm outperform the conventional FBP algorithm in suppressing the streaking artifacts and image noise under the low dose context. Our edge-preserving algorithm is superior to the TV-based algorithm in that it can preserve more information of low contrast structures and therefore maintain acceptable spatial resolution. PMID:21860076

Iterative metal artifact reduction for x-ray computed tomography using unmatched projector/backprojector pairs

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

Zhang, Hanming; Wang, Linyuan; Li, Lei

2016-06-15

Purpose: Metal artifact reduction (MAR) is a major problem and a challenging issue in x-ray computed tomography (CT) examinations. Iterative reconstruction from sinograms unaffected by metals shows promising potential in detail recovery. This reconstruction has been the subject of much research in recent years. However, conventional iterative reconstruction methods easily introduce new artifacts around metal implants because of incomplete data reconstruction and inconsistencies in practical data acquisition. Hence, this work aims at developing a method to suppress newly introduced artifacts and improve the image quality around metal implants for the iterative MAR scheme. Methods: The proposed method consists of twomore » steps based on the general iterative MAR framework. An uncorrected image is initially reconstructed, and the corresponding metal trace is obtained. The iterative reconstruction method is then used to reconstruct images from the unaffected sinogram. In the reconstruction step of this work, an iterative strategy utilizing unmatched projector/backprojector pairs is used. A ramp filter is introduced into the back-projection procedure to restrain the inconsistency components in low frequencies and generate more reliable images of the regions around metals. Furthermore, a constrained total variation (TV) minimization model is also incorporated to enhance efficiency. The proposed strategy is implemented based on an iterative FBP and an alternating direction minimization (ADM) scheme, respectively. The developed algorithms are referred to as “iFBP-TV” and “TV-FADM,” respectively. Two projection-completion-based MAR methods and three iterative MAR methods are performed simultaneously for comparison. Results: The proposed method performs reasonably on both simulation and real CT-scanned datasets. This approach could reduce streak metal artifacts effectively and avoid the mentioned effects in the vicinity of the metals. The improvements are evaluated by inspecting regions of interest and by comparing the root-mean-square errors, normalized mean absolute distance, and universal quality index metrics of the images. Both iFBP-TV and TV-FADM methods outperform other counterparts in all cases. Unlike the conventional iterative methods, the proposed strategy utilizing unmatched projector/backprojector pairs shows excellent performance in detail preservation and prevention of the introduction of new artifacts. Conclusions: Qualitative and quantitative evaluations of experimental results indicate that the developed method outperforms classical MAR algorithms in suppressing streak artifacts and preserving the edge structural information of the object. In particular, structures lying close to metals can be gradually recovered because of the reduction of artifacts caused by inconsistency effects.« less

Value Iteration Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems.

PubMed

Wei, Qinglai; Liu, Derong; Lin, Hanquan

2016-03-01

In this paper, a value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon undiscounted optimal control problems for discrete-time nonlinear systems. The present value iteration ADP algorithm permits an arbitrary positive semi-definite function to initialize the algorithm. A novel convergence analysis is developed to guarantee that the iterative value function converges to the optimal performance index function. Initialized by different initial functions, it is proven that the iterative value function will be monotonically nonincreasing, monotonically nondecreasing, or nonmonotonic and will converge to the optimum. In this paper, for the first time, the admissibility properties of the iterative control laws are developed for value iteration algorithms. It is emphasized that new termination criteria are established to guarantee the effectiveness of the iterative control laws. Neural networks are used to approximate the iterative value function and compute the iterative control law, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.

Updating finite element dynamic models using an element-by-element sensitivity methodology

NASA Technical Reports Server (NTRS)

Farhat, Charbel; Hemez, Francois M.

1993-01-01

A sensitivity-based methodology for improving the finite element model of a given structure using test modal data and a few sensors is presented. The proposed method searches for both the location and sources of the mass and stiffness errors and does not interfere with the theory behind the finite element model while correcting these errors. The updating algorithm is derived from the unconstrained minimization of the squared L sub 2 norms of the modal dynamic residuals via an iterative two-step staggered procedure. At each iteration, the measured mode shapes are first expanded assuming that the model is error free, then the model parameters are corrected assuming that the expanded mode shapes are exact. The numerical algorithm is implemented in an element-by-element fashion and is capable of 'zooming' on the detected error locations. Several simulation examples which demonstate the potential of the proposed methodology are discussed.

Assessing performance of flaw characterization methods through uncertainty propagation

NASA Astrophysics Data System (ADS)

Miorelli, R.; Le Bourdais, F.; Artusi, X.

2018-04-01

In this work, we assess the inversion performance in terms of crack characterization and localization based on synthetic signals associated to ultrasonic and eddy current physics. More precisely, two different standard iterative inversion algorithms are used to minimize the discrepancy between measurements (i.e., the tested data) and simulations. Furthermore, in order to speed up the computational time and get rid of the computational burden often associated to iterative inversion algorithms, we replace the standard forward solver by a suitable metamodel fit on a database built offline. In a second step, we assess the inversion performance by adding uncertainties on a subset of the database parameters and then, through the metamodel, we propagate these uncertainties within the inversion procedure. The fast propagation of uncertainties enables efficiently evaluating the impact due to the lack of knowledge on some parameters employed to describe the inspection scenarios, which is a situation commonly encountered in the industrial NDE context.

Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices

NASA Technical Reports Server (NTRS)

Freund, Roland

1989-01-01

We consider conjugate gradient type methods for the solution of large sparse linear system Ax equals b with complex symmetric coefficient matrices A equals A(T). Such linear systems arise in important applications, such as the numerical solution of the complex Helmholtz equation. Furthermore, most complex non-Hermitian linear systems which occur in practice are actually complex symmetric. We investigate conjugate gradient type iterations which are based on a variant of the nonsymmetric Lanczos algorithm for complex symmetric matrices. We propose a new approach with iterates defined by a quasi-minimal residual property. The resulting algorithm presents several advantages over the standard biconjugate gradient method. We also include some remarks on the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

Efficient computation paths for the systematic analysis of sensitivities

NASA Astrophysics Data System (ADS)

Greppi, Paolo; Arato, Elisabetta

2013-01-01

A systematic sensitivity analysis requires computing the model on all points of a multi-dimensional grid covering the domain of interest, defined by the ranges of variability of the inputs. The issues to efficiently perform such analyses on algebraic models are handling solution failures within and close to the feasible region and minimizing the total iteration count. Scanning the domain in the obvious order is sub-optimal in terms of total iterations and is likely to cause many solution failures. The problem of choosing a better order can be translated geometrically into finding Hamiltonian paths on certain grid graphs. This work proposes two paths, one based on a mixed-radix Gray code and the other, a quasi-spiral path, produced by a novel heuristic algorithm. Some simple, easy-to-visualize examples are presented, followed by performance results for the quasi-spiral algorithm and the practical application of the different paths in a process simulation tool.

Comparison of SIRT and SQS for Regularized Weighted Least Squares Image Reconstruction

PubMed Central

Gregor, Jens; Fessler, Jeffrey A.

2015-01-01

Tomographic image reconstruction is often formulated as a regularized weighted least squares (RWLS) problem optimized by iterative algorithms that are either inherently algebraic or derived from a statistical point of view. This paper compares a modified version of SIRT (Simultaneous Iterative Reconstruction Technique), which is of the former type, with a version of SQS (Separable Quadratic Surrogates), which is of the latter type. We show that the two algorithms minimize the same criterion function using similar forms of preconditioned gradient descent. We present near-optimal relaxation for both based on eigenvalue bounds and include a heuristic extension for use with ordered subsets. We provide empirical evidence that SIRT and SQS converge at the same rate for all intents and purposes. For context, we compare their performance with an implementation of preconditioned conjugate gradient. The illustrative application is X-ray CT of luggage for aviation security. PMID:26478906

Multiplicative noise removal through fractional order tv-based model and fast numerical schemes for its approximation

NASA Astrophysics Data System (ADS)

Ullah, Asmat; Chen, Wen; Khan, Mushtaq Ahmad

2017-07-01

This paper introduces a fractional order total variation (FOTV) based model with three different weights in the fractional order derivative definition for multiplicative noise removal purpose. The fractional-order Euler Lagrange equation which is a highly non-linear partial differential equation (PDE) is obtained by the minimization of the energy functional for image restoration. Two numerical schemes namely an iterative scheme based on the dual theory and majorization- minimization algorithm (MMA) are used. To improve the restoration results, we opt for an adaptive parameter selection procedure for the proposed model by applying the trial and error method. We report numerical simulations which show the validity and state of the art performance of the fractional-order model in visual improvement as well as an increase in the peak signal to noise ratio comparing to corresponding methods. Numerical experiments also demonstrate that MMAbased methodology is slightly better than that of an iterative scheme.

Algorithm for Identifying Erroneous Rain-Gauge Readings

NASA Technical Reports Server (NTRS)

Rickman, Doug

2005-01-01

An algorithm analyzes rain-gauge data to identify statistical outliers that could be deemed to be erroneous readings. Heretofore, analyses of this type have been performed in burdensome manual procedures that have involved subjective judgements. Sometimes, the analyses have included computational assistance for detecting values falling outside of arbitrary limits. The analyses have been performed without statistically valid knowledge of the spatial and temporal variations of precipitation within rain events. In contrast, the present algorithm makes it possible to automate such an analysis, makes the analysis objective, takes account of the spatial distribution of rain gauges in conjunction with the statistical nature of spatial variations in rainfall readings, and minimizes the use of arbitrary criteria. The algorithm implements an iterative process that involves nonparametric statistics.

Investigation of cone-beam CT image quality trade-off for image-guided radiation therapy

NASA Astrophysics Data System (ADS)

Bian, Junguo; Sharp, Gregory C.; Park, Yang-Kyun; Ouyang, Jinsong; Bortfeld, Thomas; El Fakhri, Georges

2016-05-01

It is well-known that projections acquired over an angular range slightly over 180° (so-called short scan) are sufficient for fan-beam reconstruction. However, due to practical imaging conditions (projection data and reconstruction image discretization, physical factors, and data noise), the short-scan reconstructions may have different appearances and properties from the full-scan (scans over 360°) reconstructions. Nevertheless, short-scan configurations have been used in applications such as cone-beam CT (CBCT) for head-neck-cancer image-guided radiation therapy (IGRT) that only requires a small field of view due to the potential reduced imaging time and dose. In this work, we studied the image quality trade-off for full, short, and full/short scan configurations with both conventional filtered-backprojection (FBP) reconstruction and iterative reconstruction algorithms based on total-variation (TV) minimization for head-neck-cancer IGRT. Anthropomorphic and Catphan phantoms were scanned at different exposure levels with a clinical scanner used in IGRT. Both visualization- and numerical-metric-based evaluation studies were performed. The results indicate that the optimal exposure level and number of views are in the middle range for both FBP and TV-based iterative algorithms and the optimization is object-dependent and task-dependent. The optimal view numbers decrease with the total exposure levels for both FBP and TV-based algorithms. The results also indicate there are slight differences between FBP and TV-based iterative algorithms for the image quality trade-off: FBP seems to be more in favor of larger number of views while the TV-based algorithm is more robust to different data conditions (number of views and exposure levels) than the FBP algorithm. The studies can provide a general guideline for image-quality optimization for CBCT used in IGRT and other applications.

Investigation of cone-beam CT image quality trade-off for image-guided radiation therapy.

PubMed

Bian, Junguo; Sharp, Gregory C; Park, Yang-Kyun; Ouyang, Jinsong; Bortfeld, Thomas; El Fakhri, Georges

2016-05-07

It is well-known that projections acquired over an angular range slightly over 180° (so-called short scan) are sufficient for fan-beam reconstruction. However, due to practical imaging conditions (projection data and reconstruction image discretization, physical factors, and data noise), the short-scan reconstructions may have different appearances and properties from the full-scan (scans over 360°) reconstructions. Nevertheless, short-scan configurations have been used in applications such as cone-beam CT (CBCT) for head-neck-cancer image-guided radiation therapy (IGRT) that only requires a small field of view due to the potential reduced imaging time and dose. In this work, we studied the image quality trade-off for full, short, and full/short scan configurations with both conventional filtered-backprojection (FBP) reconstruction and iterative reconstruction algorithms based on total-variation (TV) minimization for head-neck-cancer IGRT. Anthropomorphic and Catphan phantoms were scanned at different exposure levels with a clinical scanner used in IGRT. Both visualization- and numerical-metric-based evaluation studies were performed. The results indicate that the optimal exposure level and number of views are in the middle range for both FBP and TV-based iterative algorithms and the optimization is object-dependent and task-dependent. The optimal view numbers decrease with the total exposure levels for both FBP and TV-based algorithms. The results also indicate there are slight differences between FBP and TV-based iterative algorithms for the image quality trade-off: FBP seems to be more in favor of larger number of views while the TV-based algorithm is more robust to different data conditions (number of views and exposure levels) than the FBP algorithm. The studies can provide a general guideline for image-quality optimization for CBCT used in IGRT and other applications.

Improved bioluminescence and fluorescence reconstruction algorithms using diffuse optical tomography, normalized data, and optimized selection of the permissible source region

PubMed Central

Naser, Mohamed A.; Patterson, Michael S.

2011-01-01

Reconstruction algorithms are presented for two-step solutions of the bioluminescence tomography (BLT) and the fluorescence tomography (FT) problems. In the first step, a continuous wave (cw) diffuse optical tomography (DOT) algorithm is used to reconstruct the tissue optical properties assuming known anatomical information provided by x-ray computed tomography or other methods. Minimization problems are formed based on L1 norm objective functions, where normalized values for the light fluence rates and the corresponding Green’s functions are used. Then an iterative minimization solution shrinks the permissible regions where the sources are allowed by selecting points with higher probability to contribute to the source distribution. Throughout this process the permissible region shrinks from the entire object to just a few points. The optimum reconstructed bioluminescence and fluorescence distributions are chosen to be the results of the iteration corresponding to the permissible region where the objective function has its global minimum This provides efficient BLT and FT reconstruction algorithms without the need for a priori information about the bioluminescence sources or the fluorophore concentration. Multiple small sources and large distributed sources can be reconstructed with good accuracy for the location and the total source power for BLT and the total number of fluorophore molecules for the FT. For non-uniform distributed sources, the size and magnitude become degenerate due to the degrees of freedom available for possible solutions. However, increasing the number of data points by increasing the number of excitation sources can improve the accuracy of reconstruction for non-uniform fluorophore distributions. PMID:21326647

Quasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smoother

NASA Astrophysics Data System (ADS)

Fillion, Anthony; Bocquet, Marc; Gratton, Serge

2018-04-01

The analysis in nonlinear variational data assimilation is the solution of a non-quadratic minimization. Thus, the analysis efficiency relies on its ability to locate a global minimum of the cost function. If this minimization uses a Gauss-Newton (GN) method, it is critical for the starting point to be in the attraction basin of a global minimum. Otherwise the method may converge to a local extremum, which degrades the analysis. With chaotic models, the number of local extrema often increases with the temporal extent of the data assimilation window, making the former condition harder to satisfy. This is unfortunate because the assimilation performance also increases with this temporal extent. However, a quasi-static (QS) minimization may overcome these local extrema. It accomplishes this by gradually injecting the observations in the cost function. This method was introduced by Pires et al. (1996) in a 4D-Var context. We generalize this approach to four-dimensional strong-constraint nonlinear ensemble variational (EnVar) methods, which are based on both a nonlinear variational analysis and the propagation of dynamical error statistics via an ensemble. This forces one to consider the cost function minimizations in the broader context of cycled data assimilation algorithms. We adapt this QS approach to the iterative ensemble Kalman smoother (IEnKS), an exemplar of nonlinear deterministic four-dimensional EnVar methods. Using low-order models, we quantify the positive impact of the QS approach on the IEnKS, especially for long data assimilation windows. We also examine the computational cost of QS implementations and suggest cheaper algorithms.

A Universal Tare Load Prediction Algorithm for Strain-Gage Balance Calibration Data Analysis

NASA Technical Reports Server (NTRS)

Ulbrich, N.

2011-01-01

An algorithm is discussed that may be used to estimate tare loads of wind tunnel strain-gage balance calibration data. The algorithm was originally developed by R. Galway of IAR/NRC Canada and has been described in the literature for the iterative analysis technique. Basic ideas of Galway's algorithm, however, are universally applicable and work for both the iterative and the non-iterative analysis technique. A recent modification of Galway's algorithm is presented that improves the convergence behavior of the tare load prediction process if it is used in combination with the non-iterative analysis technique. The modified algorithm allows an analyst to use an alternate method for the calculation of intermediate non-linear tare load estimates whenever Galway's original approach does not lead to a convergence of the tare load iterations. It is also shown in detail how Galway's algorithm may be applied to the non-iterative analysis technique. Hand load data from the calibration of a six-component force balance is used to illustrate the application of the original and modified tare load prediction method. During the analysis of the data both the iterative and the non-iterative analysis technique were applied. Overall, predicted tare loads for combinations of the two tare load prediction methods and the two balance data analysis techniques showed excellent agreement as long as the tare load iterations converged. The modified algorithm, however, appears to have an advantage over the original algorithm when absolute voltage measurements of gage outputs are processed using the non-iterative analysis technique. In these situations only the modified algorithm converged because it uses an exact solution of the intermediate non-linear tare load estimate for the tare load iteration.

A different approach to estimate nonlinear regression model using numerical methods

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper concerns with the computational methods namely the Gauss-Newton method, Gradient algorithm methods (Newton-Raphson method, Steepest Descent or Steepest Ascent algorithm method, the Method of Scoring, the Method of Quadratic Hill-Climbing) based on numerical analysis to estimate parameters of nonlinear regression model in a very different way. Principles of matrix calculus have been used to discuss the Gradient-Algorithm methods. Yonathan Bard [1] discussed a comparison of gradient methods for the solution of nonlinear parameter estimation problems. However this article discusses an analytical approach to the gradient algorithm methods in a different way. This paper describes a new iterative technique namely Gauss-Newton method which differs from the iterative technique proposed by Gorden K. Smyth [2]. Hans Georg Bock et.al [10] proposed numerical methods for parameter estimation in DAE’s (Differential algebraic equation). Isabel Reis Dos Santos et al [11], Introduced weighted least squares procedure for estimating the unknown parameters of a nonlinear regression metamodel. For large-scale non smooth convex minimization the Hager and Zhang (HZ) conjugate gradient Method and the modified HZ (MHZ) method were presented by Gonglin Yuan et al [12].

Fast parallel MR image reconstruction via B1-based, adaptive restart, iterative soft thresholding algorithms (BARISTA).

PubMed

Muckley, Matthew J; Noll, Douglas C; Fessler, Jeffrey A

2015-02-01

Sparsity-promoting regularization is useful for combining compressed sensing assumptions with parallel MRI for reducing scan time while preserving image quality. Variable splitting algorithms are the current state-of-the-art algorithms for SENSE-type MR image reconstruction with sparsity-promoting regularization. These methods are very general and have been observed to work with almost any regularizer; however, the tuning of associated convergence parameters is a commonly-cited hindrance in their adoption. Conversely, majorize-minimize algorithms based on a single Lipschitz constant have been observed to be slow in shift-variant applications such as SENSE-type MR image reconstruction since the associated Lipschitz constants are loose bounds for the shift-variant behavior. This paper bridges the gap between the Lipschitz constant and the shift-variant aspects of SENSE-type MR imaging by introducing majorizing matrices in the range of the regularizer matrix. The proposed majorize-minimize methods (called BARISTA) converge faster than state-of-the-art variable splitting algorithms when combined with momentum acceleration and adaptive momentum restarting. Furthermore, the tuning parameters associated with the proposed methods are unitless convergence tolerances that are easier to choose than the constraint penalty parameters required by variable splitting algorithms.

Fast Parallel MR Image Reconstruction via B1-based, Adaptive Restart, Iterative Soft Thresholding Algorithms (BARISTA)

PubMed Central

Noll, Douglas C.; Fessler, Jeffrey A.

2014-01-01

Sparsity-promoting regularization is useful for combining compressed sensing assumptions with parallel MRI for reducing scan time while preserving image quality. Variable splitting algorithms are the current state-of-the-art algorithms for SENSE-type MR image reconstruction with sparsity-promoting regularization. These methods are very general and have been observed to work with almost any regularizer; however, the tuning of associated convergence parameters is a commonly-cited hindrance in their adoption. Conversely, majorize-minimize algorithms based on a single Lipschitz constant have been observed to be slow in shift-variant applications such as SENSE-type MR image reconstruction since the associated Lipschitz constants are loose bounds for the shift-variant behavior. This paper bridges the gap between the Lipschitz constant and the shift-variant aspects of SENSE-type MR imaging by introducing majorizing matrices in the range of the regularizer matrix. The proposed majorize-minimize methods (called BARISTA) converge faster than state-of-the-art variable splitting algorithms when combined with momentum acceleration and adaptive momentum restarting. Furthermore, the tuning parameters associated with the proposed methods are unitless convergence tolerances that are easier to choose than the constraint penalty parameters required by variable splitting algorithms. PMID:25330484

Efficient stabilization and acceleration of numerical simulation of fluid flows by residual recombination

NASA Astrophysics Data System (ADS)

Citro, V.; Luchini, P.; Giannetti, F.; Auteri, F.

2017-09-01

The study of the stability of a dynamical system described by a set of partial differential equations (PDEs) requires the computation of unstable states as the control parameter exceeds its critical threshold. Unfortunately, the discretization of the governing equations, especially for fluid dynamic applications, often leads to very large discrete systems. As a consequence, matrix based methods, like for example the Newton-Raphson algorithm coupled with a direct inversion of the Jacobian matrix, lead to computational costs too large in terms of both memory and execution time. We present a novel iterative algorithm, inspired by Krylov-subspace methods, which is able to compute unstable steady states and/or accelerate the convergence to stable configurations. Our new algorithm is based on the minimization of the residual norm at each iteration step with a projection basis updated at each iteration rather than at periodic restarts like in the classical GMRES method. The algorithm is able to stabilize any dynamical system without increasing the computational time of the original numerical procedure used to solve the governing equations. Moreover, it can be easily inserted into a pre-existing relaxation (integration) procedure with a call to a single black-box subroutine. The procedure is discussed for problems of different sizes, ranging from a small two-dimensional system to a large three-dimensional problem involving the Navier-Stokes equations. We show that the proposed algorithm is able to improve the convergence of existing iterative schemes. In particular, the procedure is applied to the subcritical flow inside a lid-driven cavity. We also discuss the application of Boostconv to compute the unstable steady flow past a fixed circular cylinder (2D) and boundary-layer flow over a hemispherical roughness element (3D) for supercritical values of the Reynolds number. We show that Boostconv can be used effectively with any spatial discretization, be it a finite-difference, finite-volume, finite-element or spectral method.

Clinical application and validation of an iterative forward projection matching algorithm for permanent brachytherapy seed localization from conebeam-CT x-ray projections.

PubMed

Pokhrel, Damodar; Murphy, Martin J; Todor, Dorin A; Weiss, Elisabeth; Williamson, Jeffrey F

2010-09-01

To experimentally validate a new algorithm for reconstructing the 3D positions of implanted brachytherapy seeds from postoperatively acquired 2D conebeam-CT (CBCT) projection images. The iterative forward projection matching (IFPM) algorithm finds the 3D seed geometry that minimizes the sum of the squared intensity differences between computed projections of an initial estimate of the seed configuration and radiographic projections of the implant. In-house machined phantoms, containing arrays of 12 and 72 seeds, respectively, are used to validate this method. Also, four 103Pd postimplant patients are scanned using an ACUITY digital simulator. Three to ten x-ray images are selected from the CBCT projection set and processed to create binary seed-only images. To quantify IFPM accuracy, the reconstructed seed positions are forward projected and overlaid on the measured seed images to find the nearest-neighbor distance between measured and computed seed positions for each image pair. Also, the estimated 3D seed coordinates are compared to known seed positions in the phantom and clinically obtained VariSeed planning coordinates for the patient data. For the phantom study, seed localization error is (0.58 +/- 0.33) mm. For all four patient cases, the mean registration error is better than 1 mm while compared against the measured seed projections. IFPM converges in 20-28 iterations, with a computation time of about 1.9-2.8 min/ iteration on a 1 GHz processor. The IFPM algorithm avoids the need to match corresponding seeds in each projection as required by standard back-projection methods. The authors' results demonstrate approximately 1 mm accuracy in reconstructing the 3D positions of brachytherapy seeds from the measured 2D projections. This algorithm also successfully localizes overlapping clustered and highly migrated seeds in the implant.

Clinical application and validation of an iterative forward projection matching algorithm for permanent brachytherapy seed localization from conebeam-CT x-ray projections

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

Pokhrel, Damodar; Murphy, Martin J.; Todor, Dorin A.

2010-09-15

Purpose: To experimentally validate a new algorithm for reconstructing the 3D positions of implanted brachytherapy seeds from postoperatively acquired 2D conebeam-CT (CBCT) projection images. Methods: The iterative forward projection matching (IFPM) algorithm finds the 3D seed geometry that minimizes the sum of the squared intensity differences between computed projections of an initial estimate of the seed configuration and radiographic projections of the implant. In-house machined phantoms, containing arrays of 12 and 72 seeds, respectively, are used to validate this method. Also, four {sup 103}Pd postimplant patients are scanned using an ACUITY digital simulator. Three to ten x-ray images are selectedmore » from the CBCT projection set and processed to create binary seed-only images. To quantify IFPM accuracy, the reconstructed seed positions are forward projected and overlaid on the measured seed images to find the nearest-neighbor distance between measured and computed seed positions for each image pair. Also, the estimated 3D seed coordinates are compared to known seed positions in the phantom and clinically obtained VariSeed planning coordinates for the patient data. Results: For the phantom study, seed localization error is (0.58{+-}0.33) mm. For all four patient cases, the mean registration error is better than 1 mm while compared against the measured seed projections. IFPM converges in 20-28 iterations, with a computation time of about 1.9-2.8 min/iteration on a 1 GHz processor. Conclusions: The IFPM algorithm avoids the need to match corresponding seeds in each projection as required by standard back-projection methods. The authors' results demonstrate {approx}1 mm accuracy in reconstructing the 3D positions of brachytherapy seeds from the measured 2D projections. This algorithm also successfully localizes overlapping clustered and highly migrated seeds in the implant.« less

Objective performance assessment of five computed tomography iterative reconstruction algorithms.

PubMed

Omotayo, Azeez; Elbakri, Idris

2016-11-22

Iterative algorithms are gaining clinical acceptance in CT. We performed objective phantom-based image quality evaluation of five commercial iterative reconstruction algorithms available on four different multi-detector CT (MDCT) scanners at different dose levels as well as the conventional filtered back-projection (FBP) reconstruction. Using the Catphan500 phantom, we evaluated image noise, contrast-to-noise ratio (CNR), modulation transfer function (MTF) and noise-power spectrum (NPS). The algorithms were evaluated over a CTDIvol range of 0.75-18.7 mGy on four major MDCT scanners: GE DiscoveryCT750HD (algorithms: ASIR™ and VEO™); Siemens Somatom Definition AS+ (algorithm: SAFIRE™); Toshiba Aquilion64 (algorithm: AIDR3D™); and Philips Ingenuity iCT256 (algorithm: iDose4™). Images were reconstructed using FBP and the respective iterative algorithms on the four scanners. Use of iterative algorithms decreased image noise and increased CNR, relative to FBP. In the dose range of 1.3-1.5 mGy, noise reduction using iterative algorithms was in the range of 11%-51% on GE DiscoveryCT750HD, 10%-52% on Siemens Somatom Definition AS+, 49%-62% on Toshiba Aquilion64, and 13%-44% on Philips Ingenuity iCT256. The corresponding CNR increase was in the range 11%-105% on GE, 11%-106% on Siemens, 85%-145% on Toshiba and 13%-77% on Philips respectively. Most algorithms did not affect the MTF, except for VEO™ which produced an increase in the limiting resolution of up to 30%. A shift in the peak of the NPS curve towards lower frequencies and a decrease in NPS amplitude were obtained with all iterative algorithms. VEO™ required long reconstruction times, while all other algorithms produced reconstructions in real time. Compared to FBP, iterative algorithms reduced image noise and increased CNR. The iterative algorithms available on different scanners achieved different levels of noise reduction and CNR increase while spatial resolution improvements were obtained only with VEO™. This study is useful in that it provides performance assessment of the iterative algorithms available from several mainstream CT manufacturers.

Intrusion detection using rough set classification.

PubMed

Zhang, Lian-hua; Zhang, Guan-hua; Zhang, Jie; Bai, Ying-cai

2004-09-01

Recently machine learning-based intrusion detection approaches have been subjected to extensive researches because they can detect both misuse and anomaly. In this paper, rough set classification (RSC), a modern learning algorithm, is used to rank the features extracted for detecting intrusions and generate intrusion detection models. Feature ranking is a very critical step when building the model. RSC performs feature ranking before generating rules, and converts the feature ranking to minimal hitting set problem addressed by using genetic algorithm (GA). This is done in classical approaches using Support Vector Machine (SVM) by executing many iterations, each of which removes one useless feature. Compared with those methods, our method can avoid many iterations. In addition, a hybrid genetic algorithm is proposed to increase the convergence speed and decrease the training time of RSC. The models generated by RSC take the form of "IF-THEN" rules, which have the advantage of explication. Tests and comparison of RSC with SVM on DARPA benchmark data showed that for Probe and DoS attacks both RSC and SVM yielded highly accurate results (greater than 99% accuracy on testing set).

Marine Controlled-Source Electromagnetic 2D Inversion for synthetic models.

NASA Astrophysics Data System (ADS)

Liu, Y.; Li, Y.

2016-12-01

We present a 2D inverse algorithm for frequency domain marine controlled-source electromagnetic (CSEM) data, which is based on the regularized Gauss-Newton approach. As a forward solver, our parallel adaptive finite element forward modeling program is employed. It is a self-adaptive, goal-oriented grid refinement algorithm in which a finite element analysis is performed on a sequence of refined meshes. The mesh refinement process is guided by a dual error estimate weighting to bias refinement towards elements that affect the solution at the EM receiver locations. With the use of the direct solver (MUMPS), we can effectively compute the electromagnetic fields for multi-sources and parametric sensitivities. We also implement the parallel data domain decomposition approach of Key and Ovall (2011), with the goal of being able to compute accurate responses in parallel for complicated models and a full suite of data parameters typical of offshore CSEM surveys. All minimizations are carried out by using the Gauss-Newton algorithm and model perturbations at each iteration step are obtained by using the Inexact Conjugate Gradient iteration method. Synthetic test inversions are presented.

A sequential quadratic programming algorithm using an incomplete solution of the subproblem

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

Murray, W.; Prieto, F.J.

1993-05-01

We analyze sequential quadratic programming (SQP) methods to solve nonlinear constrained optimization problems that are more flexible in their definition than standard SQP methods. The type of flexibility introduced is motivated by the necessity to deviate from the standard approach when solving large problems. Specifically we no longer require a minimizer of the QP subproblem to be determined or particular Lagrange multiplier estimates to be used. Our main focus is on an SQP algorithm that uses a particular augmented Lagrangian merit function. New results are derived for this algorithm under weaker conditions than previously assumed; in particular, it is notmore » assumed that the iterates lie on a compact set.« less

A fast method to emulate an iterative POCS image reconstruction algorithm.

PubMed

Zeng, Gengsheng L

2017-10-01

Iterative image reconstruction algorithms are commonly used to optimize an objective function, especially when the objective function is nonquadratic. Generally speaking, the iterative algorithms are computationally inefficient. This paper presents a fast algorithm that has one backprojection and no forward projection. This paper derives a new method to solve an optimization problem. The nonquadratic constraint, for example, an edge-preserving denoising constraint is implemented as a nonlinear filter. The algorithm is derived based on the POCS (projections onto projections onto convex sets) approach. A windowed FBP (filtered backprojection) algorithm enforces the data fidelity. An iterative procedure, divided into segments, enforces edge-enhancement denoising. Each segment performs nonlinear filtering. The derived iterative algorithm is computationally efficient. It contains only one backprojection and no forward projection. Low-dose CT data are used for algorithm feasibility studies. The nonlinearity is implemented as an edge-enhancing noise-smoothing filter. The patient studies results demonstrate its effectiveness in processing low-dose x ray CT data. This fast algorithm can be used to replace many iterative algorithms. © 2017 American Association of Physicists in Medicine.

Convergence Results on Iteration Algorithms to Linear Systems

PubMed Central

Wang, Zhuande; Yang, Chuansheng; Yuan, Yubo

2014-01-01

In order to solve the large scale linear systems, backward and Jacobi iteration algorithms are employed. The convergence is the most important issue. In this paper, a unified backward iterative matrix is proposed. It shows that some well-known iterative algorithms can be deduced with it. The most important result is that the convergence results have been proved. Firstly, the spectral radius of the Jacobi iterative matrix is positive and the one of backward iterative matrix is strongly positive (lager than a positive constant). Secondly, the mentioned two iterations have the same convergence results (convergence or divergence simultaneously). Finally, some numerical experiments show that the proposed algorithms are correct and have the merit of backward methods. PMID:24991640

Advanced control concepts. [for shuttle ascent vehicles

NASA Technical Reports Server (NTRS)

Sharp, J. B.; Coppey, J. M.

1973-01-01

The problems of excess control devices and insufficient trim control capability on shuttle ascent vehicles were investigated. The trim problem is solved at all time points of interest using Lagrangian multipliers and a Simplex based iterative algorithm developed as a result of the study. This algorithm has the capability to solve any bounded linear problem with physically realizable constraints, and to minimize any piecewise differentiable cost function. Both solution methods also automatically distribute the command torques to the control devices. It is shown that trim requirements are unrealizable if only the orbiter engines and the aerodynamic surfaces are used.

Direct endoscopic video registration for sinus surgery

NASA Astrophysics Data System (ADS)

Mirota, Daniel; Taylor, Russell H.; Ishii, Masaru; Hager, Gregory D.

2009-02-01

Advances in computer vision have made possible robust 3D reconstruction of monocular endoscopic video. These reconstructions accurately represent the visible anatomy and, once registered to pre-operative CT data, enable a navigation system to track directly through video eliminating the need for an external tracking system. Video registration provides the means for a direct interface between an endoscope and a navigation system and allows a shorter chain of rigid-body transformations to be used to solve the patient/navigation-system registration. To solve this registration step we propose a new 3D-3D registration algorithm based on Trimmed Iterative Closest Point (TrICP)1 and the z-buffer algorithm.2 The algorithm takes as input a 3D point cloud of relative scale with the origin at the camera center, an isosurface from the CT, and an initial guess of the scale and location. Our algorithm utilizes only the visible polygons of the isosurface from the current camera location during each iteration to minimize the search area of the target region and robustly reject outliers of the reconstruction. We present example registrations in the sinus passage applicable to both sinus surgery and transnasal surgery. To evaluate our algorithm's performance we compare it to registration via Optotrak and present closest distance point to surface error. We show our algorithm has a mean closest distance error of .2268mm.

Energy-efficient routing, modulation and spectrum allocation in elastic optical networks

NASA Astrophysics Data System (ADS)

Tan, Yanxia; Gu, Rentao; Ji, Yuefeng

2017-07-01

With tremendous growth in bandwidth demand, energy consumption problem in elastic optical networks (EONs) becomes a hot topic with wide concern. The sliceable bandwidth-variable transponder in EON, which can transmit/receive multiple optical flows, was recently proposed to improve a transponder's flexibility and save energy. In this paper, energy-efficient routing, modulation and spectrum allocation (EE-RMSA) in EONs with sliceable bandwidth-variable transponder is studied. To decrease the energy consumption, we develop a Mixed Integer Linear Programming (MILP) model with corresponding EE-RMSA algorithm for EONs. The MILP model jointly considers the modulation format and optical grooming in the process of routing and spectrum allocation with the objective of minimizing the energy consumption. With the help of genetic operators, the EE-RMSA algorithm iteratively optimizes the feasible routing path, modulation format and spectrum resources solutions by explore the whole search space. In order to save energy, the optical-layer grooming strategy is designed to transmit the lightpath requests. Finally, simulation results verify that the proposed scheme is able to reduce the energy consumption of the network while maintaining the blocking probability (BP) performance compare with the existing First-Fit-KSP algorithm, Iterative Flipping algorithm and EAMGSP algorithm especially in large network topology. Our results also demonstrate that the proposed EE-RMSA algorithm achieves almost the same performance as MILP on an 8-node network.

Selecting a restoration technique to minimize OCR error.

PubMed

Cannon, M; Fugate, M; Hush, D R; Scovel, C

2003-01-01

This paper introduces a learning problem related to the task of converting printed documents to ASCII text files. The goal of the learning procedure is to produce a function that maps documents to restoration techniques in such a way that on average the restored documents have minimum optical character recognition error. We derive a general form for the optimal function and use it to motivate the development of a nonparametric method based on nearest neighbors. We also develop a direct method of solution based on empirical error minimization for which we prove a finite sample bound on estimation error that is independent of distribution. We show that this empirical error minimization problem is an extension of the empirical optimization problem for traditional M-class classification with general loss function and prove computational hardness for this problem. We then derive a simple iterative algorithm called generalized multiclass ratchet (GMR) and prove that it produces an optimal function asymptotically (with probability 1). To obtain the GMR algorithm we introduce a new data map that extends Kesler's construction for the multiclass problem and then apply an algorithm called Ratchet to this mapped data, where Ratchet is a modification of the Pocket algorithm . Finally, we apply these methods to a collection of documents and report on the experimental results.

Energy minimization in medical image analysis: Methodologies and applications.

PubMed

Zhao, Feng; Xie, Xianghua

2016-02-01

Energy minimization is of particular interest in medical image analysis. In the past two decades, a variety of optimization schemes have been developed. In this paper, we present a comprehensive survey of the state-of-the-art optimization approaches. These algorithms are mainly classified into two categories: continuous method and discrete method. The former includes Newton-Raphson method, gradient descent method, conjugate gradient method, proximal gradient method, coordinate descent method, and genetic algorithm-based method, while the latter covers graph cuts method, belief propagation method, tree-reweighted message passing method, linear programming method, maximum margin learning method, simulated annealing method, and iterated conditional modes method. We also discuss the minimal surface method, primal-dual method, and the multi-objective optimization method. In addition, we review several comparative studies that evaluate the performance of different minimization techniques in terms of accuracy, efficiency, or complexity. These optimization techniques are widely used in many medical applications, for example, image segmentation, registration, reconstruction, motion tracking, and compressed sensing. We thus give an overview on those applications as well. Copyright © 2015 John Wiley & Sons, Ltd.

Solving the multiple-set split equality common fixed-point problem of firmly quasi-nonexpansive operators.

PubMed

Zhao, Jing; Zong, Haili

2018-01-01

In this paper, we propose parallel and cyclic iterative algorithms for solving the multiple-set split equality common fixed-point problem of firmly quasi-nonexpansive operators. We also combine the process of cyclic and parallel iterative methods and propose two mixed iterative algorithms. Our several algorithms do not need any prior information about the operator norms. Under mild assumptions, we prove weak convergence of the proposed iterative sequences in Hilbert spaces. As applications, we obtain several iterative algorithms to solve the multiple-set split equality problem.

Multi-camera sensor system for 3D segmentation and localization of multiple mobile robots.

PubMed

Losada, Cristina; Mazo, Manuel; Palazuelos, Sira; Pizarro, Daniel; Marrón, Marta

2010-01-01

This paper presents a method for obtaining the motion segmentation and 3D localization of multiple mobile robots in an intelligent space using a multi-camera sensor system. The set of calibrated and synchronized cameras are placed in fixed positions within the environment (intelligent space). The proposed algorithm for motion segmentation and 3D localization is based on the minimization of an objective function. This function includes information from all the cameras, and it does not rely on previous knowledge or invasive landmarks on board the robots. The proposed objective function depends on three groups of variables: the segmentation boundaries, the motion parameters and the depth. For the objective function minimization, we use a greedy iterative algorithm with three steps that, after initialization of segmentation boundaries and depth, are repeated until convergence.

Discrete-Time Deterministic $Q$ -Learning: A Novel Convergence Analysis.

PubMed

Wei, Qinglai; Lewis, Frank L; Sun, Qiuye; Yan, Pengfei; Song, Ruizhuo

2017-05-01

In this paper, a novel discrete-time deterministic Q -learning algorithm is developed. In each iteration of the developed Q -learning algorithm, the iterative Q function is updated for all the state and control spaces, instead of updating for a single state and a single control in traditional Q -learning algorithm. A new convergence criterion is established to guarantee that the iterative Q function converges to the optimum, where the convergence criterion of the learning rates for traditional Q -learning algorithms is simplified. During the convergence analysis, the upper and lower bounds of the iterative Q function are analyzed to obtain the convergence criterion, instead of analyzing the iterative Q function itself. For convenience of analysis, the convergence properties for undiscounted case of the deterministic Q -learning algorithm are first developed. Then, considering the discounted factor, the convergence criterion for the discounted case is established. Neural networks are used to approximate the iterative Q function and compute the iterative control law, respectively, for facilitating the implementation of the deterministic Q -learning algorithm. Finally, simulation results and comparisons are given to illustrate the performance of the developed algorithm.

A new method for computation of eigenvector derivatives with distinct and repeated eigenvalues in structural dynamic analysis

NASA Astrophysics Data System (ADS)

Li, Zhengguang; Lai, Siu-Kai; Wu, Baisheng

2018-07-01

Determining eigenvector derivatives is a challenging task due to the singularity of the coefficient matrices of the governing equations, especially for those structural dynamic systems with repeated eigenvalues. An effective strategy is proposed to construct a non-singular coefficient matrix, which can be directly used to obtain the eigenvector derivatives with distinct and repeated eigenvalues. This approach also has an advantage that only requires eigenvalues and eigenvectors of interest, without solving the particular solutions of eigenvector derivatives. The Symmetric Quasi-Minimal Residual (SQMR) method is then adopted to solve the governing equations, only the existing factored (shifted) stiffness matrix from an iterative eigensolution such as the subspace iteration method or the Lanczos algorithm is utilized. The present method can deal with both cases of simple and repeated eigenvalues in a unified manner. Three numerical examples are given to illustrate the accuracy and validity of the proposed algorithm. Highly accurate approximations to the eigenvector derivatives are obtained within a few iteration steps, making a significant reduction of the computational effort. This method can be incorporated into a coupled eigensolver/derivative software module. In particular, it is applicable for finite element models with large sparse matrices.

Robust High Data Rate MIMO Underwater Acoustic Communications

DTIC Science & Technology

2010-12-31

algorithm is referred to as periodic CAN ( PeCAN ). Unlike most existing sequence construction methods which are algebraic and deterministic in nature, we...start the iteration of PeCAN from random phase initializations and then proceed to cyclically minimize the desired metric. In this way, through...by the foe and hence are especially useful as training sequences or as spreading sequences for UAC applications. We will use PeCAN sequences for

CT coronary angiography: impact of adapted statistical iterative reconstruction (ASIR) on coronary stenosis and plaque composition analysis.

PubMed

Fuchs, Tobias A; Fiechter, Michael; Gebhard, Cathérine; Stehli, Julia; Ghadri, Jelena R; Kazakauskaite, Egle; Herzog, Bernhard A; Husmann, Lars; Gaemperli, Oliver; Kaufmann, Philipp A

2013-03-01

To assess the impact of adaptive statistical iterative reconstruction (ASIR) on coronary plaque volume and composition analysis as well as on stenosis quantification in high definition coronary computed tomography angiography (CCTA). We included 50 plaques in 29 consecutive patients who were referred for the assessment of known or suspected coronary artery disease (CAD) with contrast-enhanced CCTA on a 64-slice high definition CT scanner (Discovery HD 750, GE Healthcare). CCTA scans were reconstructed with standard filtered back projection (FBP) with no ASIR (0 %) or with increasing contributions of ASIR, i.e. 20, 40, 60, 80 and 100 % (no FBP). Plaque analysis (volume, components and stenosis degree) was performed using a previously validated automated software. Mean values for minimal diameter and minimal area as well as degree of stenosis did not change significantly using different ASIR reconstructions. There was virtually no impact of reconstruction algorithms on mean plaque volume or plaque composition (e.g. soft, intermediate and calcified component). However, with increasing ASIR contribution, the percentage of plaque volume component between 401 and 500 HU decreased significantly (p < 0.05). Modern image reconstruction algorithms such as ASIR, which has been developed for noise reduction in latest high resolution CCTA scans, can be used reliably without interfering with the plaque analysis and stenosis severity assessment.

Reliability enhancement of Navier-Stokes codes through convergence enhancement

NASA Technical Reports Server (NTRS)

Choi, K.-Y.; Dulikravich, G. S.

1993-01-01

Reduction of total computing time required by an iterative algorithm for solving Navier-Stokes equations is an important aspect of making the existing and future analysis codes more cost effective. Several attempts have been made to accelerate the convergence of an explicit Runge-Kutta time-stepping algorithm. These acceleration methods are based on local time stepping, implicit residual smoothing, enthalpy damping, and multigrid techniques. Also, an extrapolation procedure based on the power method and the Minimal Residual Method (MRM) were applied to the Jameson's multigrid algorithm. The MRM uses same values of optimal weights for the corrections to every equation in a system and has not been shown to accelerate the scheme without multigriding. Our Distributed Minimal Residual (DMR) method based on our General Nonlinear Minimal Residual (GNLMR) method allows each component of the solution vector in a system of equations to have its own convergence speed. The DMR method was found capable of reducing the computation time by 10-75 percent depending on the test case and grid used. Recently, we have developed and tested a new method termed Sensitivity Based DMR or SBMR method that is easier to implement in different codes and is even more robust and computationally efficient than our DMR method.

Reliability enhancement of Navier-Stokes codes through convergence enhancement

NASA Astrophysics Data System (ADS)

Choi, K.-Y.; Dulikravich, G. S.

1993-11-01

Reduction of total computing time required by an iterative algorithm for solving Navier-Stokes equations is an important aspect of making the existing and future analysis codes more cost effective. Several attempts have been made to accelerate the convergence of an explicit Runge-Kutta time-stepping algorithm. These acceleration methods are based on local time stepping, implicit residual smoothing, enthalpy damping, and multigrid techniques. Also, an extrapolation procedure based on the power method and the Minimal Residual Method (MRM) were applied to the Jameson's multigrid algorithm. The MRM uses same values of optimal weights for the corrections to every equation in a system and has not been shown to accelerate the scheme without multigriding. Our Distributed Minimal Residual (DMR) method based on our General Nonlinear Minimal Residual (GNLMR) method allows each component of the solution vector in a system of equations to have its own convergence speed. The DMR method was found capable of reducing the computation time by 10-75 percent depending on the test case and grid used. Recently, we have developed and tested a new method termed Sensitivity Based DMR or SBMR method that is easier to implement in different codes and is even more robust and computationally efficient than our DMR method.

Optimal tracking control for a class of nonlinear discrete-time systems with time delays based on heuristic dynamic programming.

PubMed

Zhang, Huaguang; Song, Ruizhuo; Wei, Qinglai; Zhang, Tieyan

2011-12-01

In this paper, a novel heuristic dynamic programming (HDP) iteration algorithm is proposed to solve the optimal tracking control problem for a class of nonlinear discrete-time systems with time delays. The novel algorithm contains state updating, control policy iteration, and performance index iteration. To get the optimal states, the states are also updated. Furthermore, the "backward iteration" is applied to state updating. Two neural networks are used to approximate the performance index function and compute the optimal control policy for facilitating the implementation of HDP iteration algorithm. At last, we present two examples to demonstrate the effectiveness of the proposed HDP iteration algorithm.

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.

Improved L-BFGS diagonal preconditioners for a large-scale 4D-Var inversion system: application to CO2 flux constraints and analysis error calculation

NASA Astrophysics Data System (ADS)

Bousserez, Nicolas; Henze, Daven; Bowman, Kevin; Liu, Junjie; Jones, Dylan; Keller, Martin; Deng, Feng

2013-04-01

This work presents improved analysis error estimates for 4D-Var systems. From operational NWP models to top-down constraints on trace gas emissions, many of today's data assimilation and inversion systems in atmospheric science rely on variational approaches. This success is due to both the mathematical clarity of these formulations and the availability of computationally efficient minimization algorithms. However, unlike Kalman Filter-based algorithms, these methods do not provide an estimate of the analysis or forecast error covariance matrices, these error statistics being propagated only implicitly by the system. From both a practical (cycling assimilation) and scientific perspective, assessing uncertainties in the solution of the variational problem is critical. For large-scale linear systems, deterministic or randomization approaches can be considered based on the equivalence between the inverse Hessian of the cost function and the covariance matrix of analysis error. For perfectly quadratic systems, like incremental 4D-Var, Lanczos/Conjugate-Gradient algorithms have proven to be most efficient in generating low-rank approximations of the Hessian matrix during the minimization. For weakly non-linear systems though, the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), a quasi-Newton descent algorithm, is usually considered the best method for the minimization. Suitable for large-scale optimization, this method allows one to generate an approximation to the inverse Hessian using the latest m vector/gradient pairs generated during the minimization, m depending upon the available core memory. At each iteration, an initial low-rank approximation to the inverse Hessian has to be provided, which is called preconditioning. The ability of the preconditioner to retain useful information from previous iterations largely determines the efficiency of the algorithm. Here we assess the performance of different preconditioners to estimate the inverse Hessian of a large-scale 4D-Var system. The impact of using the diagonal preconditioners proposed by Gilbert and Le Maréchal (1989) instead of the usual Oren-Spedicato scalar will be first presented. We will also introduce new hybrid methods that combine randomization estimates of the analysis error variance with L-BFGS diagonal updates to improve the inverse Hessian approximation. Results from these new algorithms will be evaluated against standard large ensemble Monte-Carlo simulations. The methods explored here are applied to the problem of inferring global atmospheric CO2 fluxes using remote sensing observations, and are intended to be integrated with the future NASA Carbon Monitoring System.

Iterative Stable Alignment and Clustering of 2D Transmission Electron Microscope Images

PubMed Central

Yang, Zhengfan; Fang, Jia; Chittuluru, Johnathan; Asturias, Francisco J.; Penczek, Pawel A.

2012-01-01

SUMMARY Identification of homogeneous subsets of images in a macromolecular electron microscopy (EM) image data set is a critical step in single-particle analysis. The task is handled by iterative algorithms, whose performance is compromised by the compounded limitations of image alignment and K-means clustering. Here we describe an approach, iterative stable alignment and clustering (ISAC) that, relying on a new clustering method and on the concepts of stability and reproducibility, can extract validated, homogeneous subsets of images. ISAC requires only a small number of simple parameters and, with minimal human intervention, can eliminate bias from two-dimensional image clustering and maximize the quality of group averages that can be used for ab initio three-dimensional structural determination and analysis of macromolecular conformational variability. Repeated testing of the stability and reproducibility of a solution within ISAC eliminates heterogeneous or incorrect classes and introduces critical validation to the process of EM image clustering. PMID:22325773

Policy Iteration for $H_\\infty $ Optimal Control of Polynomial Nonlinear Systems via Sum of Squares Programming.

PubMed

Zhu, Yuanheng; Zhao, Dongbin; Yang, Xiong; Zhang, Qichao

2018-02-01

Sum of squares (SOS) polynomials have provided a computationally tractable way to deal with inequality constraints appearing in many control problems. It can also act as an approximator in the framework of adaptive dynamic programming. In this paper, an approximate solution to the optimal control of polynomial nonlinear systems is proposed. Under a given attenuation coefficient, the Hamilton-Jacobi-Isaacs equation is relaxed to an optimization problem with a set of inequalities. After applying the policy iteration technique and constraining inequalities to SOS, the optimization problem is divided into a sequence of feasible semidefinite programming problems. With the converged solution, the attenuation coefficient is further minimized to a lower value. After iterations, approximate solutions to the smallest -gain and the associated optimal controller are obtained. Four examples are employed to verify the effectiveness of the proposed algorithm.

Investigation of iterative image reconstruction in three-dimensional optoacoustic tomography

PubMed Central

Wang, Kun; Su, Richard; Oraevsky, Alexander A; Anastasio, Mark A

2012-01-01

Iterative image reconstruction algorithms for optoacoustic tomography (OAT), also known as photoacoustic tomography, have the ability to improve image quality over analytic algorithms due to their ability to incorporate accurate models of the imaging physics, instrument response, and measurement noise. However, to date, there have been few reported attempts to employ advanced iterative image reconstruction algorithms for improving image quality in three-dimensional (3D) OAT. In this work, we implement and investigate two iterative image reconstruction methods for use with a 3D OAT small animal imager: namely, a penalized least-squares (PLS) method employing a quadratic smoothness penalty and a PLS method employing a total variation norm penalty. The reconstruction algorithms employ accurate models of the ultrasonic transducer impulse responses. Experimental data sets are employed to compare the performances of the iterative reconstruction algorithms to that of a 3D filtered backprojection (FBP) algorithm. By use of quantitative measures of image quality, we demonstrate that the iterative reconstruction algorithms can mitigate image artifacts and preserve spatial resolution more effectively than FBP algorithms. These features suggest that the use of advanced image reconstruction algorithms can improve the effectiveness of 3D OAT while reducing the amount of data required for biomedical applications. PMID:22864062

Nonlocal variational model and filter algorithm to remove multiplicative noise

NASA Astrophysics Data System (ADS)

Chen, Dai-Qiang; Zhang, Hui; Cheng, Li-Zhi

2010-07-01

The nonlocal (NL) means filter proposed by Buades, Coll, and Morel (SIAM Multiscale Model. Simul. 4(2), 490-530, 2005), which makes full use of the redundancy information in images, has shown to be very efficient for image denoising with Gauss noise added. On the basis of the NL method and a striver to minimize the conditional mean-square error, we design a NL means filter to remove multiplicative noise, and combining the NL filter to regularity method, we propose a NL total variational (TV) model and present a fast iterated algorithm for it. Experiments demonstrate that our algorithm is better than TV method; it is superior in preserving small structures and textures and can obtain an improvement in peak signal-to-noise ratio.

Angular filter refractometry analysis using simulated annealing.

PubMed

Angland, P; Haberberger, D; Ivancic, S T; Froula, D H

2017-10-01

Angular filter refractometry (AFR) is a novel technique used to characterize the density profiles of laser-produced, long-scale-length plasmas [Haberberger et al., Phys. Plasmas 21, 056304 (2014)]. A new method of analysis for AFR images was developed using an annealing algorithm to iteratively converge upon a solution. A synthetic AFR image is constructed by a user-defined density profile described by eight parameters, and the algorithm systematically alters the parameters until the comparison is optimized. The optimization and statistical uncertainty calculation is based on the minimization of the χ 2 test statistic. The algorithm was successfully applied to experimental data of plasma expanding from a flat, laser-irradiated target, resulting in an average uncertainty in the density profile of 5%-20% in the region of interest.

A hybrid binary particle swarm optimization for large capacitated multi item multi level lot sizing (CMIMLLS) problem

NASA Astrophysics Data System (ADS)

Mishra, S. K.; Sahithi, V. V. D.; Rao, C. S. P.

2016-09-01

The lot sizing problem deals with finding optimal order quantities which minimizes the ordering and holding cost of product mix. when multiple items at multiple levels with all capacity restrictions are considered, the lot sizing problem become NP hard. Many heuristics were developed in the past have inevitably failed due to size, computational complexity and time. However the authors were successful in the development of PSO based technique namely iterative improvement binary particles swarm technique to address very large capacitated multi-item multi level lot sizing (CMIMLLS) problem. First binary particle Swarm Optimization algorithm is used to find a solution in a reasonable time and iterative improvement local search mechanism is employed to improvise the solution obtained by BPSO algorithm. This hybrid mechanism of using local search on the global solution is found to improve the quality of solutions with respect to time thus IIBPSO method is found best and show excellent results.

[Preliminary application of an improved Demons deformable registration algorithm in tumor radiotherapy].

PubMed

Zhou, Lu; Zhen, Xin; Lu, Wenting; Dou, Jianhong; Zhou, Linghong

2012-01-01

To validate the efficiency of an improved Demons deformable registration algorithm and evaluate its application in registration of the treatment image and the planning image in image-guided radiotherapy (IGRT). Based on Brox's gradient constancy assumption and Malis's efficient second-order minimization algorithm, a grey value gradient similarity term was added into the original energy function, and a formula was derived to calculate the update of transformation field. The limited Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm was used to optimize the energy function for automatic determination of the iteration number. The proposed algorithm was validated using mathematically deformed images, physically deformed phantom images and clinical tumor images. Compared with the original Additive Demons algorithm, the improved Demons algorithm achieved a higher precision and a faster convergence speed. Due to the influence of different scanning conditions in fractionated radiation, the density range of the treatment image and the planning image may be different. The improved Demons algorithm can achieve faster and more accurate radiotherapy.

Acceleration of image-based resolution modelling reconstruction using an expectation maximization nested algorithm.

PubMed

Angelis, G I; Reader, A J; Markiewicz, P J; Kotasidis, F A; Lionheart, W R; Matthews, J C

2013-08-07

Recent studies have demonstrated the benefits of a resolution model within iterative reconstruction algorithms in an attempt to account for effects that degrade the spatial resolution of the reconstructed images. However, these algorithms suffer from slower convergence rates, compared to algorithms where no resolution model is used, due to the additional need to solve an image deconvolution problem. In this paper, a recently proposed algorithm, which decouples the tomographic and image deconvolution problems within an image-based expectation maximization (EM) framework, was evaluated. This separation is convenient, because more computational effort can be placed on the image deconvolution problem and therefore accelerate convergence. Since the computational cost of solving the image deconvolution problem is relatively small, multiple image-based EM iterations do not significantly increase the overall reconstruction time. The proposed algorithm was evaluated using 2D simulations, as well as measured 3D data acquired on the high-resolution research tomograph. Results showed that bias reduction can be accelerated by interleaving multiple iterations of the image-based EM algorithm solving the resolution model problem, with a single EM iteration solving the tomographic problem. Significant improvements were observed particularly for voxels that were located on the boundaries between regions of high contrast within the object being imaged and for small regions of interest, where resolution recovery is usually more challenging. Minor differences were observed using the proposed nested algorithm, compared to the single iteration normally performed, when an optimal number of iterations are performed for each algorithm. However, using the proposed nested approach convergence is significantly accelerated enabling reconstruction using far fewer tomographic iterations (up to 70% fewer iterations for small regions). Nevertheless, the optimal number of nested image-based EM iterations is hard to be defined and it should be selected according to the given application.

WE-EF-207-07: Dual Energy CT with One Full Scan and a Second Sparse-View Scan Using Structure Preserving Iterative Reconstruction (SPIR)

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

Wang, T; Zhu, L

Purpose: Conventional dual energy CT (DECT) reconstructs CT and basis material images from two full-size projection datasets with different energy spectra. To relax the data requirement, we propose an iterative DECT reconstruction algorithm using one full scan and a second sparse-view scan by utilizing redundant structural information of the same object acquired at two different energies. Methods: We first reconstruct a full-scan CT image using filtered-backprojection (FBP) algorithm. The material similarities of each pixel with other pixels are calculated by an exponential function about pixel value differences. We assume that the material similarities of pixels remains in the second CTmore » scan, although pixel values may vary. An iterative method is designed to reconstruct the second CT image from reduced projections. Under the data fidelity constraint, the algorithm minimizes the L2 norm of the difference between pixel value and its estimation, which is the average of other pixel values weighted by their similarities. The proposed algorithm, referred to as structure preserving iterative reconstruction (SPIR), is evaluated on physical phantoms. Results: On the Catphan600 phantom, SPIR-based DECT method with a second 10-view scan reduces the noise standard deviation of a full-scan FBP CT reconstruction by a factor of 4 with well-maintained spatial resolution, while iterative reconstruction using total-variation regularization (TVR) degrades the spatial resolution at the same noise level. The proposed method achieves less than 1% measurement difference on electron density map compared with the conventional two-full-scan DECT. On an anthropomorphic pediatric phantom, our method successfully reconstructs the complicated vertebra structures and decomposes bone and soft tissue. Conclusion: We develop an effective method to reduce the number of views and therefore data acquisition in DECT. We show that SPIR-based DECT using one full scan and a second 10-view scan can provide high-quality DECT images and accurate electron density maps as conventional two-full-scan DECT.« less

Calibration free beam hardening correction for cardiac CT perfusion imaging

NASA Astrophysics Data System (ADS)

Levi, Jacob; Fahmi, Rachid; Eck, Brendan L.; Fares, Anas; Wu, Hao; Vembar, Mani; Dhanantwari, Amar; Bezerra, Hiram G.; Wilson, David L.

2016-03-01

Myocardial perfusion imaging using CT (MPI-CT) and coronary CTA have the potential to make CT an ideal noninvasive gate-keeper for invasive coronary angiography. However, beam hardening artifacts (BHA) prevent accurate blood flow calculation in MPI-CT. BH Correction (BHC) methods require either energy-sensitive CT, not widely available, or typically a calibration-based method. We developed a calibration-free, automatic BHC (ABHC) method suitable for MPI-CT. The algorithm works with any BHC method and iteratively determines model parameters using proposed BHA-specific cost function. In this work, we use the polynomial BHC extended to three materials. The image is segmented into soft tissue, bone, and iodine images, based on mean HU and temporal enhancement. Forward projections of bone and iodine images are obtained, and in each iteration polynomial correction is applied. Corrections are then back projected and combined to obtain the current iteration's BHC image. This process is iterated until cost is minimized. We evaluate the algorithm on simulated and physical phantom images and on preclinical MPI-CT data. The scans were obtained on a prototype spectral detector CT (SDCT) scanner (Philips Healthcare). Mono-energetic reconstructed images were used as the reference. In the simulated phantom, BH streak artifacts were reduced from 12+/-2HU to 1+/-1HU and cupping was reduced by 81%. Similarly, in physical phantom, BH streak artifacts were reduced from 48+/-6HU to 1+/-5HU and cupping was reduced by 86%. In preclinical MPI-CT images, BHA was reduced from 28+/-6 HU to less than 4+/-4HU at peak enhancement. Results suggest that the algorithm can be used to reduce BHA in conventional CT and improve MPI-CT accuracy.

A Model and Simple Iterative Algorithm for Redundancy Analysis.

ERIC Educational Resources Information Center

Fornell, Claes; And Others

1988-01-01

This paper shows that redundancy maximization with J. K. Johansson's extension can be accomplished via a simple iterative algorithm based on H. Wold's Partial Least Squares. The model and the iterative algorithm for the least squares approach to redundancy maximization are presented. (TJH)

Robust dynamic myocardial perfusion CT deconvolution for accurate residue function estimation via adaptive-weighted tensor total variation regularization: a preclinical study.

PubMed

Zeng, Dong; Gong, Changfei; Bian, Zhaoying; Huang, Jing; Zhang, Xinyu; Zhang, Hua; Lu, Lijun; Niu, Shanzhou; Zhang, Zhang; Liang, Zhengrong; Feng, Qianjin; Chen, Wufan; Ma, Jianhua

2016-11-21

Dynamic myocardial perfusion computed tomography (MPCT) is a promising technique for quick diagnosis and risk stratification of coronary artery disease. However, one major drawback of dynamic MPCT imaging is the heavy radiation dose to patients due to its dynamic image acquisition protocol. In this work, to address this issue, we present a robust dynamic MPCT deconvolution algorithm via adaptive-weighted tensor total variation (AwTTV) regularization for accurate residue function estimation with low-mA s data acquisitions. For simplicity, the presented method is termed 'MPD-AwTTV'. More specifically, the gains of the AwTTV regularization over the original tensor total variation regularization are from the anisotropic edge property of the sequential MPCT images. To minimize the associative objective function we propose an efficient iterative optimization strategy with fast convergence rate in the framework of an iterative shrinkage/thresholding algorithm. We validate and evaluate the presented algorithm using both digital XCAT phantom and preclinical porcine data. The preliminary experimental results have demonstrated that the presented MPD-AwTTV deconvolution algorithm can achieve remarkable gains in noise-induced artifact suppression, edge detail preservation, and accurate flow-scaled residue function and MPHM estimation as compared with the other existing deconvolution algorithms in digital phantom studies, and similar gains can be obtained in the porcine data experiment.

Robust dynamic myocardial perfusion CT deconvolution for accurate residue function estimation via adaptive-weighted tensor total variation regularization: a preclinical study

NASA Astrophysics Data System (ADS)

Zeng, Dong; Gong, Changfei; Bian, Zhaoying; Huang, Jing; Zhang, Xinyu; Zhang, Hua; Lu, Lijun; Niu, Shanzhou; Zhang, Zhang; Liang, Zhengrong; Feng, Qianjin; Chen, Wufan; Ma, Jianhua

2016-11-01

Dynamic myocardial perfusion computed tomography (MPCT) is a promising technique for quick diagnosis and risk stratification of coronary artery disease. However, one major drawback of dynamic MPCT imaging is the heavy radiation dose to patients due to its dynamic image acquisition protocol. In this work, to address this issue, we present a robust dynamic MPCT deconvolution algorithm via adaptive-weighted tensor total variation (AwTTV) regularization for accurate residue function estimation with low-mA s data acquisitions. For simplicity, the presented method is termed ‘MPD-AwTTV’. More specifically, the gains of the AwTTV regularization over the original tensor total variation regularization are from the anisotropic edge property of the sequential MPCT images. To minimize the associative objective function we propose an efficient iterative optimization strategy with fast convergence rate in the framework of an iterative shrinkage/thresholding algorithm. We validate and evaluate the presented algorithm using both digital XCAT phantom and preclinical porcine data. The preliminary experimental results have demonstrated that the presented MPD-AwTTV deconvolution algorithm can achieve remarkable gains in noise-induced artifact suppression, edge detail preservation, and accurate flow-scaled residue function and MPHM estimation as compared with the other existing deconvolution algorithms in digital phantom studies, and similar gains can be obtained in the porcine data experiment.

A parallel variable metric optimization algorithm

NASA Technical Reports Server (NTRS)

Straeter, T. A.

1973-01-01

An algorithm, designed to exploit the parallel computing or vector streaming (pipeline) capabilities of computers is presented. When p is the degree of parallelism, then one cycle of the parallel variable metric algorithm is defined as follows: first, the function and its gradient are computed in parallel at p different values of the independent variable; then the metric is modified by p rank-one corrections; and finally, a single univariant minimization is carried out in the Newton-like direction. Several properties of this algorithm are established. The convergence of the iterates to the solution is proved for a quadratic functional on a real separable Hilbert space. For a finite-dimensional space the convergence is in one cycle when p equals the dimension of the space. Results of numerical experiments indicate that the new algorithm will exploit parallel or pipeline computing capabilities to effect faster convergence than serial techniques.

Non-Convex Sparse and Low-Rank Based Robust Subspace Segmentation for Data Mining.

PubMed

Cheng, Wenlong; Zhao, Mingbo; Xiong, Naixue; Chui, Kwok Tai

2017-07-15

Parsimony, including sparsity and low-rank, has shown great importance for data mining in social networks, particularly in tasks such as segmentation and recognition. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an objective function with convex l ₁-norm or nuclear norm constraints. However, the obtained results by convex optimization are usually suboptimal to solutions of original sparse or low-rank problems. In this paper, a novel robust subspace segmentation algorithm has been proposed by integrating l p -norm and Schatten p -norm constraints. Our so-obtained affinity graph can better capture local geometrical structure and the global information of the data. As a consequence, our algorithm is more generative, discriminative and robust. An efficient linearized alternating direction method is derived to realize our model. Extensive segmentation experiments are conducted on public datasets. The proposed algorithm is revealed to be more effective and robust compared to five existing algorithms.

Online learning in optical tomography: a stochastic approach

NASA Astrophysics Data System (ADS)

Chen, Ke; Li, Qin; Liu, Jian-Guo

2018-07-01

We study the inverse problem of radiative transfer equation (RTE) using stochastic gradient descent method (SGD) in this paper. Mathematically, optical tomography amounts to recovering the optical parameters in RTE using the incoming–outgoing pair of light intensity. We formulate it as a PDE-constraint optimization problem, where the mismatch of computed and measured outgoing data is minimized with same initial data and RTE constraint. The memory and computation cost it requires, however, is typically prohibitive, especially in high dimensional space. Smart iterative solvers that only use partial information in each step is called for thereafter. Stochastic gradient descent method is an online learning algorithm that randomly selects data for minimizing the mismatch. It requires minimum memory and computation, and advances fast, therefore perfectly serves the purpose. In this paper we formulate the problem, in both nonlinear and its linearized setting, apply SGD algorithm and analyze the convergence performance.

Optimal Power Allocation for CC-HARQ-based Cognitive Radio with Statistical CSI in Nakagami Slow Fading Channels

NASA Astrophysics Data System (ADS)

Xu, Ding; Li, Qun

2017-01-01

This paper addresses the power allocation problem for cognitive radio (CR) based on hybrid-automatic-repeat-request (HARQ) with chase combining (CC) in Nakagamimslow fading channels. We assume that, instead of the perfect instantaneous channel state information (CSI), only the statistical CSI is available at the secondary user (SU) transmitter. The aim is to minimize the SU outage probability under the primary user (PU) interference outage constraint. Using the Lagrange multiplier method, an iterative and recursive algorithm is derived to obtain the optimal power allocation for each transmission round. Extensive numerical results are presented to illustrate the performance of the proposed algorithm.

A low-complexity 2-point step size gradient projection method with selective function evaluations for smoothed total variation based CBCT reconstructions

NASA Astrophysics Data System (ADS)

Song, Bongyong; Park, Justin C.; Song, William Y.

2014-11-01

The Barzilai-Borwein (BB) 2-point step size gradient method is receiving attention for accelerating Total Variation (TV) based CBCT reconstructions. In order to become truly viable for clinical applications, however, its convergence property needs to be properly addressed. We propose a novel fast converging gradient projection BB method that requires ‘at most one function evaluation’ in each iterative step. This Selective Function Evaluation method, referred to as GPBB-SFE in this paper, exhibits the desired convergence property when it is combined with a ‘smoothed TV’ or any other differentiable prior. This way, the proposed GPBB-SFE algorithm offers fast and guaranteed convergence to the desired 3DCBCT image with minimal computational complexity. We first applied this algorithm to a Shepp-Logan numerical phantom. We then applied to a CatPhan 600 physical phantom (The Phantom Laboratory, Salem, NY) and a clinically-treated head-and-neck patient, both acquired from the TrueBeam™ system (Varian Medical Systems, Palo Alto, CA). Furthermore, we accelerated the reconstruction by implementing the algorithm on NVIDIA GTX 480 GPU card. We first compared GPBB-SFE with three recently proposed BB-based CBCT reconstruction methods available in the literature using Shepp-Logan numerical phantom with 40 projections. It is found that GPBB-SFE shows either faster convergence speed/time or superior convergence property compared to existing BB-based algorithms. With the CatPhan 600 physical phantom, the GPBB-SFE algorithm requires only 3 function evaluations in 30 iterations and reconstructs the standard, 364-projection FDK reconstruction quality image using only 60 projections. We then applied the algorithm to a clinically-treated head-and-neck patient. It was observed that the GPBB-SFE algorithm requires only 18 function evaluations in 30 iterations. Compared with the FDK algorithm with 364 projections, the GPBB-SFE algorithm produces visibly equivalent quality CBCT image for the head-and-neck patient with only 180 projections, in 131.7 s, further supporting its clinical applicability.

A low-complexity 2-point step size gradient projection method with selective function evaluations for smoothed total variation based CBCT reconstructions.

PubMed

Song, Bongyong; Park, Justin C; Song, William Y

2014-11-07

The Barzilai-Borwein (BB) 2-point step size gradient method is receiving attention for accelerating Total Variation (TV) based CBCT reconstructions. In order to become truly viable for clinical applications, however, its convergence property needs to be properly addressed. We propose a novel fast converging gradient projection BB method that requires 'at most one function evaluation' in each iterative step. This Selective Function Evaluation method, referred to as GPBB-SFE in this paper, exhibits the desired convergence property when it is combined with a 'smoothed TV' or any other differentiable prior. This way, the proposed GPBB-SFE algorithm offers fast and guaranteed convergence to the desired 3DCBCT image with minimal computational complexity. We first applied this algorithm to a Shepp-Logan numerical phantom. We then applied to a CatPhan 600 physical phantom (The Phantom Laboratory, Salem, NY) and a clinically-treated head-and-neck patient, both acquired from the TrueBeam™ system (Varian Medical Systems, Palo Alto, CA). Furthermore, we accelerated the reconstruction by implementing the algorithm on NVIDIA GTX 480 GPU card. We first compared GPBB-SFE with three recently proposed BB-based CBCT reconstruction methods available in the literature using Shepp-Logan numerical phantom with 40 projections. It is found that GPBB-SFE shows either faster convergence speed/time or superior convergence property compared to existing BB-based algorithms. With the CatPhan 600 physical phantom, the GPBB-SFE algorithm requires only 3 function evaluations in 30 iterations and reconstructs the standard, 364-projection FDK reconstruction quality image using only 60 projections. We then applied the algorithm to a clinically-treated head-and-neck patient. It was observed that the GPBB-SFE algorithm requires only 18 function evaluations in 30 iterations. Compared with the FDK algorithm with 364 projections, the GPBB-SFE algorithm produces visibly equivalent quality CBCT image for the head-and-neck patient with only 180 projections, in 131.7 s, further supporting its clinical applicability.

Low-rank structure learning via nonconvex heuristic recovery.

PubMed

Deng, Yue; Dai, Qionghai; Liu, Risheng; Zhang, Zengke; Hu, Sanqing

2013-03-01

In this paper, we propose a nonconvex framework to learn the essential low-rank structure from corrupted data. Different from traditional approaches, which directly utilizes convex norms to measure the sparseness, our method introduces more reasonable nonconvex measurements to enhance the sparsity in both the intrinsic low-rank structure and the sparse corruptions. We will, respectively, introduce how to combine the widely used ℓp norm (0 < p < 1) and log-sum term into the framework of low-rank structure learning. Although the proposed optimization is no longer convex, it still can be effectively solved by a majorization-minimization (MM)-type algorithm, with which the nonconvex objective function is iteratively replaced by its convex surrogate and the nonconvex problem finally falls into the general framework of reweighed approaches. We prove that the MM-type algorithm can converge to a stationary point after successive iterations. The proposed model is applied to solve two typical problems: robust principal component analysis and low-rank representation. Experimental results on low-rank structure learning demonstrate that our nonconvex heuristic methods, especially the log-sum heuristic recovery algorithm, generally perform much better than the convex-norm-based method (0 < p < 1) for both data with higher rank and with denser corruptions.

A simple algorithm for sequentially incorporating gravity observations in seismic traveltime tomography

USGS Publications Warehouse

Parsons, T.; Blakely, R.J.; Brocher, T.M.

2001-01-01

The geologic structure of the Earth's upper crust can be revealed by modeling variation in seismic arrival times and in potential field measurements. We demonstrate a simple method for sequentially satisfying seismic traveltime and observed gravity residuals in an iterative 3-D inversion. The algorithm is portable to any seismic analysis method that uses a gridded representation of velocity structure. Our technique calculates the gravity anomaly resulting from a velocity model by converting to density with Gardner's rule. The residual between calculated and observed gravity is minimized by weighted adjustments to the model velocity-depth gradient where the gradient is steepest and where seismic coverage is least. The adjustments are scaled by the sign and magnitude of the gravity residuals, and a smoothing step is performed to minimize vertical streaking. The adjusted model is then used as a starting model in the next seismic traveltime iteration. The process is repeated until one velocity model can simultaneously satisfy both the gravity anomaly and seismic traveltime observations within acceptable misfits. We test our algorithm with data gathered in the Puget Lowland of Washington state, USA (Seismic Hazards Investigation in Puget Sound [SHIPS] experiment). We perform resolution tests with synthetic traveltime and gravity observations calculated with a checkerboard velocity model using the SHIPS experiment geometry, and show that the addition of gravity significantly enhances resolution. We calculate a new velocity model for the region using SHIPS traveltimes and observed gravity, and show examples where correlation between surface geology and modeled subsurface velocity structure is enhanced.

JASMINE -- Japan Astrometry Satellite Mission for INfrared Exploration: Data Analysis and Accuracy Assessment with a Kalman Filter

NASA Astrophysics Data System (ADS)

Yamada, Y.; Shimokawa, T.; Shinomoto, S. Yano, T.; Gouda, N.

2009-09-01

For the purpose of determining the celestial coordinates of stellar positions, consecutive observational images are laid overlapping each other with clues of stars belonging to multiple plates. In the analysis, one has to estimate not only the coordinates of individual plates, but also the possible expansion and distortion of the frame. This problem reduces to a least-squares fit that can in principle be solved by a huge matrix inversion, which is, however, impracticable. Here, we propose using Kalman filtering to perform the least-squares fit and implement a practical iterative algorithm. We also estimate errors associated with this iterative method and suggest a design of overlapping plates to minimize the error.

Automatic treatment plan re-optimization for adaptive radiotherapy guided with the initial plan DVHs.

PubMed

Li, Nan; Zarepisheh, Masoud; Uribe-Sanchez, Andres; Moore, Kevin; Tian, Zhen; Zhen, Xin; Graves, Yan Jiang; Gautier, Quentin; Mell, Loren; Zhou, Linghong; Jia, Xun; Jiang, Steve

2013-12-21

Adaptive radiation therapy (ART) can reduce normal tissue toxicity and/or improve tumor control through treatment adaptations based on the current patient anatomy. Developing an efficient and effective re-planning algorithm is an important step toward the clinical realization of ART. For the re-planning process, manual trial-and-error approach to fine-tune planning parameters is time-consuming and is usually considered unpractical, especially for online ART. It is desirable to automate this step to yield a plan of acceptable quality with minimal interventions. In ART, prior information in the original plan is available, such as dose-volume histogram (DVH), which can be employed to facilitate the automatic re-planning process. The goal of this work is to develop an automatic re-planning algorithm to generate a plan with similar, or possibly better, DVH curves compared with the clinically delivered original plan. Specifically, our algorithm iterates the following two loops. An inner loop is the traditional fluence map optimization, in which we optimize a quadratic objective function penalizing the deviation of the dose received by each voxel from its prescribed or threshold dose with a set of fixed voxel weighting factors. In outer loop, the voxel weighting factors in the objective function are adjusted according to the deviation of the current DVH curves from those in the original plan. The process is repeated until the DVH curves are acceptable or maximum iteration step is reached. The whole algorithm is implemented on GPU for high efficiency. The feasibility of our algorithm has been demonstrated with three head-and-neck cancer IMRT cases, each having an initial planning CT scan and another treatment CT scan acquired in the middle of treatment course. Compared with the DVH curves in the original plan, the DVH curves in the resulting plan using our algorithm with 30 iterations are better for almost all structures. The re-optimization process takes about 30 s using our in-house optimization engine.

Voltage scheduling for low power/energy

NASA Astrophysics Data System (ADS)

Manzak, Ali

2001-07-01

Power considerations have become an increasingly dominant factor in the design of both portable and desk-top systems. An effective way to reduce power consumption is to lower the supply voltage since voltage is quadratically related to power. This dissertation considers the problem of lowering the supply voltage at (i) the system level and at (ii) the behavioral level. At the system level, the voltage of the variable voltage processor is dynamically changed with the work load. Processors with limited sized buffers as well as those with very large buffers are considered. Given the task arrival times, deadline times, execution times, periods and switching activities, task scheduling algorithms that minimize energy or peak power are developed for the processors equipped with very large buffers. A relation between the operating voltages of the tasks for minimum energy/power is determined using the Lagrange multiplier method, and an iterative algorithm that utilizes this relation is developed. Experimental results show that the voltage assignment obtained by the proposed algorithm is very close (0.1% error) to that of the optimal energy assignment and the optimal peak power (1% error) assignment. Next, on-line and off-fine minimum energy task scheduling algorithms are developed for processors with limited sized buffers. These algorithms have polynomial time complexity and present optimal (off-line) and close-to-optimal (on-line) solutions. A procedure to calculate the minimum buffer size given information about the size of the task (maximum, minimum), execution time (best case, worst case) and deadlines is also presented. At the behavioral level, resources operating at multiple voltages are used to minimize power while maintaining the throughput. Such a scheme has the advantage of allowing modules on the critical paths to be assigned to the highest voltage levels (thus meeting the required timing constraints) while allowing modules on non-critical paths to be assigned to lower voltage levels (thus reducing the power consumption). A polynomial time resource and latency constrained scheduling algorithm is developed to distribute the available slack among the nodes such that power consumption is minimum. The algorithm is iterative and utilizes the slack based on the Lagrange multiplier method.

Iterative algorithm for joint zero diagonalization with application in blind source separation.

PubMed

Zhang, Wei-Tao; Lou, Shun-Tian

2011-07-01

A new iterative algorithm for the nonunitary joint zero diagonalization of a set of matrices is proposed for blind source separation applications. On one hand, since the zero diagonalizer of the proposed algorithm is constructed iteratively by successive multiplications of an invertible matrix, the singular solutions that occur in the existing nonunitary iterative algorithms are naturally avoided. On the other hand, compared to the algebraic method for joint zero diagonalization, the proposed algorithm requires fewer matrices to be zero diagonalized to yield even better performance. The extension of the algorithm to the complex and nonsquare mixing cases is also addressed. Numerical simulations on both synthetic data and blind source separation using time-frequency distributions illustrate the performance of the algorithm and provide a comparison to the leading joint zero diagonalization schemes.

High resolution x-ray CMT: Reconstruction methods

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

Brown, J.K.

This paper qualitatively discusses the primary characteristics of methods for reconstructing tomographic images from a set of projections. These reconstruction methods can be categorized as either {open_quotes}analytic{close_quotes} or {open_quotes}iterative{close_quotes} techniques. Analytic algorithms are derived from the formal inversion of equations describing the imaging process, while iterative algorithms incorporate a model of the imaging process and provide a mechanism to iteratively improve image estimates. Analytic reconstruction algorithms are typically computationally more efficient than iterative methods; however, analytic algorithms are available for a relatively limited set of imaging geometries and situations. Thus, the framework of iterative reconstruction methods is better suited formore » high accuracy, tomographic reconstruction codes.« less

Sparse-view proton computed tomography using modulated proton beams.

PubMed

Lee, Jiseoc; Kim, Changhwan; Min, Byungjun; Kwak, Jungwon; Park, Seyjoon; Lee, Se Byeong; Park, Sungyong; Cho, Seungryong

2015-02-01

Proton imaging that uses a modulated proton beam and an intensity detector allows a relatively fast image acquisition compared to the imaging approach based on a trajectory tracking detector. In addition, it requires a relatively simple implementation in a conventional proton therapy equipment. The model of geometric straight ray assumed in conventional computed tomography (CT) image reconstruction is however challenged by multiple-Coulomb scattering and energy straggling in the proton imaging. Radiation dose to the patient is another important issue that has to be taken care of for practical applications. In this work, the authors have investigated iterative image reconstructions after a deconvolution of the sparsely view-sampled data to address these issues in proton CT. Proton projection images were acquired using the modulated proton beams and the EBT2 film as an intensity detector. Four electron-density cylinders representing normal soft tissues and bone were used as imaged object and scanned at 40 views that are equally separated over 360°. Digitized film images were converted to water-equivalent thickness by use of an empirically derived conversion curve. For improving the image quality, a deconvolution-based image deblurring with an empirically acquired point spread function was employed. They have implemented iterative image reconstruction algorithms such as adaptive steepest descent-projection onto convex sets (ASD-POCS), superiorization method-projection onto convex sets (SM-POCS), superiorization method-expectation maximization (SM-EM), and expectation maximization-total variation minimization (EM-TV). Performance of the four image reconstruction algorithms was analyzed and compared quantitatively via contrast-to-noise ratio (CNR) and root-mean-square-error (RMSE). Objects of higher electron density have been reconstructed more accurately than those of lower density objects. The bone, for example, has been reconstructed within 1% error. EM-based algorithms produced an increased image noise and RMSE as the iteration reaches about 20, while the POCS-based algorithms showed a monotonic convergence with iterations. The ASD-POCS algorithm outperformed the others in terms of CNR, RMSE, and the accuracy of the reconstructed relative stopping power in the region of lung and soft tissues. The four iterative algorithms, i.e., ASD-POCS, SM-POCS, SM-EM, and EM-TV, have been developed and applied for proton CT image reconstruction. Although it still seems that the images need to be improved for practical applications to the treatment planning, proton CT imaging by use of the modulated beams in sparse-view sampling has demonstrated its feasibility.

Evaluation of Bias and Variance in Low-count OSEM List Mode Reconstruction

PubMed Central

Jian, Y; Planeta, B; Carson, R E

2016-01-01

Statistical algorithms have been widely used in PET image reconstruction. The maximum likelihood expectation maximization (MLEM) reconstruction has been shown to produce bias in applications where images are reconstructed from a relatively small number of counts. In this study, image bias and variability in low-count OSEM reconstruction are investigated on images reconstructed with MOLAR (motion-compensation OSEM list-mode algorithm for resolution-recovery reconstruction) platform. A human brain ([11C]AFM) and a NEMA phantom are used in the simulation and real experiments respectively, for the HRRT and Biograph mCT. Image reconstructions were repeated with different combination of subsets and iterations. Regions of interest (ROIs) were defined on low-activity and high-activity regions to evaluate the bias and noise at matched effective iteration numbers (iterations x subsets). Minimal negative biases and no positive biases were found at moderate count levels and less than 5% negative bias was found using extremely low levels of counts (0.2 M NEC). At any given count level, other factors, such as subset numbers and frame-based scatter correction may introduce small biases (1–5%) in the reconstructed images. The observed bias was substantially lower than that reported in the literature, perhaps due to the use of point spread function and/or other implementation methods in MOLAR. PMID:25479254

Evaluation of bias and variance in low-count OSEM list mode reconstruction

NASA Astrophysics Data System (ADS)

Jian, Y.; Planeta, B.; Carson, R. E.

2015-01-01

Statistical algorithms have been widely used in PET image reconstruction. The maximum likelihood expectation maximization reconstruction has been shown to produce bias in applications where images are reconstructed from a relatively small number of counts. In this study, image bias and variability in low-count OSEM reconstruction are investigated on images reconstructed with MOLAR (motion-compensation OSEM list-mode algorithm for resolution-recovery reconstruction) platform. A human brain ([11C]AFM) and a NEMA phantom are used in the simulation and real experiments respectively, for the HRRT and Biograph mCT. Image reconstructions were repeated with different combinations of subsets and iterations. Regions of interest were defined on low-activity and high-activity regions to evaluate the bias and noise at matched effective iteration numbers (iterations × subsets). Minimal negative biases and no positive biases were found at moderate count levels and less than 5% negative bias was found using extremely low levels of counts (0.2 M NEC). At any given count level, other factors, such as subset numbers and frame-based scatter correction may introduce small biases (1-5%) in the reconstructed images. The observed bias was substantially lower than that reported in the literature, perhaps due to the use of point spread function and/or other implementation methods in MOLAR.

Controlled wavelet domain sparsity for x-ray tomography

NASA Astrophysics Data System (ADS)

Purisha, Zenith; Rimpeläinen, Juho; Bubba, Tatiana; Siltanen, Samuli

2018-01-01

Tomographic reconstruction is an ill-posed inverse problem that calls for regularization. One possibility is to require sparsity of the unknown in an orthonormal wavelet basis. This, in turn, can be achieved by variational regularization, where the penalty term is the sum of the absolute values of the wavelet coefficients. The primal-dual fixed point algorithm showed that the minimizer of the variational regularization functional can be computed iteratively using a soft-thresholding operation. Choosing the soft-thresholding parameter \

’In situ’ Measurement of the Ratio of Aerosol Absorption to Extinction Coefficient.

DTIC Science & Technology

1980-08-01

procedure for settling measurements was to obtain a reference (presmoke) level of stabilized power on both of the calorimeters indicated in figure 1...sizing measurements which might be appropriate and accurate for this application as also being investigated. 16 REFERENCES 1. Selby, J. E. A., and L...Projectiles," ECOM-5570, August 1975. 7. Duncan, Louis D., "An Improved Algorithm for the Iterated Minimal Information Solution for Remote Sounding of

An iteration algorithm for optimal network flows

NASA Astrophysics Data System (ADS)

Woong, C. J.

1983-09-01

A packet switching network has the desirable feature of rapidly handling short (bursty) messages of the type often found in computer communication systems. In evaluating packet switching networks, the average time delay per packet is one of the most important measures of performance. The problem of message routing to minimize time delay is analyzed here using two approaches, called "successive saturation' and "max-slack', for various traffic requirement matrices and networks with fixed topology and link capacities.

An iterative algorithm for soft tissue reconstruction from truncated flat panel projections

NASA Astrophysics Data System (ADS)

Langan, D.; Claus, B.; Edic, P.; Vaillant, R.; De Man, B.; Basu, S.; Iatrou, M.

2006-03-01

The capabilities of flat panel interventional x-ray systems continue to expand, enabling a broader array of medical applications to be performed in a minimally invasive manner. Although CT is providing pre-operative 3D information, there is a need for 3D imaging of low contrast soft tissue during interventions in a number of areas including neurology, cardiac electro-physiology, and oncology. Unlike CT systems, interventional angiographic x-ray systems provide real-time large field of view 2D imaging, patient access, and flexible gantry positioning enabling interventional procedures. However, relative to CT, these C-arm flat panel systems have additional technical challenges in 3D soft tissue imaging including slower rotation speed, gantry vibration, reduced lateral patient field of view (FOV), and increased scatter. The reduced patient FOV often results in significant data truncation. Reconstruction of truncated (incomplete) data is known an "interior problem", and it is mathematically impossible to obtain an exact reconstruction. Nevertheless, it is an important problem in 3D imaging on a C-arm to address the need to generate a 3D reconstruction representative of the object being imaged with minimal artifacts. In this work we investigate the application of an iterative Maximum Likelihood Transmission (MLTR) algorithm to truncated data. We also consider truncated data with limited views for cardiac imaging where the views are gated by the electrocardiogram(ECG) to combat motion artifacts.

Stable sequential Kuhn-Tucker theorem in iterative form or a regularized Uzawa algorithm in a regular nonlinear programming problem

NASA Astrophysics Data System (ADS)

Sumin, M. I.

2015-06-01

A parametric nonlinear programming problem in a metric space with an operator equality constraint in a Hilbert space is studied assuming that its lower semicontinuous value function at a chosen individual parameter value has certain subdifferentiability properties in the sense of nonlinear (nonsmooth) analysis. Such subdifferentiability can be understood as the existence of a proximal subgradient or a Fréchet subdifferential. In other words, an individual problem has a corresponding generalized Kuhn-Tucker vector. Under this assumption, a stable sequential Kuhn-Tucker theorem in nondifferential iterative form is proved and discussed in terms of minimizing sequences on the basis of the dual regularization method. This theorem provides necessary and sufficient conditions for the stable construction of a minimizing approximate solution in the sense of Warga in the considered problem, whose initial data can be approximately specified. A substantial difference of the proved theorem from its classical same-named analogue is that the former takes into account the possible instability of the problem in the case of perturbed initial data and, as a consequence, allows for the inherited instability of classical optimality conditions. This theorem can be treated as a regularized generalization of the classical Uzawa algorithm to nonlinear programming problems. Finally, the theorem is applied to the "simplest" nonlinear optimal control problem, namely, to a time-optimal control problem.

Robust THP Transceiver Designs for Multiuser MIMO Downlink with Imperfect CSIT

NASA Astrophysics Data System (ADS)

Ubaidulla, P.; Chockalingam, A.

2009-12-01

We present robust joint nonlinear transceiver designs for multiuser multiple-input multiple-output (MIMO) downlink in the presence of imperfections in the channel state information at the transmitter (CSIT). The base station (BS) is equipped with multiple transmit antennas, and each user terminal is equipped with one or more receive antennas. The BS employs Tomlinson-Harashima precoding (THP) for interuser interference precancellation at the transmitter. We consider robust transceiver designs that jointly optimize the transmit THP filters and receive filter for two models of CSIT errors. The first model is a stochastic error (SE) model, where the CSIT error is Gaussian-distributed. This model is applicable when the CSIT error is dominated by channel estimation error. In this case, the proposed robust transceiver design seeks to minimize a stochastic function of the sum mean square error (SMSE) under a constraint on the total BS transmit power. We propose an iterative algorithm to solve this problem. The other model we consider is a norm-bounded error (NBE) model, where the CSIT error can be specified by an uncertainty set. This model is applicable when the CSIT error is dominated by quantization errors. In this case, we consider a worst-case design. For this model, we consider robust (i) minimum SMSE, (ii) MSE-constrained, and (iii) MSE-balancing transceiver designs. We propose iterative algorithms to solve these problems, wherein each iteration involves a pair of semidefinite programs (SDPs). Further, we consider an extension of the proposed algorithm to the case with per-antenna power constraints. We evaluate the robustness of the proposed algorithms to imperfections in CSIT through simulation, and show that the proposed robust designs outperform nonrobust designs as well as robust linear transceiver designs reported in the recent literature.

[Accurate 3D free-form registration between fan-beam CT and cone-beam CT].

PubMed

Liang, Yueqiang; Xu, Hongbing; Li, Baosheng; Li, Hongsheng; Yang, Fujun

2012-06-01

Because the X-ray scatters, the CT numbers in cone-beam CT cannot exactly correspond to the electron densities. This, therefore, results in registration error when the intensity-based registration algorithm is used to register planning fan-beam CT and cone-beam CT. In order to reduce the registration error, we have developed an accurate gradient-based registration algorithm. The gradient-based deformable registration problem is described as a minimization of energy functional. Through the calculus of variations and Gauss-Seidel finite difference method, we derived the iterative formula of the deformable registration. The algorithm was implemented by GPU through OpenCL framework, with which the registration time was greatly reduced. Our experimental results showed that the proposed gradient-based registration algorithm could register more accurately the clinical cone-beam CT and fan-beam CT images compared with the intensity-based algorithm. The GPU-accelerated algorithm meets the real-time requirement in the online adaptive radiotherapy.

An iterative method for the Helmholtz equation

NASA Technical Reports Server (NTRS)

Bayliss, A.; Goldstein, C. I.; Turkel, E.

1983-01-01

An iterative algorithm for the solution of the Helmholtz equation is developed. The algorithm is based on a preconditioned conjugate gradient iteration for the normal equations. The preconditioning is based on an SSOR sweep for the discrete Laplacian. Numerical results are presented for a wide variety of problems of physical interest and demonstrate the effectiveness of the algorithm.

Iterative Nonlocal Total Variation Regularization Method for Image Restoration

PubMed Central

Xu, Huanyu; Sun, Quansen; Luo, Nan; Cao, Guo; Xia, Deshen

2013-01-01

In this paper, a Bregman iteration based total variation image restoration algorithm is proposed. Based on the Bregman iteration, the algorithm splits the original total variation problem into sub-problems that are easy to solve. Moreover, non-local regularization is introduced into the proposed algorithm, and a method to choose the non-local filter parameter locally and adaptively is proposed. Experiment results show that the proposed algorithms outperform some other regularization methods. PMID:23776560

A 2D range Hausdorff approach to 3D facial recognition.

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

Koch, Mark William; Russ, Trina Denise; Little, Charles Quentin

2004-11-01

This paper presents a 3D facial recognition algorithm based on the Hausdorff distance metric. The standard 3D formulation of the Hausdorff matching algorithm has been modified to operate on a 2D range image, enabling a reduction in computation from O(N2) to O(N) without large storage requirements. The Hausdorff distance is known for its robustness to data outliers and inconsistent data between two data sets, making it a suitable choice for dealing with the inherent problems in many 3D datasets due to sensor noise and object self-occlusion. For optimal performance, the algorithm assumes a good initial alignment between probe and templatemore » datasets. However, to minimize the error between two faces, the alignment can be iteratively refined. Results from the algorithm are presented using 3D face images from the Face Recognition Grand Challenge database version 1.0.« less

Stochastic derivative-free optimization using a trust region framework

DOE PAGES

Larson, Jeffrey; Billups, Stephen C.

2016-02-17

This study presents a trust region algorithm to minimize a function f when one has access only to noise-corrupted function values f¯. The model-based algorithm dynamically adjusts its step length, taking larger steps when the model and function agree and smaller steps when the model is less accurate. The method does not require the user to specify a fixed pattern of points used to build local models and does not repeatedly sample points. If f is sufficiently smooth and the noise is independent and identically distributed with mean zero and finite variance, we prove that our algorithm produces iterates suchmore » that the corresponding function gradients converge in probability to zero. As a result, we present a prototype of our algorithm that, while simplistic in its management of previously evaluated points, solves benchmark problems in fewer function evaluations than do existing stochastic approximation methods.« less

Approximate Computing Techniques for Iterative Graph Algorithms

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

Panyala, Ajay R.; Subasi, Omer; Halappanavar, Mahantesh

Approximate computing enables processing of large-scale graphs by trading off quality for performance. Approximate computing techniques have become critical not only due to the emergence of parallel architectures but also the availability of large scale datasets enabling data-driven discovery. Using two prototypical graph algorithms, PageRank and community detection, we present several approximate computing heuristics to scale the performance with minimal loss of accuracy. We present several heuristics including loop perforation, data caching, incomplete graph coloring and synchronization, and evaluate their efficiency. We demonstrate performance improvements of up to 83% for PageRank and up to 450x for community detection, with lowmore » impact of accuracy for both the algorithms. We expect the proposed approximate techniques will enable scalable graph analytics on data of importance to several applications in science and their subsequent adoption to scale similar graph algorithms.« less

A Generalized Method for Automatic Downhand and Wirefeed Control of a Welding Robot and Positioner

NASA Technical Reports Server (NTRS)

Fernandez, Ken; Cook, George E.

1988-01-01

A generalized method for controlling a six degree-of-freedom (DOF) robot and a two DOF positioner used for arc welding operations is described. The welding path is defined in the part reference frame, and robot/positioner joint angles of the equivalent eight DOF serial linkage are determined via an iterative solution. Three algorithms are presented: the first solution controls motion of the eight DOF mechanism such that proper torch motion is achieved while minimizing the sum-of-squares of joint displacements; the second algorithm adds two constraint equations to achieve torch control while maintaining part orientation so that welding occurs in the downhand position; and the third algorithm adds the ability to control the proper orientation of a wire feed mechanism used in gas tungsten arc (GTA) welding operations. A verification of these algorithms is given using ROBOSIM, a NASA developed computer graphic simulation software package design for robot systems development.

Control algorithms for dynamic attenuators.

PubMed

Hsieh, Scott S; Pelc, Norbert J

2014-06-01

The authors describe algorithms to control dynamic attenuators in CT and compare their performance using simulated scans. Dynamic attenuators are prepatient beam shaping filters that modulate the distribution of x-ray fluence incident on the patient on a view-by-view basis. These attenuators can reduce dose while improving key image quality metrics such as peak or mean variance. In each view, the attenuator presents several degrees of freedom which may be individually adjusted. The total number of degrees of freedom across all views is very large, making many optimization techniques impractical. The authors develop a theory for optimally controlling these attenuators. Special attention is paid to a theoretically perfect attenuator which controls the fluence for each ray individually, but the authors also investigate and compare three other, practical attenuator designs which have been previously proposed: the piecewise-linear attenuator, the translating attenuator, and the double wedge attenuator. The authors pose and solve the optimization problems of minimizing the mean and peak variance subject to a fixed dose limit. For a perfect attenuator and mean variance minimization, this problem can be solved in simple, closed form. For other attenuator designs, the problem can be decomposed into separate problems for each view to greatly reduce the computational complexity. Peak variance minimization can be approximately solved using iterated, weighted mean variance (WMV) minimization. Also, the authors develop heuristics for the perfect and piecewise-linear attenuators which do not require a priori knowledge of the patient anatomy. The authors compare these control algorithms on different types of dynamic attenuators using simulated raw data from forward projected DICOM files of a thorax and an abdomen. The translating and double wedge attenuators reduce dose by an average of 30% relative to current techniques (bowtie filter with tube current modulation) without increasing peak variance. The 15-element piecewise-linear dynamic attenuator reduces dose by an average of 42%, and the perfect attenuator reduces dose by an average of 50%. Improvements in peak variance are several times larger than improvements in mean variance. Heuristic control eliminates the need for a prescan. For the piecewise-linear attenuator, the cost of heuristic control is an increase in dose of 9%. The proposed iterated WMV minimization produces results that are within a few percent of the true solution. Dynamic attenuators show potential for significant dose reduction. A wide class of dynamic attenuators can be accurately controlled using the described methods.

Discrete-Time Stable Generalized Self-Learning Optimal Control With Approximation Errors.

PubMed

Wei, Qinglai; Li, Benkai; Song, Ruizhuo

2018-04-01

In this paper, a generalized policy iteration (GPI) algorithm with approximation errors is developed for solving infinite horizon optimal control problems for nonlinear systems. The developed stable GPI algorithm provides a general structure of discrete-time iterative adaptive dynamic programming algorithms, by which most of the discrete-time reinforcement learning algorithms can be described using the GPI structure. It is for the first time that approximation errors are explicitly considered in the GPI algorithm. The properties of the stable GPI algorithm with approximation errors are analyzed. The admissibility of the approximate iterative control law can be guaranteed if the approximation errors satisfy the admissibility criteria. The convergence of the developed algorithm is established, which shows that the iterative value function is convergent to a finite neighborhood of the optimal performance index function, if the approximate errors satisfy the convergence criterion. Finally, numerical examples and comparisons are presented.

Simultaneous digital super-resolution and nonuniformity correction for infrared imaging systems.

PubMed

Meza, Pablo; Machuca, Guillermo; Torres, Sergio; Martin, Cesar San; Vera, Esteban

2015-07-20

In this article, we present a novel algorithm to achieve simultaneous digital super-resolution and nonuniformity correction from a sequence of infrared images. We propose to use spatial regularization terms that exploit nonlocal means and the absence of spatial correlation between the scene and the nonuniformity noise sources. We derive an iterative optimization algorithm based on a gradient descent minimization strategy. Results from infrared image sequences corrupted with simulated and real fixed-pattern noise show a competitive performance compared with state-of-the-art methods. A qualitative analysis on the experimental results obtained with images from a variety of infrared cameras indicates that the proposed method provides super-resolution images with significantly less fixed-pattern noise.

On the convergence of a linesearch based proximal-gradient method for nonconvex optimization

NASA Astrophysics Data System (ADS)

Bonettini, S.; Loris, I.; Porta, F.; Prato, M.; Rebegoldi, S.

2017-05-01

We consider a variable metric linesearch based proximal gradient method for the minimization of the sum of a smooth, possibly nonconvex function plus a convex, possibly nonsmooth term. We prove convergence of this iterative algorithm to a critical point if the objective function satisfies the Kurdyka-Łojasiewicz property at each point of its domain, under the assumption that a limit point exists. The proposed method is applied to a wide collection of image processing problems and our numerical tests show that our algorithm results to be flexible, robust and competitive when compared to recently proposed approaches able to address the optimization problems arising in the considered applications.

Algorithm for predicting the evolution of series of dynamics of complex systems in solving information problems

NASA Astrophysics Data System (ADS)

Kasatkina, T. I.; Dushkin, A. V.; Pavlov, V. A.; Shatovkin, R. R.

2018-03-01

In the development of information, systems and programming to predict the series of dynamics, neural network methods have recently been applied. They are more flexible, in comparison with existing analogues and are capable of taking into account the nonlinearities of the series. In this paper, we propose a modified algorithm for predicting the series of dynamics, which includes a method for training neural networks, an approach to describing and presenting input data, based on the prediction by the multilayer perceptron method. To construct a neural network, the values of a series of dynamics at the extremum points and time values corresponding to them, formed based on the sliding window method, are used as input data. The proposed algorithm can act as an independent approach to predicting the series of dynamics, and be one of the parts of the forecasting system. The efficiency of predicting the evolution of the dynamics series for a short-term one-step and long-term multi-step forecast by the classical multilayer perceptron method and a modified algorithm using synthetic and real data is compared. The result of this modification was the minimization of the magnitude of the iterative error that arises from the previously predicted inputs to the inputs to the neural network, as well as the increase in the accuracy of the iterative prediction of the neural network.

3D reconstruction of the magnetic vector potential using model based iterative reconstruction

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

Prabhat, K. C.; Aditya Mohan, K.; Phatak, Charudatta

Lorentz transmission electron microscopy (TEM) observations of magnetic nanoparticles contain information on the magnetic and electrostatic potentials. Vector field electron tomography (VFET) can be used to reconstruct electromagnetic potentials of the nanoparticles from their corresponding LTEM images. The VFET approach is based on the conventional filtered back projection approach to tomographic reconstructions and the availability of an incomplete set of measurements due to experimental limitations means that the reconstructed vector fields exhibit significant artifacts. In this paper, we outline a model-based iterative reconstruction (MBIR) algorithm to reconstruct the magnetic vector potential of magnetic nanoparticles. We combine a forward model formore » image formation in TEM experiments with a prior model to formulate the tomographic problem as a maximum a-posteriori probability estimation problem (MAP). The MAP cost function is minimized iteratively to determine the vector potential. Here, a comparative reconstruction study of simulated as well as experimental data sets show that the MBIR approach yields quantifiably better reconstructions than the VFET approach.« less

3D reconstruction of the magnetic vector potential using model based iterative reconstruction.

PubMed

Prabhat, K C; Aditya Mohan, K; Phatak, Charudatta; Bouman, Charles; De Graef, Marc

2017-11-01

Lorentz transmission electron microscopy (TEM) observations of magnetic nanoparticles contain information on the magnetic and electrostatic potentials. Vector field electron tomography (VFET) can be used to reconstruct electromagnetic potentials of the nanoparticles from their corresponding LTEM images. The VFET approach is based on the conventional filtered back projection approach to tomographic reconstructions and the availability of an incomplete set of measurements due to experimental limitations means that the reconstructed vector fields exhibit significant artifacts. In this paper, we outline a model-based iterative reconstruction (MBIR) algorithm to reconstruct the magnetic vector potential of magnetic nanoparticles. We combine a forward model for image formation in TEM experiments with a prior model to formulate the tomographic problem as a maximum a-posteriori probability estimation problem (MAP). The MAP cost function is minimized iteratively to determine the vector potential. A comparative reconstruction study of simulated as well as experimental data sets show that the MBIR approach yields quantifiably better reconstructions than the VFET approach. Copyright © 2017 Elsevier B.V. All rights reserved.

3D reconstruction of the magnetic vector potential using model based iterative reconstruction

DOE PAGES

Prabhat, K. C.; Aditya Mohan, K.; Phatak, Charudatta; ...

2017-07-03

Lorentz transmission electron microscopy (TEM) observations of magnetic nanoparticles contain information on the magnetic and electrostatic potentials. Vector field electron tomography (VFET) can be used to reconstruct electromagnetic potentials of the nanoparticles from their corresponding LTEM images. The VFET approach is based on the conventional filtered back projection approach to tomographic reconstructions and the availability of an incomplete set of measurements due to experimental limitations means that the reconstructed vector fields exhibit significant artifacts. In this paper, we outline a model-based iterative reconstruction (MBIR) algorithm to reconstruct the magnetic vector potential of magnetic nanoparticles. We combine a forward model formore » image formation in TEM experiments with a prior model to formulate the tomographic problem as a maximum a-posteriori probability estimation problem (MAP). The MAP cost function is minimized iteratively to determine the vector potential. Here, a comparative reconstruction study of simulated as well as experimental data sets show that the MBIR approach yields quantifiably better reconstructions than the VFET approach.« less

A pseudo-discrete algebraic reconstruction technique (PDART) prior image-based suppression of high density artifacts in computed tomography

NASA Astrophysics Data System (ADS)

Pua, Rizza; Park, Miran; Wi, Sunhee; Cho, Seungryong

2016-12-01

We propose a hybrid metal artifact reduction (MAR) approach for computed tomography (CT) that is computationally more efficient than a fully iterative reconstruction method, but at the same time achieves superior image quality to the interpolation-based in-painting techniques. Our proposed MAR method, an image-based artifact subtraction approach, utilizes an intermediate prior image reconstructed via PDART to recover the background information underlying the high density objects. For comparison, prior images generated by total-variation minimization (TVM) algorithm, as a realization of fully iterative approach, were also utilized as intermediate images. From the simulation and real experimental results, it has been shown that PDART drastically accelerates the reconstruction to an acceptable quality of prior images. Incorporating PDART-reconstructed prior images in the proposed MAR scheme achieved higher quality images than those by a conventional in-painting method. Furthermore, the results were comparable to the fully iterative MAR that uses high-quality TVM prior images.

First-order convex feasibility algorithms for x-ray CT

PubMed Central

Sidky, Emil Y.; Jørgensen, Jakob S.; Pan, Xiaochuan

2013-01-01

Purpose: Iterative image reconstruction (IIR) algorithms in computed tomography (CT) are based on algorithms for solving a particular optimization problem. Design of the IIR algorithm, therefore, is aided by knowledge of the solution to the optimization problem on which it is based. Often times, however, it is impractical to achieve accurate solution to the optimization of interest, which complicates design of IIR algorithms. This issue is particularly acute for CT with a limited angular-range scan, which leads to poorly conditioned system matrices and difficult to solve optimization problems. In this paper, we develop IIR algorithms which solve a certain type of optimization called convex feasibility. The convex feasibility approach can provide alternatives to unconstrained optimization approaches and at the same time allow for rapidly convergent algorithms for their solution—thereby facilitating the IIR algorithm design process. Methods: An accelerated version of the Chambolle−Pock (CP) algorithm is adapted to various convex feasibility problems of potential interest to IIR in CT. One of the proposed problems is seen to be equivalent to least-squares minimization, and two other problems provide alternatives to penalized, least-squares minimization. Results: The accelerated CP algorithms are demonstrated on a simulation of circular fan-beam CT with a limited scanning arc of 144°. The CP algorithms are seen in the empirical results to converge to the solution of their respective convex feasibility problems. Conclusions: Formulation of convex feasibility problems can provide a useful alternative to unconstrained optimization when designing IIR algorithms for CT. The approach is amenable to recent methods for accelerating first-order algorithms which may be particularly useful for CT with limited angular-range scanning. The present paper demonstrates the methodology, and future work will illustrate its utility in actual CT application. PMID:23464295

A Generic 1D Forward Modeling and Inversion Algorithm for TEM Sounding with an Arbitrary Horizontal Loop

NASA Astrophysics Data System (ADS)

Li, Zhanhui; Huang, Qinghua; Xie, Xingbing; Tang, Xingong; Chang, Liao

2016-08-01

We present a generic 1D forward modeling and inversion algorithm for transient electromagnetic (TEM) data with an arbitrary horizontal transmitting loop and receivers at any depth in a layered earth. Both the Hankel and sine transforms required in the forward algorithm are calculated using the filter method. The adjoint-equation method is used to derive the formulation of data sensitivity at any depth in non-permeable media. The inversion algorithm based on this forward modeling algorithm and sensitivity formulation is developed using the Gauss-Newton iteration method combined with the Tikhonov regularization. We propose a new data-weighting method to minimize the initial model dependence that enhances the convergence stability. On a laptop with a CPU of i7-5700HQ@3.5 GHz, the inversion iteration of a 200 layered input model with a single receiver takes only 0.34 s, while it increases to only 0.53 s for the data from four receivers at a same depth. For the case of four receivers at different depths, the inversion iteration runtime increases to 1.3 s. Modeling the data with an irregular loop and an equal-area square loop indicates that the effect of the loop geometry is significant at early times and vanishes gradually along the diffusion of TEM field. For a stratified earth, inversion of data from more than one receiver is useful in noise reducing to get a more credible layered earth. However, for a resistive layer shielded below a conductive layer, increasing the number of receivers on the ground does not have significant improvement in recovering the resistive layer. Even with a down-hole TEM sounding, the shielded resistive layer cannot be recovered if all receivers are above the shielded resistive layer. However, our modeling demonstrates remarkable improvement in detecting the resistive layer with receivers in or under this layer.

An accelerated non-Gaussianity based multichannel predictive deconvolution method with the limited supporting region of filters

NASA Astrophysics Data System (ADS)

Li, Zhong-xiao; Li, Zhen-chun

2016-09-01

The multichannel predictive deconvolution can be conducted in overlapping temporal and spatial data windows to solve the 2D predictive filter for multiple removal. Generally, the 2D predictive filter can better remove multiples at the cost of more computation time compared with the 1D predictive filter. In this paper we first use the cross-correlation strategy to determine the limited supporting region of filters where the coefficients play a major role for multiple removal in the filter coefficient space. To solve the 2D predictive filter the traditional multichannel predictive deconvolution uses the least squares (LS) algorithm, which requires primaries and multiples are orthogonal. To relax the orthogonality assumption the iterative reweighted least squares (IRLS) algorithm and the fast iterative shrinkage thresholding (FIST) algorithm have been used to solve the 2D predictive filter in the multichannel predictive deconvolution with the non-Gaussian maximization (L1 norm minimization) constraint of primaries. The FIST algorithm has been demonstrated as a faster alternative to the IRLS algorithm. In this paper we introduce the FIST algorithm to solve the filter coefficients in the limited supporting region of filters. Compared with the FIST based multichannel predictive deconvolution without the limited supporting region of filters the proposed method can reduce the computation burden effectively while achieving a similar accuracy. Additionally, the proposed method can better balance multiple removal and primary preservation than the traditional LS based multichannel predictive deconvolution and FIST based single channel predictive deconvolution. Synthetic and field data sets demonstrate the effectiveness of the proposed method.

A novel decoding algorithm based on the hierarchical reliable strategy for SCG-LDPC codes in optical communications

NASA Astrophysics Data System (ADS)

Yuan, Jian-guo; Tong, Qing-zhen; Huang, Sheng; Wang, Yong

2013-11-01

An effective hierarchical reliable belief propagation (HRBP) decoding algorithm is proposed according to the structural characteristics of systematically constructed Gallager low-density parity-check (SCG-LDPC) codes. The novel decoding algorithm combines the layered iteration with the reliability judgment, and can greatly reduce the number of the variable nodes involved in the subsequent iteration process and accelerate the convergence rate. The result of simulation for SCG-LDPC(3969,3720) code shows that the novel HRBP decoding algorithm can greatly reduce the computing amount at the condition of ensuring the performance compared with the traditional belief propagation (BP) algorithm. The bit error rate (BER) of the HRBP algorithm is considerable at the threshold value of 15, but in the subsequent iteration process, the number of the variable nodes for the HRBP algorithm can be reduced by about 70% at the high signal-to-noise ratio (SNR) compared with the BP algorithm. When the threshold value is further increased, the HRBP algorithm will gradually degenerate into the layered-BP algorithm, but at the BER of 10-7 and the maximal iteration number of 30, the net coding gain (NCG) of the HRBP algorithm is 0.2 dB more than that of the BP algorithm, and the average iteration times can be reduced by about 40% at the high SNR. Therefore, the novel HRBP decoding algorithm is more suitable for optical communication systems.

GPU-accelerated regularized iterative reconstruction for few-view cone beam CT

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

Matenine, Dmitri, E-mail: dmitri.matenine.1@ulaval.ca; Goussard, Yves, E-mail: yves.goussard@polymtl.ca; Després, Philippe, E-mail: philippe.despres@phy.ulaval.ca

2015-04-15

Purpose: The present work proposes an iterative reconstruction technique designed for x-ray transmission computed tomography (CT). The main objective is to provide a model-based solution to the cone-beam CT reconstruction problem, yielding accurate low-dose images via few-views acquisitions in clinically acceptable time frames. Methods: The proposed technique combines a modified ordered subsets convex (OSC) algorithm and the total variation minimization (TV) regularization technique and is called OSC-TV. The number of subsets of each OSC iteration follows a reduction pattern in order to ensure the best performance of the regularization method. Considering the high computational cost of the algorithm, it ismore » implemented on a graphics processing unit, using parallelization to accelerate computations. Results: The reconstructions were performed on computer-simulated as well as human pelvic cone-beam CT projection data and image quality was assessed. In terms of convergence and image quality, OSC-TV performs well in reconstruction of low-dose cone-beam CT data obtained via a few-view acquisition protocol. It compares favorably to the few-view TV-regularized projections onto convex sets (POCS-TV) algorithm. It also appears to be a viable alternative to full-dataset filtered backprojection. Execution times are of 1–2 min and are compatible with the typical clinical workflow for nonreal-time applications. Conclusions: Considering the image quality and execution times, this method may be useful for reconstruction of low-dose clinical acquisitions. It may be of particular benefit to patients who undergo multiple acquisitions by reducing the overall imaging radiation dose and associated risks.« less

Priori mask guided image reconstruction (p-MGIR) for ultra-low dose cone-beam computed tomography

NASA Astrophysics Data System (ADS)

Park, Justin C.; Zhang, Hao; Chen, Yunmei; Fan, Qiyong; Kahler, Darren L.; Liu, Chihray; Lu, Bo

2015-11-01

Recently, the compressed sensing (CS) based iterative reconstruction method has received attention because of its ability to reconstruct cone beam computed tomography (CBCT) images with good quality using sparsely sampled or noisy projections, thus enabling dose reduction. However, some challenges remain. In particular, there is always a tradeoff between image resolution and noise/streak artifact reduction based on the amount of regularization weighting that is applied uniformly across the CBCT volume. The purpose of this study is to develop a novel low-dose CBCT reconstruction algorithm framework called priori mask guided image reconstruction (p-MGIR) that allows reconstruction of high-quality low-dose CBCT images while preserving the image resolution. In p-MGIR, the unknown CBCT volume was mathematically modeled as a combination of two regions: (1) where anatomical structures are complex, and (2) where intensities are relatively uniform. The priori mask, which is the key concept of the p-MGIR algorithm, was defined as the matrix that distinguishes between the two separate CBCT regions where the resolution needs to be preserved and where streak or noise needs to be suppressed. We then alternately updated each part of image by solving two sub-minimization problems iteratively, where one minimization was focused on preserving the edge information of the first part while the other concentrated on the removal of noise/artifacts from the latter part. To evaluate the performance of the p-MGIR algorithm, a numerical head-and-neck phantom, a Catphan 600 physical phantom, and a clinical head-and-neck cancer case were used for analysis. The results were compared with the standard Feldkamp-Davis-Kress as well as conventional CS-based algorithms. Examination of the p-MGIR algorithm showed that high-quality low-dose CBCT images can be reconstructed without compromising the image resolution. For both phantom and the patient cases, the p-MGIR is able to achieve a clinically-reasonable image with 60 projections. Therefore, a clinically-viable, high-resolution head-and-neck CBCT image can be obtained while cutting the dose by 83%. Moreover, the image quality obtained using p-MGIR is better than the quality obtained using other algorithms. In this work, we propose a novel low-dose CBCT reconstruction algorithm called p-MGIR. It can be potentially used as a CBCT reconstruction algorithm with low dose scan requests

Array architectures for iterative algorithms

NASA Technical Reports Server (NTRS)

Jagadish, Hosagrahar V.; Rao, Sailesh K.; Kailath, Thomas

1987-01-01

Regular mesh-connected arrays are shown to be isomorphic to a class of so-called regular iterative algorithms. For a wide variety of problems it is shown how to obtain appropriate iterative algorithms and then how to translate these algorithms into arrays in a systematic fashion. Several 'systolic' arrays presented in the literature are shown to be specific cases of the variety of architectures that can be derived by the techniques presented here. These include arrays for Fourier Transform, Matrix Multiplication, and Sorting.

Error minimization algorithm for comparative quantitative PCR analysis: Q-Anal.

PubMed

OConnor, William; Runquist, Elizabeth A

2008-07-01

Current methods for comparative quantitative polymerase chain reaction (qPCR) analysis, the threshold and extrapolation methods, either make assumptions about PCR efficiency that require an arbitrary threshold selection process or extrapolate to estimate relative levels of messenger RNA (mRNA) transcripts. Here we describe an algorithm, Q-Anal, that blends elements from current methods to by-pass assumptions regarding PCR efficiency and improve the threshold selection process to minimize error in comparative qPCR analysis. This algorithm uses iterative linear regression to identify the exponential phase for both target and reference amplicons and then selects, by minimizing linear regression error, a fluorescence threshold where efficiencies for both amplicons have been defined. From this defined fluorescence threshold, cycle time (Ct) and the error for both amplicons are calculated and used to determine the expression ratio. Ratios in complementary DNA (cDNA) dilution assays from qPCR data were analyzed by the Q-Anal method and compared with the threshold method and an extrapolation method. Dilution ratios determined by the Q-Anal and threshold methods were 86 to 118% of the expected cDNA ratios, but relative errors for the Q-Anal method were 4 to 10% in comparison with 4 to 34% for the threshold method. In contrast, ratios determined by an extrapolation method were 32 to 242% of the expected cDNA ratios, with relative errors of 67 to 193%. Q-Anal will be a valuable and quick method for minimizing error in comparative qPCR analysis.

Fisher's method of scoring in statistical image reconstruction: comparison of Jacobi and Gauss-Seidel iterative schemes.

PubMed

Hudson, H M; Ma, J; Green, P

1994-01-01

Many algorithms for medical image reconstruction adopt versions of the expectation-maximization (EM) algorithm. In this approach, parameter estimates are obtained which maximize a complete data likelihood or penalized likelihood, in each iteration. Implicitly (and sometimes explicitly) penalized algorithms require smoothing of the current reconstruction in the image domain as part of their iteration scheme. In this paper, we discuss alternatives to EM which adapt Fisher's method of scoring (FS) and other methods for direct maximization of the incomplete data likelihood. Jacobi and Gauss-Seidel methods for non-linear optimization provide efficient algorithms applying FS in tomography. One approach uses smoothed projection data in its iterations. We investigate the convergence of Jacobi and Gauss-Seidel algorithms with clinical tomographic projection data.

GENFIRE: A generalized Fourier iterative reconstruction algorithm for high-resolution 3D imaging

DOE PAGES

Pryor, Alan; Yang, Yongsoo; Rana, Arjun; ...

2017-09-05

Tomography has made a radical impact on diverse fields ranging from the study of 3D atomic arrangements in matter to the study of human health in medicine. Despite its very diverse applications, the core of tomography remains the same, that is, a mathematical method must be implemented to reconstruct the 3D structure of an object from a number of 2D projections. Here, we present the mathematical implementation of a tomographic algorithm, termed GENeralized Fourier Iterative REconstruction (GENFIRE), for high-resolution 3D reconstruction from a limited number of 2D projections. GENFIRE first assembles a 3D Fourier grid with oversampling and then iteratesmore » between real and reciprocal space to search for a global solution that is concurrently consistent with the measured data and general physical constraints. The algorithm requires minimal human intervention and also incorporates angular refinement to reduce the tilt angle error. We demonstrate that GENFIRE can produce superior results relative to several other popular tomographic reconstruction techniques through numerical simulations and by experimentally reconstructing the 3D structure of a porous material and a frozen-hydrated marine cyanobacterium. As a result, equipped with a graphical user interface, GENFIRE is freely available from our website and is expected to find broad applications across different disciplines.« less

GENFIRE: A generalized Fourier iterative reconstruction algorithm for high-resolution 3D imaging

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

Pryor, Alan; Yang, Yongsoo; Rana, Arjun

Tomography has made a radical impact on diverse fields ranging from the study of 3D atomic arrangements in matter to the study of human health in medicine. Despite its very diverse applications, the core of tomography remains the same, that is, a mathematical method must be implemented to reconstruct the 3D structure of an object from a number of 2D projections. Here, we present the mathematical implementation of a tomographic algorithm, termed GENeralized Fourier Iterative REconstruction (GENFIRE), for high-resolution 3D reconstruction from a limited number of 2D projections. GENFIRE first assembles a 3D Fourier grid with oversampling and then iteratesmore » between real and reciprocal space to search for a global solution that is concurrently consistent with the measured data and general physical constraints. The algorithm requires minimal human intervention and also incorporates angular refinement to reduce the tilt angle error. We demonstrate that GENFIRE can produce superior results relative to several other popular tomographic reconstruction techniques through numerical simulations and by experimentally reconstructing the 3D structure of a porous material and a frozen-hydrated marine cyanobacterium. As a result, equipped with a graphical user interface, GENFIRE is freely available from our website and is expected to find broad applications across different disciplines.« less

An iterative three-dimensional electron density imaging algorithm using uncollimated compton scattered x rays from a polyenergetic primary pencil beam.

PubMed

Van Uytven, Eric; Pistorius, Stephen; Gordon, Richard

2007-01-01

X-ray film-screen mammography is currently the gold standard for detecting breast cancer. However, one disadvantage is that it projects a three-dimensional (3D) object onto a two-dimensional (2D) image, reducing contrast between small lesions and layers of normal tissue. Another limitation is its reduced sensitivity in women with mammographically dense breasts. Computed tomography (CT) produces a 3D image yet has had a limited role in mammography due to its relatively high dose, low resolution, and low contrast. As a first step towards implementing quantitative 3D mammography, which may improve the ability to detect and specify breast tumors, we have developed an analytical technique that can use Compton scatter to obtain 3D information of an object from a single projection. Imaging material with a pencil beam of polychromatic x rays produces a characteristic scattered photon spectrum at each point on the detector plane. A comparable distribution may be calculated using a known incident x-ray energy spectrum, beam shape, and an initial estimate of the object's 3D mass attenuation and electron density. Our iterative minimization algorithm changes the initially arbitrary electron density voxel matrix to reduce regular differences between the analytically predicted and experimentally measured spectra at each point on the detector plane. The simulated electron density converges to that of the object as the differences are minimized. The reconstruction algorithm has been validated using simulated data produced by the EGSnrc Monte Carlo code system. We applied the imaging algorithm to a cylindrically symmetric breast tissue phantom containing multiple inhomogeneities. A preliminary ROC analysis scores greater than 0.96, which indicate that under the described simplifying conditions, this approach shows promise in identifying and localizing inhomogeneities which simulate 0.5 mm calcifications with an image voxel resolution of 0.25 cm and at a dose comparable to mammography.

Analytic TOF PET reconstruction algorithm within DIRECT data partitioning framework

PubMed Central

Matej, Samuel; Daube-Witherspoon, Margaret E.; Karp, Joel S.

2016-01-01

Iterative reconstruction algorithms are routinely used for clinical practice; however, analytic algorithms are relevant candidates for quantitative research studies due to their linear behavior. While iterative algorithms also benefit from the inclusion of accurate data and noise models the widespread use of TOF scanners with less sensitivity to noise and data imperfections make analytic algorithms even more promising. In our previous work we have developed a novel iterative reconstruction approach (Direct Image Reconstruction for TOF) providing convenient TOF data partitioning framework and leading to very efficient reconstructions. In this work we have expanded DIRECT to include an analytic TOF algorithm with confidence weighting incorporating models of both TOF and spatial resolution kernels. Feasibility studies using simulated and measured data demonstrate that analytic-DIRECT with appropriate resolution and regularization filters is able to provide matched bias vs. variance performance to iterative TOF reconstruction with a matched resolution model. PMID:27032968

Analytic TOF PET reconstruction algorithm within DIRECT data partitioning framework

NASA Astrophysics Data System (ADS)

Matej, Samuel; Daube-Witherspoon, Margaret E.; Karp, Joel S.

2016-05-01

Iterative reconstruction algorithms are routinely used for clinical practice; however, analytic algorithms are relevant candidates for quantitative research studies due to their linear behavior. While iterative algorithms also benefit from the inclusion of accurate data and noise models the widespread use of time-of-flight (TOF) scanners with less sensitivity to noise and data imperfections make analytic algorithms even more promising. In our previous work we have developed a novel iterative reconstruction approach (DIRECT: direct image reconstruction for TOF) providing convenient TOF data partitioning framework and leading to very efficient reconstructions. In this work we have expanded DIRECT to include an analytic TOF algorithm with confidence weighting incorporating models of both TOF and spatial resolution kernels. Feasibility studies using simulated and measured data demonstrate that analytic-DIRECT with appropriate resolution and regularization filters is able to provide matched bias versus variance performance to iterative TOF reconstruction with a matched resolution model.

Development of iterative techniques for the solution of unsteady compressible viscous flows

NASA Technical Reports Server (NTRS)

Sankar, Lakshmi N.; Hixon, Duane

1992-01-01

The development of efficient iterative solution methods for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations is discussed. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. In this work, another approach based on the classical conjugate gradient method, known as the Generalized Minimum Residual (GMRES) algorithm is investigated. The GMRES algorithm has been used in the past by a number of researchers for solving steady viscous and inviscid flow problems. Here, we investigate the suitability of this algorithm for solving the system of non-linear equations that arise in unsteady Navier-Stokes solvers at each time step.

Iterative channel decoding of FEC-based multiple-description codes.

PubMed

Chang, Seok-Ho; Cosman, Pamela C; Milstein, Laurence B

2012-03-01

Multiple description coding has been receiving attention as a robust transmission framework for multimedia services. This paper studies the iterative decoding of FEC-based multiple description codes. The proposed decoding algorithms take advantage of the error detection capability of Reed-Solomon (RS) erasure codes. The information of correctly decoded RS codewords is exploited to enhance the error correction capability of the Viterbi algorithm at the next iteration of decoding. In the proposed algorithm, an intradescription interleaver is synergistically combined with the iterative decoder. The interleaver does not affect the performance of noniterative decoding but greatly enhances the performance when the system is iteratively decoded. We also address the optimal allocation of RS parity symbols for unequal error protection. For the optimal allocation in iterative decoding, we derive mathematical equations from which the probability distributions of description erasures can be generated in a simple way. The performance of the algorithm is evaluated over an orthogonal frequency-division multiplexing system. The results show that the performance of the multiple description codes is significantly enhanced.

Shape-based diffeomorphic registration on hippocampal surfaces using Beltrami holomorphic flow.

PubMed

Lui, Lok Ming; Wong, Tsz Wai; Thompson, Paul; Chan, Tony; Gu, Xianfeng; Yau, Shing-Tung

2010-01-01

We develop a new algorithm to automatically register hippocampal (HP) surfaces with complete geometric matching, avoiding the need to manually label landmark features. A good registration depends on a reasonable choice of shape energy that measures the dissimilarity between surfaces. In our work, we first propose a complete shape index using the Beltrami coefficient and curvatures, which measures subtle local differences. The proposed shape energy is zero if and only if two shapes are identical up to a rigid motion. We then seek the best surface registration by minimizing the shape energy. We propose a simple representation of surface diffeomorphisms using Beltrami coefficients, which simplifies the optimization process. We then iteratively minimize the shape energy using the proposed Beltrami Holomorphic flow (BHF) method. Experimental results on 212 HP of normal and diseased (Alzheimer's disease) subjects show our proposed algorithm is effective in registering HP surfaces with complete geometric matching. The proposed shape energy can also capture local shape differences between HP for disease analysis.

Dual energy CT with one full scan and a second sparse-view scan using structure preserving iterative reconstruction (SPIR)

NASA Astrophysics Data System (ADS)

Wang, Tonghe; Zhu, Lei

2016-09-01

Conventional dual-energy CT (DECT) reconstruction requires two full-size projection datasets with two different energy spectra. In this study, we propose an iterative algorithm to enable a new data acquisition scheme which requires one full scan and a second sparse-view scan for potential reduction in imaging dose and engineering cost of DECT. A bilateral filter is calculated as a similarity matrix from the first full-scan CT image to quantify the similarity between any two pixels, which is assumed unchanged on a second CT image since DECT scans are performed on the same object. The second CT image from reduced projections is reconstructed by an iterative algorithm which updates the image by minimizing the total variation of the difference between the image and its filtered image by the similarity matrix under data fidelity constraint. As the redundant structural information of the two CT images is contained in the similarity matrix for CT reconstruction, we refer to the algorithm as structure preserving iterative reconstruction (SPIR). The proposed method is evaluated on both digital and physical phantoms, and is compared with the filtered-backprojection (FBP) method, the conventional total-variation-regularization-based algorithm (TVR) and prior-image-constrained-compressed-sensing (PICCS). SPIR with a second 10-view scan reduces the image noise STD by a factor of one order of magnitude with same spatial resolution as full-view FBP image. SPIR substantially improves over TVR on the reconstruction accuracy of a 10-view scan by decreasing the reconstruction error from 6.18% to 1.33%, and outperforms TVR at 50 and 20-view scans on spatial resolution with a higher frequency at the modulation transfer function value of 10% by an average factor of 4. Compared with the 20-view scan PICCS result, the SPIR image has 7 times lower noise STD with similar spatial resolution. The electron density map obtained from the SPIR-based DECT images with a second 10-view scan has an average error of less than 1%.

Compressive sensing of electrocardiogram signals by promoting sparsity on the second-order difference and by using dictionary learning.

PubMed

Pant, Jeevan K; Krishnan, Sridhar

2014-04-01

A new algorithm for the reconstruction of electrocardiogram (ECG) signals and a dictionary learning algorithm for the enhancement of its reconstruction performance for a class of signals are proposed. The signal reconstruction algorithm is based on minimizing the lp pseudo-norm of the second-order difference, called as the lp(2d) pseudo-norm, of the signal. The optimization involved is carried out using a sequential conjugate-gradient algorithm. The dictionary learning algorithm uses an iterative procedure wherein a signal reconstruction and a dictionary update steps are repeated until a convergence criterion is satisfied. The signal reconstruction step is implemented by using the proposed signal reconstruction algorithm and the dictionary update step is implemented by using the linear least-squares method. Extensive simulation results demonstrate that the proposed algorithm yields improved reconstruction performance for temporally correlated ECG signals relative to the state-of-the-art lp(1d)-regularized least-squares and Bayesian learning based algorithms. Also for a known class of signals, the reconstruction performance of the proposed algorithm can be improved by applying it in conjunction with a dictionary obtained using the proposed dictionary learning algorithm.

Fast l₁-SPIRiT compressed sensing parallel imaging MRI: scalable parallel implementation and clinically feasible runtime.

PubMed

Murphy, Mark; Alley, Marcus; Demmel, James; Keutzer, Kurt; Vasanawala, Shreyas; Lustig, Michael

2012-06-01

We present l₁-SPIRiT, a simple algorithm for auto calibrating parallel imaging (acPI) and compressed sensing (CS) that permits an efficient implementation with clinically-feasible runtimes. We propose a CS objective function that minimizes cross-channel joint sparsity in the wavelet domain. Our reconstruction minimizes this objective via iterative soft-thresholding, and integrates naturally with iterative self-consistent parallel imaging (SPIRiT). Like many iterative magnetic resonance imaging reconstructions, l₁-SPIRiT's image quality comes at a high computational cost. Excessively long runtimes are a barrier to the clinical use of any reconstruction approach, and thus we discuss our approach to efficiently parallelizing l₁-SPIRiT and to achieving clinically-feasible runtimes. We present parallelizations of l₁-SPIRiT for both multi-GPU systems and multi-core CPUs, and discuss the software optimization and parallelization decisions made in our implementation. The performance of these alternatives depends on the processor architecture, the size of the image matrix, and the number of parallel imaging channels. Fundamentally, achieving fast runtime requires the correct trade-off between cache usage and parallelization overheads. We demonstrate image quality via a case from our clinical experimentation, using a custom 3DFT spoiled gradient echo (SPGR) sequence with up to 8× acceleration via Poisson-disc undersampling in the two phase-encoded directions.

Fast ℓ1-SPIRiT Compressed Sensing Parallel Imaging MRI: Scalable Parallel Implementation and Clinically Feasible Runtime

PubMed Central

Murphy, Mark; Alley, Marcus; Demmel, James; Keutzer, Kurt; Vasanawala, Shreyas; Lustig, Michael

2012-01-01

We present ℓ1-SPIRiT, a simple algorithm for auto calibrating parallel imaging (acPI) and compressed sensing (CS) that permits an efficient implementation with clinically-feasible runtimes. We propose a CS objective function that minimizes cross-channel joint sparsity in the Wavelet domain. Our reconstruction minimizes this objective via iterative soft-thresholding, and integrates naturally with iterative Self-Consistent Parallel Imaging (SPIRiT). Like many iterative MRI reconstructions, ℓ1-SPIRiT’s image quality comes at a high computational cost. Excessively long runtimes are a barrier to the clinical use of any reconstruction approach, and thus we discuss our approach to efficiently parallelizing ℓ1-SPIRiT and to achieving clinically-feasible runtimes. We present parallelizations of ℓ1-SPIRiT for both multi-GPU systems and multi-core CPUs, and discuss the software optimization and parallelization decisions made in our implementation. The performance of these alternatives depends on the processor architecture, the size of the image matrix, and the number of parallel imaging channels. Fundamentally, achieving fast runtime requires the correct trade-off between cache usage and parallelization overheads. We demonstrate image quality via a case from our clinical experimentation, using a custom 3DFT Spoiled Gradient Echo (SPGR) sequence with up to 8× acceleration via poisson-disc undersampling in the two phase-encoded directions. PMID:22345529

Evaluation of the OSC-TV iterative reconstruction algorithm for cone-beam optical CT

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

Matenine, Dmitri, E-mail: dmitri.matenine.1@ulaval.ca; Mascolo-Fortin, Julia, E-mail: julia.mascolo-fortin.1@ulaval.ca; Goussard, Yves, E-mail: yves.goussard@polymtl.ca

Purpose: The present work evaluates an iterative reconstruction approach, namely, the ordered subsets convex (OSC) algorithm with regularization via total variation (TV) minimization in the field of cone-beam optical computed tomography (optical CT). One of the uses of optical CT is gel-based 3D dosimetry for radiation therapy, where it is employed to map dose distributions in radiosensitive gels. Model-based iterative reconstruction may improve optical CT image quality and contribute to a wider use of optical CT in clinical gel dosimetry. Methods: This algorithm was evaluated using experimental data acquired by a cone-beam optical CT system, as well as complementary numericalmore » simulations. A fast GPU implementation of OSC-TV was used to achieve reconstruction times comparable to those of conventional filtered backprojection. Images obtained via OSC-TV were compared with the corresponding filtered backprojections. Spatial resolution and uniformity phantoms were scanned and respective reconstructions were subject to evaluation of the modulation transfer function, image uniformity, and accuracy. The artifacts due to refraction and total signal loss from opaque objects were also studied. Results: The cone-beam optical CT data reconstructions showed that OSC-TV outperforms filtered backprojection in terms of image quality, thanks to a model-based simulation of the photon attenuation process. It was shown to significantly improve the image spatial resolution and reduce image noise. The accuracy of the estimation of linear attenuation coefficients remained similar to that obtained via filtered backprojection. Certain image artifacts due to opaque objects were reduced. Nevertheless, the common artifact due to the gel container walls could not be eliminated. Conclusions: The use of iterative reconstruction improves cone-beam optical CT image quality in many ways. The comparisons between OSC-TV and filtered backprojection presented in this paper demonstrate that OSC-TV can potentially improve the rendering of spatial features and reduce cone-beam optical CT artifacts.« less

Extending substructure based iterative solvers to multiple load and repeated analyses

NASA Technical Reports Server (NTRS)

Farhat, Charbel

1993-01-01

Direct solvers currently dominate commercial finite element structural software, but do not scale well in the fine granularity regime targeted by emerging parallel processors. Substructure based iterative solvers--often called also domain decomposition algorithms--lend themselves better to parallel processing, but must overcome several obstacles before earning their place in general purpose structural analysis programs. One such obstacle is the solution of systems with many or repeated right hand sides. Such systems arise, for example, in multiple load static analyses and in implicit linear dynamics computations. Direct solvers are well-suited for these problems because after the system matrix has been factored, the multiple or repeated solutions can be obtained through relatively inexpensive forward and backward substitutions. On the other hand, iterative solvers in general are ill-suited for these problems because they often must restart from scratch for every different right hand side. In this paper, we present a methodology for extending the range of applications of domain decomposition methods to problems with multiple or repeated right hand sides. Basically, we formulate the overall problem as a series of minimization problems over K-orthogonal and supplementary subspaces, and tailor the preconditioned conjugate gradient algorithm to solve them efficiently. The resulting solution method is scalable, whereas direct factorization schemes and forward and backward substitution algorithms are not. We illustrate the proposed methodology with the solution of static and dynamic structural problems, and highlight its potential to outperform forward and backward substitutions on parallel computers. As an example, we show that for a linear structural dynamics problem with 11640 degrees of freedom, every time-step beyond time-step 15 is solved in a single iteration and consumes 1.0 second on a 32 processor iPSC-860 system; for the same problem and the same parallel processor, a pair of forward/backward substitutions at each step consumes 15.0 seconds.

Evaluation of the OSC-TV iterative reconstruction algorithm for cone-beam optical CT.

PubMed

Matenine, Dmitri; Mascolo-Fortin, Julia; Goussard, Yves; Després, Philippe

2015-11-01

The present work evaluates an iterative reconstruction approach, namely, the ordered subsets convex (OSC) algorithm with regularization via total variation (TV) minimization in the field of cone-beam optical computed tomography (optical CT). One of the uses of optical CT is gel-based 3D dosimetry for radiation therapy, where it is employed to map dose distributions in radiosensitive gels. Model-based iterative reconstruction may improve optical CT image quality and contribute to a wider use of optical CT in clinical gel dosimetry. This algorithm was evaluated using experimental data acquired by a cone-beam optical CT system, as well as complementary numerical simulations. A fast GPU implementation of OSC-TV was used to achieve reconstruction times comparable to those of conventional filtered backprojection. Images obtained via OSC-TV were compared with the corresponding filtered backprojections. Spatial resolution and uniformity phantoms were scanned and respective reconstructions were subject to evaluation of the modulation transfer function, image uniformity, and accuracy. The artifacts due to refraction and total signal loss from opaque objects were also studied. The cone-beam optical CT data reconstructions showed that OSC-TV outperforms filtered backprojection in terms of image quality, thanks to a model-based simulation of the photon attenuation process. It was shown to significantly improve the image spatial resolution and reduce image noise. The accuracy of the estimation of linear attenuation coefficients remained similar to that obtained via filtered backprojection. Certain image artifacts due to opaque objects were reduced. Nevertheless, the common artifact due to the gel container walls could not be eliminated. The use of iterative reconstruction improves cone-beam optical CT image quality in many ways. The comparisons between OSC-TV and filtered backprojection presented in this paper demonstrate that OSC-TV can potentially improve the rendering of spatial features and reduce cone-beam optical CT artifacts.

Iterative load-balancing method with multigrid level relaxation for particle simulation with short-range interactions

NASA Astrophysics Data System (ADS)

Furuichi, Mikito; Nishiura, Daisuke

2017-10-01

We developed dynamic load-balancing algorithms for Particle Simulation Methods (PSM) involving short-range interactions, such as Smoothed Particle Hydrodynamics (SPH), Moving Particle Semi-implicit method (MPS), and Discrete Element method (DEM). These are needed to handle billions of particles modeled in large distributed-memory computer systems. Our method utilizes flexible orthogonal domain decomposition, allowing the sub-domain boundaries in the column to be different for each row. The imbalances in the execution time between parallel logical processes are treated as a nonlinear residual. Load-balancing is achieved by minimizing the residual within the framework of an iterative nonlinear solver, combined with a multigrid technique in the local smoother. Our iterative method is suitable for adjusting the sub-domain frequently by monitoring the performance of each computational process because it is computationally cheaper in terms of communication and memory costs than non-iterative methods. Numerical tests demonstrated the ability of our approach to handle workload imbalances arising from a non-uniform particle distribution, differences in particle types, or heterogeneous computer architecture which was difficult with previously proposed methods. We analyzed the parallel efficiency and scalability of our method using Earth simulator and K-computer supercomputer systems.

Blind motion image deblurring using nonconvex higher-order total variation model

NASA Astrophysics Data System (ADS)

Li, Weihong; Chen, Rui; Xu, Shangwen; Gong, Weiguo

2016-09-01

We propose a nonconvex higher-order total variation (TV) method for blind motion image deblurring. First, we introduce a nonconvex higher-order TV differential operator to define a new model of the blind motion image deblurring, which can effectively eliminate the staircase effect of the deblurred image; meanwhile, we employ an image sparse prior to improve the edge recovery quality. Second, to improve the accuracy of the estimated motion blur kernel, we use L1 norm and H1 norm as the blur kernel regularization term, considering the sparsity and smoothing of the motion blur kernel. Third, because it is difficult to solve the numerically computational complexity problem of the proposed model owing to the intrinsic nonconvexity, we propose a binary iterative strategy, which incorporates a reweighted minimization approximating scheme in the outer iteration, and a split Bregman algorithm in the inner iteration. And we also discuss the convergence of the proposed binary iterative strategy. Last, we conduct extensive experiments on both synthetic and real-world degraded images. The results demonstrate that the proposed method outperforms the previous representative methods in both quality of visual perception and quantitative measurement.

Minimizing Cache Misses Using Minimum-Surface Bodies

NASA Technical Reports Server (NTRS)

Frumkin, Michael; VanderWijngaart, Rob; Biegel, Bryan (Technical Monitor)

2002-01-01

A number of known techniques for improving cache performance in scientific computations involve the reordering of the iteration space. Some of these reorderings can be considered as coverings of the iteration space with the sets having good surface-to-volume ratio. Use of such sets reduces the number of cache misses in computations of local operators having the iteration space as a domain. First, we derive lower bounds which any algorithm must suffer while computing a local operator on a grid. Then we explore coverings of iteration spaces represented by structured and unstructured grids which allow us to approach these lower bounds. For structured grids we introduce a covering by successive minima tiles of the interference lattice of the grid. We show that the covering has low surface-to-volume ratio and present a computer experiment showing actual reduction of the cache misses achieved by using these tiles. For planar unstructured grids we show existence of a covering which reduces the number of cache misses to the level of structured grids. On the other hand, we present a triangulation of a 3-dimensional cube such that any local operator on the corresponding grid has significantly larger number of cache misses than a similar operator on a structured grid.

Sinogram-based adaptive iterative reconstruction for sparse view x-ray computed tomography

NASA Astrophysics Data System (ADS)

Trinca, D.; Zhong, Y.; Wang, Y.-Z.; Mamyrbayev, T.; Libin, E.

2016-10-01

With the availability of more powerful computing processors, iterative reconstruction algorithms have recently been successfully implemented as an approach to achieving significant dose reduction in X-ray CT. In this paper, we propose an adaptive iterative reconstruction algorithm for X-ray CT, that is shown to provide results comparable to those obtained by proprietary algorithms, both in terms of reconstruction accuracy and execution time. The proposed algorithm is thus provided for free to the scientific community, for regular use, and for possible further optimization.

Leapfrog variants of iterative methods for linear algebra equations

NASA Technical Reports Server (NTRS)

Saylor, Paul E.

1988-01-01

Two iterative methods are considered, Richardson's method and a general second order method. For both methods, a variant of the method is derived for which only even numbered iterates are computed. The variant is called a leapfrog method. Comparisons between the conventional form of the methods and the leapfrog form are made under the assumption that the number of unknowns is large. In the case of Richardson's method, it is possible to express the final iterate in terms of only the initial approximation, a variant of the iteration called the grand-leap method. In the case of the grand-leap variant, a set of parameters is required. An algorithm is presented to compute these parameters that is related to algorithms to compute the weights and abscissas for Gaussian quadrature. General algorithms to implement the leapfrog and grand-leap methods are presented. Algorithms for the important special case of the Chebyshev method are also given.

A Fast Implementation of the ISOCLUS Algorithm

NASA Technical Reports Server (NTRS)

Memarsadeghi, Nargess; Mount, David M.; Netanyahu, Nathan S.; LeMoigne, Jacqueline

2003-01-01

Unsupervised clustering is a fundamental building block in numerous image processing applications. One of the most popular and widely used clustering schemes for remote sensing applications is the ISOCLUS algorithm, which is based on the ISODATA method. The algorithm is given a set of n data points in d-dimensional space, an integer k indicating the initial number of clusters, and a number of additional parameters. The general goal is to compute the coordinates of a set of cluster centers in d-space, such that those centers minimize the mean squared distance from each data point to its nearest center. This clustering algorithm is similar to another well-known clustering method, called k-means. One significant feature of ISOCLUS over k-means is that the actual number of clusters reported might be fewer or more than the number supplied as part of the input. The algorithm uses different heuristics to determine whether to merge lor split clusters. As ISOCLUS can run very slowly, particularly on large data sets, there has been a growing .interest in the remote sensing community in computing it efficiently. We have developed a faster implementation of the ISOCLUS algorithm. Our improvement is based on a recent acceleration to the k-means algorithm of Kanungo, et al. They showed that, by using a kd-tree data structure for storing the data, it is possible to reduce the running time of k-means. We have adapted this method for the ISOCLUS algorithm, and we show that it is possible to achieve essentially the same results as ISOCLUS on large data sets, but with significantly lower running times. This adaptation involves computing a number of cluster statistics that are needed for ISOCLUS but not for k-means. Both the k-means and ISOCLUS algorithms are based on iterative schemes, in which nearest neighbors are calculated until some convergence criterion is satisfied. Each iteration requires that the nearest center for each data point be computed. Naively, this requires O(kn) time, where k denotes the current number of centers. Traditional techniques for accelerating nearest neighbor searching involve storing the k centers in a data structure. However, because of the iterative nature of the algorithm, this data structure would need to be rebuilt with each new iteration. Our approach is to store the data points in a kd-tree data structure. The assignment of points to nearest neighbors is carried out by a filtering process, which successively eliminates centers that can not possibly be the nearest neighbor for a given region of space. This algorithm is significantly faster, because large groups of data points can be assigned to their nearest center in a single operation. Preliminary results on a number of real Landsat datasets show that our revised ISOCLUS-like scheme runs about twice as fast.

Automatic treatment plan re-optimization for adaptive radiotherapy guided with the initial plan DVHs

NASA Astrophysics Data System (ADS)

Li, Nan; Zarepisheh, Masoud; Uribe-Sanchez, Andres; Moore, Kevin; Tian, Zhen; Zhen, Xin; Jiang Graves, Yan; Gautier, Quentin; Mell, Loren; Zhou, Linghong; Jia, Xun; Jiang, Steve

2013-12-01

Adaptive radiation therapy (ART) can reduce normal tissue toxicity and/or improve tumor control through treatment adaptations based on the current patient anatomy. Developing an efficient and effective re-planning algorithm is an important step toward the clinical realization of ART. For the re-planning process, manual trial-and-error approach to fine-tune planning parameters is time-consuming and is usually considered unpractical, especially for online ART. It is desirable to automate this step to yield a plan of acceptable quality with minimal interventions. In ART, prior information in the original plan is available, such as dose-volume histogram (DVH), which can be employed to facilitate the automatic re-planning process. The goal of this work is to develop an automatic re-planning algorithm to generate a plan with similar, or possibly better, DVH curves compared with the clinically delivered original plan. Specifically, our algorithm iterates the following two loops. An inner loop is the traditional fluence map optimization, in which we optimize a quadratic objective function penalizing the deviation of the dose received by each voxel from its prescribed or threshold dose with a set of fixed voxel weighting factors. In outer loop, the voxel weighting factors in the objective function are adjusted according to the deviation of the current DVH curves from those in the original plan. The process is repeated until the DVH curves are acceptable or maximum iteration step is reached. The whole algorithm is implemented on GPU for high efficiency. The feasibility of our algorithm has been demonstrated with three head-and-neck cancer IMRT cases, each having an initial planning CT scan and another treatment CT scan acquired in the middle of treatment course. Compared with the DVH curves in the original plan, the DVH curves in the resulting plan using our algorithm with 30 iterations are better for almost all structures. The re-optimization process takes about 30 s using our in-house optimization engine. This work was originally presented at the 54th AAPM annual meeting in Charlotte, NC, July 29-August 2, 2012.

Acceleration of convergence of vector sequences

NASA Technical Reports Server (NTRS)

Sidi, A.; Ford, W. F.; Smith, D. A.

1983-01-01

A general approach to the construction of convergence acceleration methods for vector sequence is proposed. Using this approach, one can generate some known methods, such as the minimal polynomial extrapolation, the reduced rank extrapolation, and the topological epsilon algorithm, and also some new ones. Some of the new methods are easier to implement than the known methods and are observed to have similar numerical properties. The convergence analysis of these new methods is carried out, and it is shown that they are especially suitable for accelerating the convergence of vector sequences that are obtained when one solves linear systems of equations iteratively. A stability analysis is also given, and numerical examples are provided. The convergence and stability properties of the topological epsilon algorithm are likewise given.

Network immunization under limited budget using graph spectra

NASA Astrophysics Data System (ADS)

Zahedi, R.; Khansari, M.

2016-03-01

In this paper, we propose a new algorithm that minimizes the worst expected growth of an epidemic by reducing the size of the largest connected component (LCC) of the underlying contact network. The proposed algorithm is applicable to any level of available resources and, despite the greedy approaches of most immunization strategies, selects nodes simultaneously. In each iteration, the proposed method partitions the LCC into two groups. These are the best candidates for communities in that component, and the available resources are sufficient to separate them. Using Laplacian spectral partitioning, the proposed method performs community detection inference with a time complexity that rivals that of the best previous methods. Experiments show that our method outperforms targeted immunization approaches in both real and synthetic networks.

Compartmentalized Low-Rank Recovery for High-Resolution Lipid Unsuppressed MRSI

PubMed Central

Bhattacharya, Ipshita; Jacob, Mathews

2017-01-01

Purpose To introduce a novel algorithm for the recovery of high-resolution magnetic resonance spectroscopic imaging (MRSI) data with minimal lipid leakage artifacts, from dual-density spiral acquisition. Methods The reconstruction of MRSI data from dual-density spiral data is formulated as a compartmental low-rank recovery problem. The MRSI dataset is modeled as the sum of metabolite and lipid signals, each of which is support limited to the brain and extracranial regions, respectively, in addition to being orthogonal to each other. The reconstruction problem is formulated as an optimization problem, which is solved using iterative reweighted nuclear norm minimization. Results The comparisons of the scheme against dual-resolution reconstruction algorithm on numerical phantom and in vivo datasets demonstrate the ability of the scheme to provide higher spatial resolution and lower lipid leakage artifacts. The experiments demonstrate the ability of the scheme to recover the metabolite maps, from lipid unsuppressed datasets with echo time (TE)=55 ms. Conclusion The proposed reconstruction method and data acquisition strategy provide an efficient way to achieve high-resolution metabolite maps without lipid suppression. This algorithm would be beneficial for fast metabolic mapping and extension to multislice acquisitions. PMID:27851875

Joint reconstruction of dynamic PET activity and kinetic parametric images using total variation constrained dictionary sparse coding

NASA Astrophysics Data System (ADS)

Yu, Haiqing; Chen, Shuhang; Chen, Yunmei; Liu, Huafeng

2017-05-01

Dynamic positron emission tomography (PET) is capable of providing both spatial and temporal information of radio tracers in vivo. In this paper, we present a novel joint estimation framework to reconstruct temporal sequences of dynamic PET images and the coefficients characterizing the system impulse response function, from which the associated parametric images of the system macro parameters for tracer kinetics can be estimated. The proposed algorithm, which combines statistical data measurement and tracer kinetic models, integrates a dictionary sparse coding (DSC) into a total variational minimization based algorithm for simultaneous reconstruction of the activity distribution and parametric map from measured emission sinograms. DSC, based on the compartmental theory, provides biologically meaningful regularization, and total variation regularization is incorporated to provide edge-preserving guidance. We rely on techniques from minimization algorithms (the alternating direction method of multipliers) to first generate the estimated activity distributions with sub-optimal kinetic parameter estimates, and then recover the parametric maps given these activity estimates. These coupled iterative steps are repeated as necessary until convergence. Experiments with synthetic, Monte Carlo generated data, and real patient data have been conducted, and the results are very promising.

JWST Wavefront Control Toolbox

NASA Technical Reports Server (NTRS)

Shin, Shahram Ron; Aronstein, David L.

2011-01-01

A Matlab-based toolbox has been developed for the wavefront control and optimization of segmented optical surfaces to correct for possible misalignments of James Webb Space Telescope (JWST) using influence functions. The toolbox employs both iterative and non-iterative methods to converge to an optimal solution by minimizing the cost function. The toolbox could be used in either of constrained and unconstrained optimizations. The control process involves 1 to 7 degrees-of-freedom perturbations per segment of primary mirror in addition to the 5 degrees of freedom of secondary mirror. The toolbox consists of a series of Matlab/Simulink functions and modules, developed based on a "wrapper" approach, that handles the interface and data flow between existing commercial optical modeling software packages such as Zemax and Code V. The limitations of the algorithm are dictated by the constraints of the moving parts in the mirrors.

Arterial cannula shape optimization by means of the rotational firefly algorithm

NASA Astrophysics Data System (ADS)

Tesch, K.; Kaczorowska, K.

2016-03-01

This article presents global optimization results of arterial cannula shapes by means of the newly modified firefly algorithm. The search for the optimal arterial cannula shape is necessary in order to minimize losses and prepare the flow that leaves the circulatory support system of a ventricle (i.e. blood pump) before it reaches the heart. A modification of the standard firefly algorithm, the so-called rotational firefly algorithm, is introduced. It is shown that the rotational firefly algorithm allows for better exploration of search spaces which results in faster convergence and better solutions in comparison with its standard version. This is particularly pronounced for smaller population sizes. Furthermore, it maintains greater diversity of populations for a longer time. A small population size and a low number of iterations are necessary to keep to a minimum the computational cost of the objective function of the problem, which comes from numerical solution of the nonlinear partial differential equations. Moreover, both versions of the firefly algorithm are compared to the state of the art, namely the differential evolution and covariance matrix adaptation evolution strategies.

A Least-Squares Commutator in the Iterative Subspace Method for Accelerating Self-Consistent Field Convergence.

PubMed

Li, Haichen; Yaron, David J

2016-11-08

A least-squares commutator in the iterative subspace (LCIIS) approach is explored for accelerating self-consistent field (SCF) calculations. LCIIS is similar to direct inversion of the iterative subspace (DIIS) methods in that the next iterate of the density matrix is obtained as a linear combination of past iterates. However, whereas DIIS methods find the linear combination by minimizing a sum of error vectors, LCIIS minimizes the Frobenius norm of the commutator between the density matrix and the Fock matrix. This minimization leads to a quartic problem that can be solved iteratively through a constrained Newton's method. The relationship between LCIIS and DIIS is discussed. Numerical experiments suggest that LCIIS leads to faster convergence than other SCF convergence accelerating methods in a statistically significant sense, and in a number of cases LCIIS leads to stable SCF solutions that are not found by other methods. The computational cost involved in solving the quartic minimization problem is small compared to the typical cost of SCF iterations and the approach is easily integrated into existing codes. LCIIS can therefore serve as a powerful addition to SCF convergence accelerating methods in computational quantum chemistry packages.

An iterative sinogram gap-filling method with object- and scanner-dedicated discrete cosine transform (DCT)-domain filters for high resolution PET scanners.

PubMed

Kim, Kwangdon; Lee, Kisung; Lee, Hakjae; Joo, Sungkwan; Kang, Jungwon

2018-01-01

We aimed to develop a gap-filling algorithm, in particular the filter mask design method of the algorithm, which optimizes the filter to the imaging object by an adaptive and iterative process, rather than by manual means. Two numerical phantoms (Shepp-Logan and Jaszczak) were used for sinogram generation. The algorithm works iteratively, not only on the gap-filling iteration but also on the mask generation, to identify the object-dedicated low frequency area in the DCT-domain that is to be preserved. We redefine the low frequency preserving region of the filter mask at every gap-filling iteration, and the region verges on the property of the original image in the DCT domain. The previous DCT2 mask for each phantom case had been manually well optimized, and the results show little difference from the reference image and sinogram. We observed little or no difference between the results of the manually optimized DCT2 algorithm and those of the proposed algorithm. The proposed algorithm works well for various types of scanning object and shows results that compare to those of the manually optimized DCT2 algorithm without perfect or full information of the imaging object.

GPU-based fast cone beam CT reconstruction from undersampled and noisy projection data via total variation.

PubMed

Jia, Xun; Lou, Yifei; Li, Ruijiang; Song, William Y; Jiang, Steve B

2010-04-01

Cone-beam CT (CBCT) plays an important role in image guided radiation therapy (IGRT). However, the large radiation dose from serial CBCT scans in most IGRT procedures raises a clinical concern, especially for pediatric patients who are essentially excluded from receiving IGRT for this reason. The goal of this work is to develop a fast GPU-based algorithm to reconstruct CBCT from undersampled and noisy projection data so as to lower the imaging dose. The CBCT is reconstructed by minimizing an energy functional consisting of a data fidelity term and a total variation regularization term. The authors developed a GPU-friendly version of the forward-backward splitting algorithm to solve this model. A multigrid technique is also employed. It is found that 20-40 x-ray projections are sufficient to reconstruct images with satisfactory quality for IGRT. The reconstruction time ranges from 77 to 130 s on an NVIDIA Tesla C1060 (NVIDIA, Santa Clara, CA) GPU card, depending on the number of projections used, which is estimated about 100 times faster than similar iterative reconstruction approaches. Moreover, phantom studies indicate that the algorithm enables the CBCT to be reconstructed under a scanning protocol with as low as 0.1 mA s/projection. Comparing with currently widely used full-fan head and neck scanning protocol of approximately 360 projections with 0.4 mA s/projection, it is estimated that an overall 36-72 times dose reduction has been achieved in our fast CBCT reconstruction algorithm. This work indicates that the developed GPU-based CBCT reconstruction algorithm is capable of lowering imaging dose considerably. The high computation efficiency in this algorithm makes the iterative CBCT reconstruction approach applicable in real clinical environments.

Separation of Undersampled Composite Signals Using the Dantzig Selector with Overcomplete Dictionaries

DTIC Science & Technology

2014-06-02

2011). [22] Li, Q., Micchelli, C., Shen, L., and Xu, Y. A proximity algorithm acelerated by Gauss - Seidel iterations for L1/TV denoising models. Inverse...system of equations and their relationship to the solution of Model (2) and present an algorithm with an iterative approach for finding these solutions...Using the fixed-point characterization above, the (k + 1)th iteration of the prox- imity operator algorithm to find the solution of the Dantzig

Error bounds of adaptive dynamic programming algorithms for solving undiscounted optimal control problems.

PubMed

Liu, Derong; Li, Hongliang; Wang, Ding

2015-06-01

In this paper, we establish error bounds of adaptive dynamic programming algorithms for solving undiscounted infinite-horizon optimal control problems of discrete-time deterministic nonlinear systems. We consider approximation errors in the update equations of both value function and control policy. We utilize a new assumption instead of the contraction assumption in discounted optimal control problems. We establish the error bounds for approximate value iteration based on a new error condition. Furthermore, we also establish the error bounds for approximate policy iteration and approximate optimistic policy iteration algorithms. It is shown that the iterative approximate value function can converge to a finite neighborhood of the optimal value function under some conditions. To implement the developed algorithms, critic and action neural networks are used to approximate the value function and control policy, respectively. Finally, a simulation example is given to demonstrate the effectiveness of the developed algorithms.

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

Partitioning Algorithms for Simultaneously Balancing Iterative and Direct Methods

DTIC Science & Technology

2004-03-03

is defined as 57698&:&;=<$>?8A@B8 DC E & /F <G8H IJ0 K L 012 1NM? which is the ratio of the highest partition weight over the average...OQPSR , 57698T:;=<$>U8T@B8 DC E & /VXWZYK[\\O , and E :^] E_CU`4ab /V is minimized. The load imbalance is the constraint we have to satisfy, and...that the initial partitioning can be improved [16, 19, 20]. 3 Problem Definition and Challenges Consider a graph )c2 with d e f vertices

Fast projection/backprojection and incremental methods applied to synchrotron light tomographic reconstruction.

PubMed

de Lima, Camila; Salomão Helou, Elias

2018-01-01

Iterative methods for tomographic image reconstruction have the computational cost of each iteration dominated by the computation of the (back)projection operator, which take roughly O(N 3 ) floating point operations (flops) for N × N pixels images. Furthermore, classical iterative algorithms may take too many iterations in order to achieve acceptable images, thereby making the use of these techniques unpractical for high-resolution images. Techniques have been developed in the literature in order to reduce the computational cost of the (back)projection operator to O(N 2 logN) flops. Also, incremental algorithms have been devised that reduce by an order of magnitude the number of iterations required to achieve acceptable images. The present paper introduces an incremental algorithm with a cost of O(N 2 logN) flops per iteration and applies it to the reconstruction of very large tomographic images obtained from synchrotron light illuminated data.

Angular filter refractometry analysis using simulated annealing [An improved method for characterizing plasma density profiles using angular filter refractometry

DOE PAGES

Angland, P.; Haberberger, D.; Ivancic, S. T.; ...

2017-10-30

Here, a new method of analysis for angular filter refractometry images was developed to characterize laser-produced, long-scale-length plasmas using an annealing algorithm to iterative converge upon a solution. Angular filter refractometry (AFR) is a novel technique used to characterize the density pro files of laser-produced, long-scale-length plasmas. A synthetic AFR image is constructed by a user-defined density profile described by eight parameters, and the algorithm systematically alters the parameters until the comparison is optimized. The optimization and statistical uncertainty calculation is based on a minimization of themore » $$\\chi$$2 test statistic. The algorithm was successfully applied to experimental data of plasma expanding from a flat, laser-irradiated target, resulting in average uncertainty in the density profile of 5-10% in the region of interest.« less

Angular filter refractometry analysis using simulated annealing [An improved method for characterizing plasma density profiles using angular filter refractometry

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

Angland, P.; Haberberger, D.; Ivancic, S. T.

Here, a new method of analysis for angular filter refractometry images was developed to characterize laser-produced, long-scale-length plasmas using an annealing algorithm to iterative converge upon a solution. Angular filter refractometry (AFR) is a novel technique used to characterize the density pro files of laser-produced, long-scale-length plasmas. A synthetic AFR image is constructed by a user-defined density profile described by eight parameters, and the algorithm systematically alters the parameters until the comparison is optimized. The optimization and statistical uncertainty calculation is based on a minimization of themore » $$\\chi$$2 test statistic. The algorithm was successfully applied to experimental data of plasma expanding from a flat, laser-irradiated target, resulting in average uncertainty in the density profile of 5-10% in the region of interest.« less

A novel algorithm for simplification of complex gene classifiers in cancer

PubMed Central

Wilson, Raphael A.; Teng, Ling; Bachmeyer, Karen M.; Bissonnette, Mei Lin Z.; Husain, Aliya N.; Parham, David M.; Triche, Timothy J.; Wing, Michele R.; Gastier-Foster, Julie M.; Barr, Frederic G.; Hawkins, Douglas S.; Anderson, James R.; Skapek, Stephen X.; Volchenboum, Samuel L.

2013-01-01

The clinical application of complex molecular classifiers as diagnostic or prognostic tools has been limited by the time and cost needed to apply them to patients. Using an existing fifty-gene expression signature known to separate two molecular subtypes of the pediatric cancer rhabdomyosarcoma, we show that an exhaustive iterative search algorithm can distill this complex classifier down to two or three features with equal discrimination. We validated the two-gene signatures using three separate and distinct data sets, including one that uses degraded RNA extracted from formalin-fixed, paraffin-embedded material. Finally, to demonstrate the generalizability of our algorithm, we applied it to a lung cancer data set to find minimal gene signatures that can distinguish survival. Our approach can easily be generalized and coupled to existing technical platforms to facilitate the discovery of simplified signatures that are ready for routine clinical use. PMID:23913937

General simulation algorithm for autocorrelated binary processes.

PubMed

Serinaldi, Francesco; Lombardo, Federico

2017-02-01

The apparent ubiquity of binary random processes in physics and many other fields has attracted considerable attention from the modeling community. However, generation of binary sequences with prescribed autocorrelation is a challenging task owing to the discrete nature of the marginal distributions, which makes the application of classical spectral techniques problematic. We show that such methods can effectively be used if we focus on the parent continuous process of beta distributed transition probabilities rather than on the target binary process. This change of paradigm results in a simulation procedure effectively embedding a spectrum-based iterative amplitude-adjusted Fourier transform method devised for continuous processes. The proposed algorithm is fully general, requires minimal assumptions, and can easily simulate binary signals with power-law and exponentially decaying autocorrelation functions corresponding, for instance, to Hurst-Kolmogorov and Markov processes. An application to rainfall intermittency shows that the proposed algorithm can also simulate surrogate data preserving the empirical autocorrelation.

A New Stochastic Technique for Painlevé Equation-I Using Neural Network Optimized with Swarm Intelligence

PubMed Central

Raja, Muhammad Asif Zahoor; Khan, Junaid Ali; Ahmad, Siraj-ul-Islam; Qureshi, Ijaz Mansoor

2012-01-01

A methodology for solution of Painlevé equation-I is presented using computational intelligence technique based on neural networks and particle swarm optimization hybridized with active set algorithm. The mathematical model of the equation is developed with the help of linear combination of feed-forward artificial neural networks that define the unsupervised error of the model. This error is minimized subject to the availability of appropriate weights of the networks. The learning of the weights is carried out using particle swarm optimization algorithm used as a tool for viable global search method, hybridized with active set algorithm for rapid local convergence. The accuracy, convergence rate, and computational complexity of the scheme are analyzed based on large number of independents runs and their comprehensive statistical analysis. The comparative studies of the results obtained are made with MATHEMATICA solutions, as well as, with variational iteration method and homotopy perturbation method. PMID:22919371

Application of the perturbation iteration method to boundary layer type problems.

PubMed

Pakdemirli, Mehmet

2016-01-01

The recently developed perturbation iteration method is applied to boundary layer type singular problems for the first time. As a preliminary work on the topic, the simplest algorithm of PIA(1,1) is employed in the calculations. Linear and nonlinear problems are solved to outline the basic ideas of the new solution technique. The inner and outer solutions are determined with the iteration algorithm and matched to construct a composite expansion valid within all parts of the domain. The solutions are contrasted with the available exact or numerical solutions. It is shown that the perturbation-iteration algorithm can be effectively used for solving boundary layer type problems.

Tomography by iterative convolution - Empirical study and application to interferometry

NASA Technical Reports Server (NTRS)

Vest, C. M.; Prikryl, I.

1984-01-01

An algorithm for computer tomography has been developed that is applicable to reconstruction from data having incomplete projections because an opaque object blocks some of the probing radiation as it passes through the object field. The algorithm is based on iteration between the object domain and the projection (Radon transform) domain. Reconstructions are computed during each iteration by the well-known convolution method. Although it is demonstrated that this algorithm does not converge, an empirically justified criterion for terminating the iteration when the most accurate estimate has been computed is presented. The algorithm has been studied by using it to reconstruct several different object fields with several different opaque regions. It also has been used to reconstruct aerodynamic density fields from interferometric data recorded in wind tunnel tests.

Superiorization with level control

NASA Astrophysics Data System (ADS)

Cegielski, Andrzej; Al-Musallam, Fadhel

2017-04-01

The convex feasibility problem is to find a common point of a finite family of closed convex subsets. In many applications one requires something more, namely finding a common point of closed convex subsets which minimizes a continuous convex function. The latter requirement leads to an application of the superiorization methodology which is actually settled between methods for convex feasibility problem and the convex constrained minimization. Inspired by the superiorization idea we introduce a method which sequentially applies a long-step algorithm for a sequence of convex feasibility problems; the method employs quasi-nonexpansive operators as well as subgradient projections with level control and does not require evaluation of the metric projection. We replace a perturbation of the iterations (applied in the superiorization methodology) by a perturbation of the current level in minimizing the objective function. We consider the method in the Euclidean space in order to guarantee the strong convergence, although the method is well defined in a Hilbert space.

A novel iterative scheme and its application to differential equations.

PubMed

Khan, Yasir; Naeem, F; Šmarda, Zdeněk

2014-01-01

The purpose of this paper is to employ an alternative approach to reconstruct the standard variational iteration algorithm II proposed by He, including Lagrange multiplier, and to give a simpler formulation of Adomian decomposition and modified Adomian decomposition method in terms of newly proposed variational iteration method-II (VIM). Through careful investigation of the earlier variational iteration algorithm and Adomian decomposition method, we find unnecessary calculations for Lagrange multiplier and also repeated calculations involved in each iteration, respectively. Several examples are given to verify the reliability and efficiency of the method.

A globally convergent Lagrange and barrier function iterative algorithm for the traveling salesman problem.

PubMed

Dang, C; Xu, L

2001-03-01

In this paper a globally convergent Lagrange and barrier function iterative algorithm is proposed for approximating a solution of the traveling salesman problem. The algorithm employs an entropy-type barrier function to deal with nonnegativity constraints and Lagrange multipliers to handle linear equality constraints, and attempts to produce a solution of high quality by generating a minimum point of a barrier problem for a sequence of descending values of the barrier parameter. For any given value of the barrier parameter, the algorithm searches for a minimum point of the barrier problem in a feasible descent direction, which has a desired property that the nonnegativity constraints are always satisfied automatically if the step length is a number between zero and one. At each iteration the feasible descent direction is found by updating Lagrange multipliers with a globally convergent iterative procedure. For any given value of the barrier parameter, the algorithm converges to a stationary point of the barrier problem without any condition on the objective function. Theoretical and numerical results show that the algorithm seems more effective and efficient than the softassign algorithm.

Parabolized Navier-Stokes Code for Computing Magneto-Hydrodynamic Flowfields

NASA Technical Reports Server (NTRS)

Mehta, Unmeel B. (Technical Monitor); Tannehill, J. C.

2003-01-01

This report consists of two published papers, 'Computation of Magnetohydrodynamic Flows Using an Iterative PNS Algorithm' and 'Numerical Simulation of Turbulent MHD Flows Using an Iterative PNS Algorithm'.

Line Thinning Algorithm

NASA Astrophysics Data System (ADS)

Feigin, G.; Ben-Yosef, N.

1983-10-01

A thinning algorithm, of the banana-peel type, is presented. In each iteration pixels are attacked from all directions (there are no sub-iterations), and the deletion criteria depend on the 24 nearest neighbours.

Automated flight path planning for virtual endoscopy.

PubMed

Paik, D S; Beaulieu, C F; Jeffrey, R B; Rubin, G D; Napel, S

1998-05-01

In this paper, a novel technique for rapid and automatic computation of flight paths for guiding virtual endoscopic exploration of three-dimensional medical images is described. While manually planning flight paths is a tedious and time consuming task, our algorithm is automated and fast. Our method for positioning the virtual camera is based on the medial axis transform but is much more computationally efficient. By iteratively correcting a path toward the medial axis, the necessity of evaluating simple point criteria during morphological thinning is eliminated. The virtual camera is also oriented in a stable viewing direction, avoiding sudden twists and turns. We tested our algorithm on volumetric data sets of eight colons, one aorta and one bronchial tree. The algorithm computed the flight paths in several minutes per volume on an inexpensive workstation with minimal computation time added for multiple paths through branching structures (10%-13% per extra path). The results of our algorithm are smooth, centralized paths that aid in the task of navigation in virtual endoscopic exploration of three-dimensional medical images.

Robust dynamic myocardial perfusion CT deconvolution using adaptive-weighted tensor total variation regularization

NASA Astrophysics Data System (ADS)

Gong, Changfei; Zeng, Dong; Bian, Zhaoying; Huang, Jing; Zhang, Xinyu; Zhang, Hua; Lu, Lijun; Feng, Qianjin; Liang, Zhengrong; Ma, Jianhua

2016-03-01

Dynamic myocardial perfusion computed tomography (MPCT) is a promising technique for diagnosis and risk stratification of coronary artery disease by assessing the myocardial perfusion hemodynamic maps (MPHM). Meanwhile, the repeated scanning of the same region results in a relatively large radiation dose to patients potentially. In this work, we present a robust MPCT deconvolution algorithm with adaptive-weighted tensor total variation regularization to estimate residue function accurately under the low-dose context, which is termed `MPD-AwTTV'. More specifically, the AwTTV regularization takes into account the anisotropic edge property of the MPCT images compared with the conventional total variation (TV) regularization, which can mitigate the drawbacks of TV regularization. Subsequently, an effective iterative algorithm was adopted to minimize the associative objective function. Experimental results on a modified XCAT phantom demonstrated that the present MPD-AwTTV algorithm outperforms and is superior to other existing deconvolution algorithms in terms of noise-induced artifacts suppression, edge details preservation and accurate MPHM estimation.

A physics-based algorithm for real-time simulation of electrosurgery procedures in minimally invasive surgery.

PubMed

Lu, Zhonghua; Arikatla, Venkata S; Han, Zhongqing; Allen, Brian F; De, Suvranu

2014-12-01

High-frequency electricity is used in the majority of surgical interventions. However, modern computer-based training and simulation systems rely on physically unrealistic models that fail to capture the interplay of the electrical, mechanical and thermal properties of biological tissue. We present a real-time and physically realistic simulation of electrosurgery by modelling the electrical, thermal and mechanical properties as three iteratively solved finite element models. To provide subfinite-element graphical rendering of vaporized tissue, a dual-mesh dynamic triangulation algorithm based on isotherms is proposed. The block compressed row storage (BCRS) structure is shown to be critical in allowing computationally efficient changes in the tissue topology due to vaporization. We have demonstrated our physics-based electrosurgery cutting algorithm through various examples. Our matrix manipulation algorithms designed for topology changes have shown low computational cost. Our simulator offers substantially greater physical fidelity compared to previous simulators that use simple geometry-based heat characterization. Copyright © 2013 John Wiley & Sons, Ltd.

Comparison between iterative wavefront control algorithm and direct gradient wavefront control algorithm for adaptive optics system

NASA Astrophysics Data System (ADS)

Cheng, Sheng-Yi; Liu, Wen-Jin; Chen, Shan-Qiu; Dong, Li-Zhi; Yang, Ping; Xu, Bing

2015-08-01

Among all kinds of wavefront control algorithms in adaptive optics systems, the direct gradient wavefront control algorithm is the most widespread and common method. This control algorithm obtains the actuator voltages directly from wavefront slopes through pre-measuring the relational matrix between deformable mirror actuators and Hartmann wavefront sensor with perfect real-time characteristic and stability. However, with increasing the number of sub-apertures in wavefront sensor and deformable mirror actuators of adaptive optics systems, the matrix operation in direct gradient algorithm takes too much time, which becomes a major factor influencing control effect of adaptive optics systems. In this paper we apply an iterative wavefront control algorithm to high-resolution adaptive optics systems, in which the voltages of each actuator are obtained through iteration arithmetic, which gains great advantage in calculation and storage. For AO system with thousands of actuators, the computational complexity estimate is about O(n2) ˜ O(n3) in direct gradient wavefront control algorithm, while the computational complexity estimate in iterative wavefront control algorithm is about O(n) ˜ (O(n)3/2), in which n is the number of actuators of AO system. And the more the numbers of sub-apertures and deformable mirror actuators, the more significant advantage the iterative wavefront control algorithm exhibits. Project supported by the National Key Scientific and Research Equipment Development Project of China (Grant No. ZDYZ2013-2), the National Natural Science Foundation of China (Grant No. 11173008), and the Sichuan Provincial Outstanding Youth Academic Technology Leaders Program, China (Grant No. 2012JQ0012).

Control algorithms for dynamic attenuators

PubMed Central

Hsieh, Scott S.; Pelc, Norbert J.

2014-01-01

Purpose: The authors describe algorithms to control dynamic attenuators in CT and compare their performance using simulated scans. Dynamic attenuators are prepatient beam shaping filters that modulate the distribution of x-ray fluence incident on the patient on a view-by-view basis. These attenuators can reduce dose while improving key image quality metrics such as peak or mean variance. In each view, the attenuator presents several degrees of freedom which may be individually adjusted. The total number of degrees of freedom across all views is very large, making many optimization techniques impractical. The authors develop a theory for optimally controlling these attenuators. Special attention is paid to a theoretically perfect attenuator which controls the fluence for each ray individually, but the authors also investigate and compare three other, practical attenuator designs which have been previously proposed: the piecewise-linear attenuator, the translating attenuator, and the double wedge attenuator. Methods: The authors pose and solve the optimization problems of minimizing the mean and peak variance subject to a fixed dose limit. For a perfect attenuator and mean variance minimization, this problem can be solved in simple, closed form. For other attenuator designs, the problem can be decomposed into separate problems for each view to greatly reduce the computational complexity. Peak variance minimization can be approximately solved using iterated, weighted mean variance (WMV) minimization. Also, the authors develop heuristics for the perfect and piecewise-linear attenuators which do not require a priori knowledge of the patient anatomy. The authors compare these control algorithms on different types of dynamic attenuators using simulated raw data from forward projected DICOM files of a thorax and an abdomen. Results: The translating and double wedge attenuators reduce dose by an average of 30% relative to current techniques (bowtie filter with tube current modulation) without increasing peak variance. The 15-element piecewise-linear dynamic attenuator reduces dose by an average of 42%, and the perfect attenuator reduces dose by an average of 50%. Improvements in peak variance are several times larger than improvements in mean variance. Heuristic control eliminates the need for a prescan. For the piecewise-linear attenuator, the cost of heuristic control is an increase in dose of 9%. The proposed iterated WMV minimization produces results that are within a few percent of the true solution. Conclusions: Dynamic attenuators show potential for significant dose reduction. A wide class of dynamic attenuators can be accurately controlled using the described methods. PMID:24877818

Iterative methods for mixed finite element equations

NASA Technical Reports Server (NTRS)

Nakazawa, S.; Nagtegaal, J. C.; Zienkiewicz, O. C.

1985-01-01

Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.

Iterative algorithms for large sparse linear systems on parallel computers

NASA Technical Reports Server (NTRS)

Adams, L. M.

1982-01-01

Algorithms for assembling in parallel the sparse system of linear equations that result from finite difference or finite element discretizations of elliptic partial differential equations, such as those that arise in structural engineering are developed. Parallel linear stationary iterative algorithms and parallel preconditioned conjugate gradient algorithms are developed for solving these systems. In addition, a model for comparing parallel algorithms on array architectures is developed and results of this model for the algorithms are given.

A Block Preconditioned Conjugate Gradient-type Iterative Solver for Linear Systems in Thermal Reservoir Simulation

NASA Astrophysics Data System (ADS)

Betté, Srinivas; Diaz, Julio C.; Jines, William R.; Steihaug, Trond

1986-11-01

A preconditioned residual-norm-reducing iterative solver is described. Based on a truncated form of the generalized-conjugate-gradient method for nonsymmetric systems of linear equations, the iterative scheme is very effective for linear systems generated in reservoir simulation of thermal oil recovery processes. As a consequence of employing an adaptive implicit finite-difference scheme to solve the model equations, the number of variables per cell-block varies dynamically over the grid. The data structure allows for 5- and 9-point operators in the areal model, 5-point in the cross-sectional model, and 7- and 11-point operators in the three-dimensional model. Block-diagonal-scaling of the linear system, done prior to iteration, is found to have a significant effect on the rate of convergence. Block-incomplete-LU-decomposition (BILU) and block-symmetric-Gauss-Seidel (BSGS) methods, which result in no fill-in, are used as preconditioning procedures. A full factorization is done on the well terms, and the cells are ordered in a manner which minimizes the fill-in in the well-column due to this factorization. The convergence criterion for the linear (inner) iteration is linked to that of the nonlinear (Newton) iteration, thereby enhancing the efficiency of the computation. The algorithm, with both BILU and BSGS preconditioners, is evaluated in the context of a variety of thermal simulation problems. The solver is robust and can be used with little or no user intervention.

Parallel conjugate gradient algorithms for manipulator dynamic simulation

NASA Technical Reports Server (NTRS)

Fijany, Amir; Scheld, Robert E.

1989-01-01

Parallel conjugate gradient algorithms for the computation of multibody dynamics are developed for the specialized case of a robot manipulator. For an n-dimensional positive-definite linear system, the Classical Conjugate Gradient (CCG) algorithms are guaranteed to converge in n iterations, each with a computation cost of O(n); this leads to a total computational cost of O(n sq) on a serial processor. A conjugate gradient algorithms is presented that provide greater efficiency using a preconditioner, which reduces the number of iterations required, and by exploiting parallelism, which reduces the cost of each iteration. Two Preconditioned Conjugate Gradient (PCG) algorithms are proposed which respectively use a diagonal and a tridiagonal matrix, composed of the diagonal and tridiagonal elements of the mass matrix, as preconditioners. Parallel algorithms are developed to compute the preconditioners and their inversions in O(log sub 2 n) steps using n processors. A parallel algorithm is also presented which, on the same architecture, achieves the computational time of O(log sub 2 n) for each iteration. Simulation results for a seven degree-of-freedom manipulator are presented. Variants of the proposed algorithms are also developed which can be efficiently implemented on the Robot Mathematics Processor (RMP).

Wavelet-based edge correlation incorporated iterative reconstruction for undersampled MRI.

PubMed

Hu, Changwei; Qu, Xiaobo; Guo, Di; Bao, Lijun; Chen, Zhong

2011-09-01

Undersampling k-space is an effective way to decrease acquisition time for MRI. However, aliasing artifacts introduced by undersampling may blur the edges of magnetic resonance images, which often contain important information for clinical diagnosis. Moreover, k-space data is often contaminated by the noise signals of unknown intensity. To better preserve the edge features while suppressing the aliasing artifacts and noises, we present a new wavelet-based algorithm for undersampled MRI reconstruction. The algorithm solves the image reconstruction as a standard optimization problem including a ℓ(2) data fidelity term and ℓ(1) sparsity regularization term. Rather than manually setting the regularization parameter for the ℓ(1) term, which is directly related to the threshold, an automatic estimated threshold adaptive to noise intensity is introduced in our proposed algorithm. In addition, a prior matrix based on edge correlation in wavelet domain is incorporated into the regularization term. Compared with nonlinear conjugate gradient descent algorithm, iterative shrinkage/thresholding algorithm, fast iterative soft-thresholding algorithm and the iterative thresholding algorithm using exponentially decreasing threshold, the proposed algorithm yields reconstructions with better edge recovery and noise suppression. Copyright © 2011 Elsevier Inc. All rights reserved.

Survey on the Performance of Source Localization Algorithms.

PubMed

Fresno, José Manuel; Robles, Guillermo; Martínez-Tarifa, Juan Manuel; Stewart, Brian G

2017-11-18

The localization of emitters using an array of sensors or antennas is a prevalent issue approached in several applications. There exist different techniques for source localization, which can be classified into multilateration, received signal strength (RSS) and proximity methods. The performance of multilateration techniques relies on measured time variables: the time of flight (ToF) of the emission from the emitter to the sensor, the time differences of arrival (TDoA) of the emission between sensors and the pseudo-time of flight (pToF) of the emission to the sensors. The multilateration algorithms presented and compared in this paper can be classified as iterative and non-iterative methods. Both standard least squares (SLS) and hyperbolic least squares (HLS) are iterative and based on the Newton-Raphson technique to solve the non-linear equation system. The metaheuristic technique particle swarm optimization (PSO) used for source localisation is also studied. This optimization technique estimates the source position as the optimum of an objective function based on HLS and is also iterative in nature. Three non-iterative algorithms, namely the hyperbolic positioning algorithms (HPA), the maximum likelihood estimator (MLE) and Bancroft algorithm, are also presented. A non-iterative combined algorithm, MLE-HLS, based on MLE and HLS, is further proposed in this paper. The performance of all algorithms is analysed and compared in terms of accuracy in the localization of the position of the emitter and in terms of computational time. The analysis is also undertaken with three different sensor layouts since the positions of the sensors affect the localization; several source positions are also evaluated to make the comparison more robust. The analysis is carried out using theoretical time differences, as well as including errors due to the effect of digital sampling of the time variables. It is shown that the most balanced algorithm, yielding better results than the other algorithms in terms of accuracy and short computational time, is the combined MLE-HLS algorithm.

Survey on the Performance of Source Localization Algorithms

PubMed Central

2017-01-01

The localization of emitters using an array of sensors or antennas is a prevalent issue approached in several applications. There exist different techniques for source localization, which can be classified into multilateration, received signal strength (RSS) and proximity methods. The performance of multilateration techniques relies on measured time variables: the time of flight (ToF) of the emission from the emitter to the sensor, the time differences of arrival (TDoA) of the emission between sensors and the pseudo-time of flight (pToF) of the emission to the sensors. The multilateration algorithms presented and compared in this paper can be classified as iterative and non-iterative methods. Both standard least squares (SLS) and hyperbolic least squares (HLS) are iterative and based on the Newton–Raphson technique to solve the non-linear equation system. The metaheuristic technique particle swarm optimization (PSO) used for source localisation is also studied. This optimization technique estimates the source position as the optimum of an objective function based on HLS and is also iterative in nature. Three non-iterative algorithms, namely the hyperbolic positioning algorithms (HPA), the maximum likelihood estimator (MLE) and Bancroft algorithm, are also presented. A non-iterative combined algorithm, MLE-HLS, based on MLE and HLS, is further proposed in this paper. The performance of all algorithms is analysed and compared in terms of accuracy in the localization of the position of the emitter and in terms of computational time. The analysis is also undertaken with three different sensor layouts since the positions of the sensors affect the localization; several source positions are also evaluated to make the comparison more robust. The analysis is carried out using theoretical time differences, as well as including errors due to the effect of digital sampling of the time variables. It is shown that the most balanced algorithm, yielding better results than the other algorithms in terms of accuracy and short computational time, is the combined MLE-HLS algorithm. PMID:29156565

Quantitative phase and amplitude imaging using Differential-Interference Contrast (DIC) microscopy

NASA Astrophysics Data System (ADS)

Preza, Chrysanthe; O'Sullivan, Joseph A.

2009-02-01

We present an extension of the development of an alternating minimization (AM) method for the computation of a specimen's complex transmittance function (magnitude and phase) from DIC images. The ability to extract both quantitative phase and amplitude information from two rotationally-diverse DIC images (i.e., acquired by rotating the sample) extends previous efforts in computational DIC microscopy that have focused on quantitative phase imaging only. Simulation results show that the inverse problem at hand is sensitive to noise as well as to the choice of the AM algorithm parameters. The AM framework allows constraints and penalties on the magnitude and phase estimates to be incorporated in a principled manner. Towards this end, Green and De Pierro's "log-cosh" regularization penalty is applied to the magnitude of differences of neighboring values of the complex-valued function of the specimen during the AM iterations. The penalty is shown to be convex in the complex space. A procedure to approximate the penalty within the iterations is presented. In addition, a methodology to pre-compute AM parameters that are optimal with respect to the convergence rate of the AM algorithm is also presented. Both extensions of the AM method are investigated with simulations.

Fast divide-and-conquer algorithm for evaluating polarization in classical force fields

NASA Astrophysics Data System (ADS)

Nocito, Dominique; Beran, Gregory J. O.

2017-03-01

Evaluation of the self-consistent polarization energy forms a major computational bottleneck in polarizable force fields. In large systems, the linear polarization equations are typically solved iteratively with techniques based on Jacobi iterations (JI) or preconditioned conjugate gradients (PCG). Two new variants of JI are proposed here that exploit domain decomposition to accelerate the convergence of the induced dipoles. The first, divide-and-conquer JI (DC-JI), is a block Jacobi algorithm which solves the polarization equations within non-overlapping sub-clusters of atoms directly via Cholesky decomposition, and iterates to capture interactions between sub-clusters. The second, fuzzy DC-JI, achieves further acceleration by employing overlapping blocks. Fuzzy DC-JI is analogous to an additive Schwarz method, but with distance-based weighting when averaging the fuzzy dipoles from different blocks. Key to the success of these algorithms is the use of K-means clustering to identify natural atomic sub-clusters automatically for both algorithms and to determine the appropriate weights in fuzzy DC-JI. The algorithm employs knowledge of the 3-D spatial interactions to group important elements in the 2-D polarization matrix. When coupled with direct inversion in the iterative subspace (DIIS) extrapolation, fuzzy DC-JI/DIIS in particular converges in a comparable number of iterations as PCG, but with lower computational cost per iteration. In the end, the new algorithms demonstrated here accelerate the evaluation of the polarization energy by 2-3 fold compared to existing implementations of PCG or JI/DIIS.

Improved Savitzky-Golay-method-based fluorescence subtraction algorithm for rapid recovery of Raman spectra.

PubMed

Chen, Kun; Zhang, Hongyuan; Wei, Haoyun; Li, Yan

2014-08-20

In this paper, we propose an improved subtraction algorithm for rapid recovery of Raman spectra that can substantially reduce the computation time. This algorithm is based on an improved Savitzky-Golay (SG) iterative smoothing method, which involves two key novel approaches: (a) the use of the Gauss-Seidel method and (b) the introduction of a relaxation factor into the iterative procedure. By applying a novel successive relaxation (SG-SR) iterative method to the relaxation factor, additional improvement in the convergence speed over the standard Savitzky-Golay procedure is realized. The proposed improved algorithm (the RIA-SG-SR algorithm), which uses SG-SR-based iteration instead of Savitzky-Golay iteration, has been optimized and validated with a mathematically simulated Raman spectrum, as well as experimentally measured Raman spectra from non-biological and biological samples. The method results in a significant reduction in computing cost while yielding consistent rejection of fluorescence and noise for spectra with low signal-to-fluorescence ratios and varied baselines. In the simulation, RIA-SG-SR achieved 1 order of magnitude improvement in iteration number and 2 orders of magnitude improvement in computation time compared with the range-independent background-subtraction algorithm (RIA). Furthermore the computation time of the experimentally measured raw Raman spectrum processing from skin tissue decreased from 6.72 to 0.094 s. In general, the processing of the SG-SR method can be conducted within dozens of milliseconds, which can provide a real-time procedure in practical situations.

Metal implants on CT: comparison of iterative reconstruction algorithms for reduction of metal artifacts with single energy and spectral CT scanning in a phantom model.

PubMed

Fang, Jieming; Zhang, Da; Wilcox, Carol; Heidinger, Benedikt; Raptopoulos, Vassilios; Brook, Alexander; Brook, Olga R

2017-03-01

To assess single energy metal artifact reduction (SEMAR) and spectral energy metal artifact reduction (MARS) algorithms in reducing artifacts generated by different metal implants. Phantom was scanned with and without SEMAR (Aquilion One, Toshiba) and MARS (Discovery CT750 HD, GE), with various metal implants. Images were evaluated objectively by measuring standard deviation in regions of interests and subjectively by two independent reviewers grading on a scale of 0 (no artifact) to 4 (severe artifact). Reviewers also graded new artifacts introduced by metal artifact reduction algorithms. SEMAR and MARS significantly decreased variability of the density measurement adjacent to the metal implant, with median SD (standard deviation of density measurement) of 52.1 HU without SEMAR, vs. 12.3 HU with SEMAR, p < 0.001. Median SD without MARS of 63.1 HU decreased to 25.9 HU with MARS, p < 0.001. Median SD with SEMAR is significantly lower than median SD with MARS (p = 0.0011). SEMAR improved subjective image quality with reduction in overall artifacts grading from 3.2 ± 0.7 to 1.4 ± 0.9, p < 0.001. Improvement of overall image quality by MARS has not reached statistical significance (3.2 ± 0.6 to 2.6 ± 0.8, p = 0.088). There was a significant introduction of artifacts introduced by metal artifact reduction algorithm for MARS with 2.4 ± 1.0, but minimal with SEMAR 0.4 ± 0.7, p < 0.001. CT iterative reconstruction algorithms with single and spectral energy are both effective in reduction of metal artifacts. Single energy-based algorithm provides better overall image quality than spectral CT-based algorithm. Spectral metal artifact reduction algorithm introduces mild to moderate artifacts in the far field.

Combined iterative reconstruction and image-domain decomposition for dual energy CT using total-variation regularization

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

Dong, Xue; Niu, Tianye; Zhu, Lei, E-mail: leizhu@gatech.edu

2014-05-15

Purpose: Dual-energy CT (DECT) is being increasingly used for its capability of material decomposition and energy-selective imaging. A generic problem of DECT, however, is that the decomposition process is unstable in the sense that the relative magnitude of decomposed signals is reduced due to signal cancellation while the image noise is accumulating from the two CT images of independent scans. Direct image decomposition, therefore, leads to severe degradation of signal-to-noise ratio on the resultant images. Existing noise suppression techniques are typically implemented in DECT with the procedures of reconstruction and decomposition performed independently, which do not explore the statistical propertiesmore » of decomposed images during the reconstruction for noise reduction. In this work, the authors propose an iterative approach that combines the reconstruction and the signal decomposition procedures to minimize the DECT image noise without noticeable loss of resolution. Methods: The proposed algorithm is formulated as an optimization problem, which balances the data fidelity and total variation of decomposed images in one framework, and the decomposition step is carried out iteratively together with reconstruction. The noise in the CT images from the proposed algorithm becomes well correlated even though the noise of the raw projections is independent on the two CT scans. Due to this feature, the proposed algorithm avoids noise accumulation during the decomposition process. The authors evaluate the method performance on noise suppression and spatial resolution using phantom studies and compare the algorithm with conventional denoising approaches as well as combined iterative reconstruction methods with different forms of regularization. Results: On the Catphan©600 phantom, the proposed method outperforms the existing denoising methods on preserving spatial resolution at the same level of noise suppression, i.e., a reduction of noise standard deviation by one order of magnitude. This improvement is mainly attributed to the high noise correlation in the CT images reconstructed by the proposed algorithm. Iterative reconstruction using different regularization, including quadratic orq-generalized Gaussian Markov random field regularization, achieves similar noise suppression from high noise correlation. However, the proposed TV regularization obtains a better edge preserving performance. Studies of electron density measurement also show that our method reduces the average estimation error from 9.5% to 7.1%. On the anthropomorphic head phantom, the proposed method suppresses the noise standard deviation of the decomposed images by a factor of ∼14 without blurring the fine structures in the sinus area. Conclusions: The authors propose a practical method for DECT imaging reconstruction, which combines the image reconstruction and material decomposition into one optimization framework. Compared to the existing approaches, our method achieves a superior performance on DECT imaging with respect to decomposition accuracy, noise reduction, and spatial resolution.« less

Validation of an improved 'diffeomorphic demons' algorithm for deformable image registration in image-guided radiation therapy.

PubMed

Zhou, Lu; Zhou, Linghong; Zhang, Shuxu; Zhen, Xin; Yu, Hui; Zhang, Guoqian; Wang, Ruihao

2014-01-01

Deformable image registration (DIR) was widely used in radiation therapy, such as in automatic contour generation, dose accumulation, tumor growth or regression analysis. To achieve higher registration accuracy and faster convergence, an improved 'diffeomorphic demons' registration algorithm was proposed and validated. Based on Brox et al.'s gradient constancy assumption and Malis's efficient second-order minimization (ESM) algorithm, a grey value gradient similarity term and a transformation error term were added into the demons energy function, and a formula was derived to calculate the update of transformation field. The limited Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm was used to optimize the energy function so that the iteration number could be determined automatically. The proposed algorithm was validated using mathematically deformed images and physically deformed phantom images. Compared with the original 'diffeomorphic demons' algorithm, the registration method proposed achieve a higher precision and a faster convergence speed. Due to the influence of different scanning conditions in fractionated radiation, the density range of the treatment image and the planning image may be different. In such a case, the improved demons algorithm can achieve faster and more accurate radiotherapy.

Evaluation of Dynamic Channel and Power Assignment for Cognitive Networks

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

Syed A. Ahmad; Umesh Shukla; Ryan E. Irwin

2011-03-01

In this paper, we develop a unifying optimization formulation to describe the Dynamic Channel and Power Assignment (DCPA) problem and evaluation method for comparing DCPA algorithms. DCPA refers to the allocation of transmit power and frequency channels to links in a cognitive network so as to maximize the total number of feasible links while minimizing the aggregate transmit power. We apply our evaluation method to five algorithms representative of DCPA used in literature. This comparison illustrates the tradeoffs between control modes (centralized versus distributed) and channel/power assignment techniques. We estimate the complexity of each algorithm. Through simulations, we evaluate themore » effectiveness of the algorithms in achieving feasible link allocations in the network, as well as their power efficiency. Our results indicate that, when few channels are available, the effectiveness of all algorithms is comparable and thus the one with smallest complexity should be selected. The Least Interfering Channel and Iterative Power Assignment (LICIPA) algorithm does not require cross-link gain information, has the overall lowest run time, and highest feasibility ratio of all the distributed algorithms; however, this comes at a cost of higher average power per link.« less

Utilizing the Iterative Closest Point (ICP) algorithm for enhanced registration of high resolution surface models - more than a simple black-box application

NASA Astrophysics Data System (ADS)

Stöcker, Claudia; Eltner, Anette

2016-04-01

Advances in computer vision and digital photogrammetry (i.e. structure from motion) allow for fast and flexible high resolution data supply. Within geoscience applications and especially in the field of small surface topography, high resolution digital terrain models and dense 3D point clouds are valuable data sources to capture actual states as well as for multi-temporal studies. However, there are still some limitations regarding robust registration and accuracy demands (e.g. systematic positional errors) which impede the comparison and/or combination of multi-sensor data products. Therefore, post-processing of 3D point clouds can heavily enhance data quality. In this matter the Iterative Closest Point (ICP) algorithm represents an alignment tool which iteratively minimizes distances of corresponding points within two datasets. Even though tool is widely used; it is often applied as a black-box application within 3D data post-processing for surface reconstruction. Aiming for precise and accurate combination of multi-sensor data sets, this study looks closely at different variants of the ICP algorithm including sub-steps of point selection, point matching, weighting, rejection, error metric and minimization. Therefore, an agricultural utilized field was investigated simultaneously by terrestrial laser scanning (TLS) and unmanned aerial vehicle (UAV) sensors two times (once covered with sparse vegetation and once bare soil). Due to different perspectives both data sets show diverse consistency in terms of shadowed areas and thus gaps so that data merging would provide consistent surface reconstruction. Although photogrammetric processing already included sub-cm accurate ground control surveys, UAV point cloud exhibits an offset towards TLS point cloud. In order to achieve the transformation matrix for fine registration of UAV point clouds, different ICP variants were tested. Statistical analyses of the results show that final success of registration and therefore data quality depends particularly on parameterization and choice of error metric, especially for erroneous data sets as in the case of sparse vegetation cover. At this, the point-to-point metric is more sensitive to data "noise" than the point-to-plane metric which results in considerably higher cloud-to-cloud distances. Concluding, in order to comply with accuracy demands of high resolution surface reconstruction and the aspect that ground control surveys can reach their limits both in time exposure and terrain accessibility ICP algorithm represents a great tool to refine rough initial alignment. Here different variants of registration modules allow for individual application according to the quality of the input data.

A hybrid genetic algorithm for solving bi-objective traveling salesman problems

NASA Astrophysics Data System (ADS)

Ma, Mei; Li, Hecheng

2017-08-01

The traveling salesman problem (TSP) is a typical combinatorial optimization problem, in a traditional TSP only tour distance is taken as a unique objective to be minimized. When more than one optimization objective arises, the problem is known as a multi-objective TSP. In the present paper, a bi-objective traveling salesman problem (BOTSP) is taken into account, where both the distance and the cost are taken as optimization objectives. In order to efficiently solve the problem, a hybrid genetic algorithm is proposed. Firstly, two satisfaction degree indices are provided for each edge by considering the influences of the distance and the cost weight. The first satisfaction degree is used to select edges in a “rough” way, while the second satisfaction degree is executed for a more “refined” choice. Secondly, two satisfaction degrees are also applied to generate new individuals in the iteration process. Finally, based on genetic algorithm framework as well as 2-opt selection strategy, a hybrid genetic algorithm is proposed. The simulation illustrates the efficiency of the proposed algorithm.

Accelerated fast iterative shrinkage thresholding algorithms for sparsity-regularized cone-beam CT image reconstruction

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

Xu, Qiaofeng; Sawatzky, Alex; Anastasio, Mark A., E-mail: anastasio@wustl.edu

Purpose: The development of iterative image reconstruction algorithms for cone-beam computed tomography (CBCT) remains an active and important research area. Even with hardware acceleration, the overwhelming majority of the available 3D iterative algorithms that implement nonsmooth regularizers remain computationally burdensome and have not been translated for routine use in time-sensitive applications such as image-guided radiation therapy (IGRT). In this work, two variants of the fast iterative shrinkage thresholding algorithm (FISTA) are proposed and investigated for accelerated iterative image reconstruction in CBCT. Methods: Algorithm acceleration was achieved by replacing the original gradient-descent step in the FISTAs by a subproblem that ismore » solved by use of the ordered subset simultaneous algebraic reconstruction technique (OS-SART). Due to the preconditioning matrix adopted in the OS-SART method, two new weighted proximal problems were introduced and corresponding fast gradient projection-type algorithms were developed for solving them. We also provided efficient numerical implementations of the proposed algorithms that exploit the massive data parallelism of multiple graphics processing units. Results: The improved rates of convergence of the proposed algorithms were quantified in computer-simulation studies and by use of clinical projection data corresponding to an IGRT study. The accelerated FISTAs were shown to possess dramatically improved convergence properties as compared to the standard FISTAs. For example, the number of iterations to achieve a specified reconstruction error could be reduced by an order of magnitude. Volumetric images reconstructed from clinical data were produced in under 4 min. Conclusions: The FISTA achieves a quadratic convergence rate and can therefore potentially reduce the number of iterations required to produce an image of a specified image quality as compared to first-order methods. We have proposed and investigated accelerated FISTAs for use with two nonsmooth penalty functions that will lead to further reductions in image reconstruction times while preserving image quality. Moreover, with the help of a mixed sparsity-regularization, better preservation of soft-tissue structures can be potentially obtained. The algorithms were systematically evaluated by use of computer-simulated and clinical data sets.« less

Accelerated fast iterative shrinkage thresholding algorithms for sparsity-regularized cone-beam CT image reconstruction.

PubMed

Xu, Qiaofeng; Yang, Deshan; Tan, Jun; Sawatzky, Alex; Anastasio, Mark A

2016-04-01

The development of iterative image reconstruction algorithms for cone-beam computed tomography (CBCT) remains an active and important research area. Even with hardware acceleration, the overwhelming majority of the available 3D iterative algorithms that implement nonsmooth regularizers remain computationally burdensome and have not been translated for routine use in time-sensitive applications such as image-guided radiation therapy (IGRT). In this work, two variants of the fast iterative shrinkage thresholding algorithm (FISTA) are proposed and investigated for accelerated iterative image reconstruction in CBCT. Algorithm acceleration was achieved by replacing the original gradient-descent step in the FISTAs by a subproblem that is solved by use of the ordered subset simultaneous algebraic reconstruction technique (OS-SART). Due to the preconditioning matrix adopted in the OS-SART method, two new weighted proximal problems were introduced and corresponding fast gradient projection-type algorithms were developed for solving them. We also provided efficient numerical implementations of the proposed algorithms that exploit the massive data parallelism of multiple graphics processing units. The improved rates of convergence of the proposed algorithms were quantified in computer-simulation studies and by use of clinical projection data corresponding to an IGRT study. The accelerated FISTAs were shown to possess dramatically improved convergence properties as compared to the standard FISTAs. For example, the number of iterations to achieve a specified reconstruction error could be reduced by an order of magnitude. Volumetric images reconstructed from clinical data were produced in under 4 min. The FISTA achieves a quadratic convergence rate and can therefore potentially reduce the number of iterations required to produce an image of a specified image quality as compared to first-order methods. We have proposed and investigated accelerated FISTAs for use with two nonsmooth penalty functions that will lead to further reductions in image reconstruction times while preserving image quality. Moreover, with the help of a mixed sparsity-regularization, better preservation of soft-tissue structures can be potentially obtained. The algorithms were systematically evaluated by use of computer-simulated and clinical data sets.

Accelerated fast iterative shrinkage thresholding algorithms for sparsity-regularized cone-beam CT image reconstruction

PubMed Central

Xu, Qiaofeng; Yang, Deshan; Tan, Jun; Sawatzky, Alex; Anastasio, Mark A.

2016-01-01

Purpose: The development of iterative image reconstruction algorithms for cone-beam computed tomography (CBCT) remains an active and important research area. Even with hardware acceleration, the overwhelming majority of the available 3D iterative algorithms that implement nonsmooth regularizers remain computationally burdensome and have not been translated for routine use in time-sensitive applications such as image-guided radiation therapy (IGRT). In this work, two variants of the fast iterative shrinkage thresholding algorithm (FISTA) are proposed and investigated for accelerated iterative image reconstruction in CBCT. Methods: Algorithm acceleration was achieved by replacing the original gradient-descent step in the FISTAs by a subproblem that is solved by use of the ordered subset simultaneous algebraic reconstruction technique (OS-SART). Due to the preconditioning matrix adopted in the OS-SART method, two new weighted proximal problems were introduced and corresponding fast gradient projection-type algorithms were developed for solving them. We also provided efficient numerical implementations of the proposed algorithms that exploit the massive data parallelism of multiple graphics processing units. Results: The improved rates of convergence of the proposed algorithms were quantified in computer-simulation studies and by use of clinical projection data corresponding to an IGRT study. The accelerated FISTAs were shown to possess dramatically improved convergence properties as compared to the standard FISTAs. For example, the number of iterations to achieve a specified reconstruction error could be reduced by an order of magnitude. Volumetric images reconstructed from clinical data were produced in under 4 min. Conclusions: The FISTA achieves a quadratic convergence rate and can therefore potentially reduce the number of iterations required to produce an image of a specified image quality as compared to first-order methods. We have proposed and investigated accelerated FISTAs for use with two nonsmooth penalty functions that will lead to further reductions in image reconstruction times while preserving image quality. Moreover, with the help of a mixed sparsity-regularization, better preservation of soft-tissue structures can be potentially obtained. The algorithms were systematically evaluated by use of computer-simulated and clinical data sets. PMID:27036582

Fast secant methods for the iterative solution of large nonsymmetric linear systems

NASA Technical Reports Server (NTRS)

Deuflhard, Peter; Freund, Roland; Walter, Artur

1990-01-01

A family of secant methods based on general rank-1 updates was revisited in view of the construction of iterative solvers for large non-Hermitian linear systems. As it turns out, both Broyden's good and bad update techniques play a special role, but should be associated with two different line search principles. For Broyden's bad update technique, a minimum residual principle is natural, thus making it theoretically comparable with a series of well known algorithms like GMRES. Broyden's good update technique, however, is shown to be naturally linked with a minimum next correction principle, which asymptotically mimics a minimum error principle. The two minimization principles differ significantly for sufficiently large system dimension. Numerical experiments on discretized partial differential equations of convection diffusion type in 2-D with integral layers give a first impression of the possible power of the derived good Broyden variant.

New algorithms to compute the nearness symmetric solution of the matrix equation.

PubMed

Peng, Zhen-Yun; Fang, Yang-Zhi; Xiao, Xian-Wei; Du, Dan-Dan

2016-01-01

In this paper we consider the nearness symmetric solution of the matrix equation AXB = C to a given matrix [Formula: see text] in the sense of the Frobenius norm. By discussing equivalent form of the considered problem, we derive some necessary and sufficient conditions for the matrix [Formula: see text] is a solution of the considered problem. Based on the idea of the alternating variable minimization with multiplier method, we propose two iterative methods to compute the solution of the considered problem, and analyze the global convergence results of the proposed algorithms. Numerical results illustrate the proposed methods are more effective than the existing two methods proposed in Peng et al. (Appl Math Comput 160:763-777, 2005) and Peng (Int J Comput Math 87: 1820-1830, 2010).

Simulation of dense amorphous polymers by generating representative atomistic models

NASA Astrophysics Data System (ADS)

Curcó, David; Alemán, Carlos

2003-08-01

A method for generating atomistic models of dense amorphous polymers is presented. The generated models can be used as starting structures of Monte Carlo and molecular dynamics simulations, but also are suitable for the direct evaluation physical properties. The method is organized in a two-step procedure. First, structures are generated using an algorithm that minimizes the torsional strain. After this, an iterative algorithm is applied to relax the nonbonding interactions. In order to check the performance of the method we examined structure-dependent properties for three polymeric systems: polyethyelene (ρ=0.85 g/cm3), poly(L,D-lactic) acid (ρ=1.25 g/cm3), and polyglycolic acid (ρ=1.50 g/cm3). The method successfully generated representative packings for such dense systems using minimum computational resources.

Photoacoustic image reconstruction via deep learning

NASA Astrophysics Data System (ADS)

Antholzer, Stephan; Haltmeier, Markus; Nuster, Robert; Schwab, Johannes

2018-02-01

Applying standard algorithms to sparse data problems in photoacoustic tomography (PAT) yields low-quality images containing severe under-sampling artifacts. To some extent, these artifacts can be reduced by iterative image reconstruction algorithms which allow to include prior knowledge such as smoothness, total variation (TV) or sparsity constraints. These algorithms tend to be time consuming as the forward and adjoint problems have to be solved repeatedly. Further, iterative algorithms have additional drawbacks. For example, the reconstruction quality strongly depends on a-priori model assumptions about the objects to be recovered, which are often not strictly satisfied in practical applications. To overcome these issues, in this paper, we develop direct and efficient reconstruction algorithms based on deep learning. As opposed to iterative algorithms, we apply a convolutional neural network, whose parameters are trained before the reconstruction process based on a set of training data. For actual image reconstruction, a single evaluation of the trained network yields the desired result. Our presented numerical results (using two different network architectures) demonstrate that the proposed deep learning approach reconstructs images with a quality comparable to state of the art iterative reconstruction methods.

Metal-induced streak artifact reduction using iterative reconstruction algorithms in x-ray computed tomography image of the dentoalveolar region.

PubMed

Dong, Jian; Hayakawa, Yoshihiko; Kannenberg, Sven; Kober, Cornelia

2013-02-01

The objective of this study was to reduce metal-induced streak artifact on oral and maxillofacial x-ray computed tomography (CT) images by developing the fast statistical image reconstruction system using iterative reconstruction algorithms. Adjacent CT images often depict similar anatomical structures in thin slices. So, first, images were reconstructed using the same projection data of an artifact-free image. Second, images were processed by the successive iterative restoration method where projection data were generated from reconstructed image in sequence. Besides the maximum likelihood-expectation maximization algorithm, the ordered subset-expectation maximization algorithm (OS-EM) was examined. Also, small region of interest (ROI) setting and reverse processing were applied for improving performance. Both algorithms reduced artifacts instead of slightly decreasing gray levels. The OS-EM and small ROI reduced the processing duration without apparent detriments. Sequential and reverse processing did not show apparent effects. Two alternatives in iterative reconstruction methods were effective for artifact reduction. The OS-EM algorithm and small ROI setting improved the performance. Copyright © 2012 Elsevier Inc. All rights reserved.

Implementation of the Iterative Proportion Fitting Algorithm for Geostatistical Facies Modeling

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

Li Yupeng, E-mail: yupeng@ualberta.ca; Deutsch, Clayton V.

2012-06-15

In geostatistics, most stochastic algorithm for simulation of categorical variables such as facies or rock types require a conditional probability distribution. The multivariate probability distribution of all the grouped locations including the unsampled location permits calculation of the conditional probability directly based on its definition. In this article, the iterative proportion fitting (IPF) algorithm is implemented to infer this multivariate probability. Using the IPF algorithm, the multivariate probability is obtained by iterative modification to an initial estimated multivariate probability using lower order bivariate probabilities as constraints. The imposed bivariate marginal probabilities are inferred from profiles along drill holes or wells.more » In the IPF process, a sparse matrix is used to calculate the marginal probabilities from the multivariate probability, which makes the iterative fitting more tractable and practical. This algorithm can be extended to higher order marginal probability constraints as used in multiple point statistics. The theoretical framework is developed and illustrated with estimation and simulation example.« less

Composition of web services using Markov decision processes and dynamic programming.

PubMed

Uc-Cetina, Víctor; Moo-Mena, Francisco; Hernandez-Ucan, Rafael

2015-01-01

We propose a Markov decision process model for solving the Web service composition (WSC) problem. Iterative policy evaluation, value iteration, and policy iteration algorithms are used to experimentally validate our approach, with artificial and real data. The experimental results show the reliability of the model and the methods employed, with policy iteration being the best one in terms of the minimum number of iterations needed to estimate an optimal policy, with the highest Quality of Service attributes. Our experimental work shows how the solution of a WSC problem involving a set of 100,000 individual Web services and where a valid composition requiring the selection of 1,000 services from the available set can be computed in the worst case in less than 200 seconds, using an Intel Core i5 computer with 6 GB RAM. Moreover, a real WSC problem involving only 7 individual Web services requires less than 0.08 seconds, using the same computational power. Finally, a comparison with two popular reinforcement learning algorithms, sarsa and Q-learning, shows that these algorithms require one or two orders of magnitude and more time than policy iteration, iterative policy evaluation, and value iteration to handle WSC problems of the same complexity.

SU-E-J-02: 4D Digital Tomosynthesis Based On Algebraic Image Reconstruction and Total-Variation Minimization for the Improvement of Image Quality

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

Kim, D; Kang, S; Kim, T

2014-06-01

Purpose: In this paper, we implemented the four-dimensional (4D) digital tomosynthesis (DTS) imaging based on algebraic image reconstruction technique and total-variation minimization method in order to compensate the undersampled projection data and improve the image quality. Methods: The projection data were acquired as supposed the cone-beam computed tomography system in linear accelerator by the Monte Carlo simulation and the in-house 4D digital phantom generation program. We performed 4D DTS based upon simultaneous algebraic reconstruction technique (SART) among the iterative image reconstruction technique and total-variation minimization method (TVMM). To verify the effectiveness of this reconstruction algorithm, we performed systematic simulation studiesmore » to investigate the imaging performance. Results: The 4D DTS algorithm based upon the SART and TVMM seems to give better results than that based upon the existing method, or filtered-backprojection. Conclusion: The advanced image reconstruction algorithm for the 4D DTS would be useful to validate each intra-fraction motion during radiation therapy. In addition, it will be possible to give advantage to real-time imaging for the adaptive radiation therapy. This research was supported by Leading Foreign Research Institute Recruitment Program (Grant No.2009-00420) and Basic Atomic Energy Research Institute (BAERI); (Grant No. 2009-0078390) through the National Research Foundation of Korea(NRF) funded by the Ministry of Science, ICT and Future Planning (MSIP)« less

Fast and accurate matrix completion via truncated nuclear norm regularization.

PubMed

Hu, Yao; Zhang, Debing; Ye, Jieping; Li, Xuelong; He, Xiaofei

2013-09-01

Recovering a large matrix from a small subset of its entries is a challenging problem arising in many real applications, such as image inpainting and recommender systems. Many existing approaches formulate this problem as a general low-rank matrix approximation problem. Since the rank operator is nonconvex and discontinuous, most of the recent theoretical studies use the nuclear norm as a convex relaxation. One major limitation of the existing approaches based on nuclear norm minimization is that all the singular values are simultaneously minimized, and thus the rank may not be well approximated in practice. In this paper, we propose to achieve a better approximation to the rank of matrix by truncated nuclear norm, which is given by the nuclear norm subtracted by the sum of the largest few singular values. In addition, we develop a novel matrix completion algorithm by minimizing the Truncated Nuclear Norm. We further develop three efficient iterative procedures, TNNR-ADMM, TNNR-APGL, and TNNR-ADMMAP, to solve the optimization problem. TNNR-ADMM utilizes the alternating direction method of multipliers (ADMM), while TNNR-AGPL applies the accelerated proximal gradient line search method (APGL) for the final optimization. For TNNR-ADMMAP, we make use of an adaptive penalty according to a novel update rule for ADMM to achieve a faster convergence rate. Our empirical study shows encouraging results of the proposed algorithms in comparison to the state-of-the-art matrix completion algorithms on both synthetic and real visual datasets.

3-D shape estimation of DNA molecules from stereo cryo-electron micro-graphs using a projection-steerable snake.

PubMed

Jacob, Mathews; Blu, Thierry; Vaillant, Cedric; Maddocks, John H; Unser, Michael

2006-01-01

We introduce a three-dimensional (3-D) parametric active contour algorithm for the shape estimation of DNA molecules from stereo cryo-electron micrographs. We estimate the shape by matching the projections of a 3-D global shape model with the micrographs; we choose the global model as a 3-D filament with a B-spline skeleton and a specified radial profile. The active contour algorithm iteratively updates the B-spline coefficients, which requires us to evaluate the projections and match them with the micrographs at every iteration. Since the evaluation of the projections of the global model is computationally expensive, we propose a fast algorithm based on locally approximating it by elongated blob-like templates. We introduce the concept of projection-steerability and derive a projection-steerable elongated template. Since the two-dimensional projections of such a blob at any 3-D orientation can be expressed as a linear combination of a few basis functions, matching the projections of such a 3-D template involves evaluating a weighted sum of inner products between the basis functions and the micrographs. The weights are simple functions of the 3-D orientation and the inner-products are evaluated efficiently by separable filtering. We choose an internal energy term that penalizes the average curvature magnitude. Since the exact length of the DNA molecule is known a priori, we introduce a constraint energy term that forces the curve to have this specified length. The sum of these energies along with the image energy derived from the matching process is minimized using the conjugate gradients algorithm. We validate the algorithm using real, as well as simulated, data and show that it performs well.

Markov random field model-based edge-directed image interpolation.

PubMed

Li, Min; Nguyen, Truong Q

2008-07-01

This paper presents an edge-directed image interpolation algorithm. In the proposed algorithm, the edge directions are implicitly estimated with a statistical-based approach. In opposite to explicit edge directions, the local edge directions are indicated by length-16 weighting vectors. Implicitly, the weighting vectors are used to formulate geometric regularity (GR) constraint (smoothness along edges and sharpness across edges) and the GR constraint is imposed on the interpolated image through the Markov random field (MRF) model. Furthermore, under the maximum a posteriori-MRF framework, the desired interpolated image corresponds to the minimal energy state of a 2-D random field given the low-resolution image. Simulated annealing methods are used to search for the minimal energy state from the state space. To lower the computational complexity of MRF, a single-pass implementation is designed, which performs nearly as well as the iterative optimization. Simulation results show that the proposed MRF model-based edge-directed interpolation method produces edges with strong geometric regularity. Compared to traditional methods and other edge-directed interpolation methods, the proposed method improves the subjective quality of the interpolated edges while maintaining a high PSNR level.

About approximation of integer factorization problem by the combination fixed-point iteration method and Bayesian rounding for quantum cryptography

NASA Astrophysics Data System (ADS)

Ogorodnikov, Yuri; Khachay, Michael; Pljonkin, Anton

2018-04-01

We describe the possibility of employing the special case of the 3-SAT problem stemming from the well known integer factorization problem for the quantum cryptography. It is known, that for every instance of our 3-SAT setting the given 3-CNF is satisfiable by a unique truth assignment, and the goal is to find this assignment. Since the complexity status of the factorization problem is still undefined, development of approximation algorithms and heuristics adopts interest of numerous researchers. One of promising approaches to construction of approximation techniques is based on real-valued relaxation of the given 3-CNF followed by minimizing of the appropriate differentiable loss function, and subsequent rounding of the fractional minimizer obtained. Actually, algorithms developed this way differ by the rounding scheme applied on their final stage. We propose a new rounding scheme based on Bayesian learning. The article shows that the proposed method can be used to determine the security in quantum key distribution systems. In the quantum distribution the Shannon rules is applied and the factorization problem is paramount when decrypting secret keys.

Comparison of Low-Thrust Control Laws for Application in Planetocentric Space

NASA Technical Reports Server (NTRS)

Falck, Robert D.; Sjauw, Waldy K.; Smith, David A.

2014-01-01

Recent interest at NASA for the application of solar electric propulsion for the transfer of significant payloads in cislunar space has led to the development of high-fidelity simulations of such missions. With such transfers involving transfer times on the order of months, simulation time can be significant. In the past, the examination of such missions typically began with the use of lower-fidelity trajectory optimization tools such as SEPSPOT to develop and tune guidance laws which delivered optimal or near- optimal trajectories, where optimal is generally defined as minimizing propellant expenditure or time of flight. The transfer of these solutions to a high-fidelity simulation is typically an iterative process whereby the initial solution may nearly, but not precisely, meet mission objectives. Further tuning of the guidance algorithm is typically necessary when accounting for high-fidelity perturbations such as those due to more detailed gravity models, secondary-body effects, solar radiation pressure, etc. While trajectory optimization is a useful method for determining optimal performance metrics, algorithms which deliver nearly optimal performance with minimal tuning are an attractive alternative.

A superlinear interior points algorithm for engineering design optimization

NASA Technical Reports Server (NTRS)

Herskovits, J.; Asquier, J.

1990-01-01

We present a quasi-Newton interior points algorithm for nonlinear constrained optimization. It is based on a general approach consisting of the iterative solution in the primal and dual spaces of the equalities in Karush-Kuhn-Tucker optimality conditions. This is done in such a way to have primal and dual feasibility at each iteration, which ensures satisfaction of those optimality conditions at the limit points. This approach is very strong and efficient, since at each iteration it only requires the solution of two linear systems with the same matrix, instead of quadratic programming subproblems. It is also particularly appropriate for engineering design optimization inasmuch at each iteration a feasible design is obtained. The present algorithm uses a quasi-Newton approximation of the second derivative of the Lagrangian function in order to have superlinear asymptotic convergence. We discuss theoretical aspects of the algorithm and its computer implementation.

Iterative methods for plasma sheath calculations: Application to spherical probe

NASA Technical Reports Server (NTRS)

Parker, L. W.; Sullivan, E. C.

1973-01-01

The computer cost of a Poisson-Vlasov iteration procedure for the numerical solution of a steady-state collisionless plasma-sheath problem depends on: (1) the nature of the chosen iterative algorithm, (2) the position of the outer boundary of the grid, and (3) the nature of the boundary condition applied to simulate a condition at infinity (as in three-dimensional probe or satellite-wake problems). Two iterative algorithms, in conjunction with three types of boundary conditions, are analyzed theoretically and applied to the computation of current-voltage characteristics of a spherical electrostatic probe. The first algorithm was commonly used by physicists, and its computer costs depend primarily on the boundary conditions and are only slightly affected by the mesh interval. The second algorithm is not commonly used, and its costs depend primarily on the mesh interval and slightly on the boundary conditions.

A methodology for finding the optimal iteration number of the SIRT algorithm for quantitative Electron Tomography.

PubMed

Okariz, Ana; Guraya, Teresa; Iturrondobeitia, Maider; Ibarretxe, Julen

2017-02-01

The SIRT (Simultaneous Iterative Reconstruction Technique) algorithm is commonly used in Electron Tomography to calculate the original volume of the sample from noisy images, but the results provided by this iterative procedure are strongly dependent on the specific implementation of the algorithm, as well as on the number of iterations employed for the reconstruction. In this work, a methodology for selecting the iteration number of the SIRT reconstruction that provides the most accurate segmentation is proposed. The methodology is based on the statistical analysis of the intensity profiles at the edge of the objects in the reconstructed volume. A phantom which resembles a a carbon black aggregate has been created to validate the methodology and the SIRT implementations of two free software packages (TOMOJ and TOMO3D) have been used. Copyright © 2016 Elsevier B.V. All rights reserved.

Iterative projection algorithms for ab initio phasing in virus crystallography.

PubMed

Lo, Victor L; Kingston, Richard L; Millane, Rick P

2016-12-01

Iterative projection algorithms are proposed as a tool for ab initio phasing in virus crystallography. The good global convergence properties of these algorithms, coupled with the spherical shape and high structural redundancy of icosahedral viruses, allows high resolution phases to be determined with no initial phase information. This approach is demonstrated by determining the electron density of a virus crystal with 5-fold non-crystallographic symmetry, starting with only a spherical shell envelope. The electron density obtained is sufficiently accurate for model building. The results indicate that iterative projection algorithms should be routinely applicable in virus crystallography, without the need for ancillary phase information. Copyright © 2016 Elsevier Inc. All rights reserved.

Tunable output-frequency filter algorithm for imaging through scattering media under LED illumination

NASA Astrophysics Data System (ADS)

Zhou, Meiling; Singh, Alok Kumar; Pedrini, Giancarlo; Osten, Wolfgang; Min, Junwei; Yao, Baoli

2018-03-01

We present a tunable output-frequency filter (TOF) algorithm to reconstruct the object from noisy experimental data under low-power partially coherent illumination, such as LED, when imaging through scattering media. In the iterative algorithm, we employ Gaussian functions with different filter windows at different stages of iteration process to reduce corruption from experimental noise to search for a global minimum in the reconstruction. In comparison with the conventional iterative phase retrieval algorithm, we demonstrate that the proposed TOF algorithm achieves consistent and reliable reconstruction in the presence of experimental noise. Moreover, the spatial resolution and distinctive features are retained in the reconstruction since the filter is applied only to the region outside the object. The feasibility of the proposed method is proved by experimental results.

Planning additional drilling campaign using two-space genetic algorithm: A game theoretical approach

NASA Astrophysics Data System (ADS)

Kumral, Mustafa; Ozer, Umit

2013-03-01

Grade and tonnage are the most important technical uncertainties in mining ventures because of the use of estimations/simulations, which are mostly generated from drill data. Open pit mines are planned and designed on the basis of the blocks representing the entire orebody. Each block has different estimation/simulation variance reflecting uncertainty to some extent. The estimation/simulation realizations are submitted to mine production scheduling process. However, the use of a block model with varying estimation/simulation variances will lead to serious risk in the scheduling. In the medium of multiple simulations, the dispersion variances of blocks can be thought to regard technical uncertainties. However, the dispersion variance cannot handle uncertainty associated with varying estimation/simulation variances of blocks. This paper proposes an approach that generates the configuration of the best additional drilling campaign to generate more homogenous estimation/simulation variances of blocks. In other words, the objective is to find the best drilling configuration in such a way as to minimize grade uncertainty under budget constraint. Uncertainty measure of the optimization process in this paper is interpolation variance, which considers data locations and grades. The problem is expressed as a minmax problem, which focuses on finding the best worst-case performance i.e., minimizing interpolation variance of the block generating maximum interpolation variance. Since the optimization model requires computing the interpolation variances of blocks being simulated/estimated in each iteration, the problem cannot be solved by standard optimization tools. This motivates to use two-space genetic algorithm (GA) approach to solve the problem. The technique has two spaces: feasible drill hole configuration with minimization of interpolation variance and drill hole simulations with maximization of interpolation variance. Two-space interacts to find a minmax solution iteratively. A case study was conducted to demonstrate the performance of approach. The findings showed that the approach could be used to plan a new drilling campaign.

Reconstruction of brachytherapy seed positions and orientations from cone-beam CT x-ray projections via a novel iterative forward projection matching method.

PubMed

Pokhrel, Damodar; Murphy, Martin J; Todor, Dorin A; Weiss, Elisabeth; Williamson, Jeffrey F

2011-01-01

To generalize and experimentally validate a novel algorithm for reconstructing the 3D pose (position and orientation) of implanted brachytherapy seeds from a set of a few measured 2D cone-beam CT (CBCT) x-ray projections. The iterative forward projection matching (IFPM) algorithm was generalized to reconstruct the 3D pose, as well as the centroid, of brachytherapy seeds from three to ten measured 2D projections. The gIFPM algorithm finds the set of seed poses that minimizes the sum-of-squared-difference of the pixel-by-pixel intensities between computed and measured autosegmented radiographic projections of the implant. Numerical simulations of clinically realistic brachytherapy seed configurations were performed to demonstrate the proof of principle. An in-house machined brachytherapy phantom, which supports precise specification of seed position and orientation at known values for simulated implant geometries, was used to experimentally validate this algorithm. The phantom was scanned on an ACUITY CBCT digital simulator over a full 660 sinogram projections. Three to ten x-ray images were selected from the full set of CBCT sinogram projections and postprocessed to create binary seed-only images. In the numerical simulations, seed reconstruction position and orientation errors were approximately 0.6 mm and 5 degrees, respectively. The physical phantom measurements demonstrated an absolute positional accuracy of (0.78 +/- 0.57) mm or less. The theta and phi angle errors were found to be (5.7 +/- 4.9) degrees and (6.0 +/- 4.1) degrees, respectively, or less when using three projections; with six projections, results were slightly better. The mean registration error was better than 1 mm/6 degrees compared to the measured seed projections. Each test trial converged in 10-20 iterations with computation time of 12-18 min/iteration on a 1 GHz processor. This work describes a novel, accurate, and completely automatic method for reconstructing seed orientations, as well as centroids, from a small number of radiographic projections, in support of intraoperative planning and adaptive replanning. Unlike standard back-projection methods, gIFPM avoids the need to match corresponding seed images on the projections. This algorithm also successfully reconstructs overlapping clustered and highly migrated seeds in the implant. The accuracy of better than 1 mm and 6 degrees demonstrates that gIFPM has the potential to support 2D Task Group 43 calculations in clinical practice.

Reconstruction of brachytherapy seed positions and orientations from cone-beam CT x-ray projections via a novel iterative forward projection matching method

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

Pokhrel, Damodar; Murphy, Martin J.; Todor, Dorin A.

2011-01-15

Purpose: To generalize and experimentally validate a novel algorithm for reconstructing the 3D pose (position and orientation) of implanted brachytherapy seeds from a set of a few measured 2D cone-beam CT (CBCT) x-ray projections. Methods: The iterative forward projection matching (IFPM) algorithm was generalized to reconstruct the 3D pose, as well as the centroid, of brachytherapy seeds from three to ten measured 2D projections. The gIFPM algorithm finds the set of seed poses that minimizes the sum-of-squared-difference of the pixel-by-pixel intensities between computed and measured autosegmented radiographic projections of the implant. Numerical simulations of clinically realistic brachytherapy seed configurations weremore » performed to demonstrate the proof of principle. An in-house machined brachytherapy phantom, which supports precise specification of seed position and orientation at known values for simulated implant geometries, was used to experimentally validate this algorithm. The phantom was scanned on an ACUITY CBCT digital simulator over a full 660 sinogram projections. Three to ten x-ray images were selected from the full set of CBCT sinogram projections and postprocessed to create binary seed-only images. Results: In the numerical simulations, seed reconstruction position and orientation errors were approximately 0.6 mm and 5 deg., respectively. The physical phantom measurements demonstrated an absolute positional accuracy of (0.78{+-}0.57) mm or less. The {theta} and {phi} angle errors were found to be (5.7{+-}4.9) deg. and (6.0{+-}4.1) deg., respectively, or less when using three projections; with six projections, results were slightly better. The mean registration error was better than 1 mm/6 deg. compared to the measured seed projections. Each test trial converged in 10-20 iterations with computation time of 12-18 min/iteration on a 1 GHz processor. Conclusions: This work describes a novel, accurate, and completely automatic method for reconstructing seed orientations, as well as centroids, from a small number of radiographic projections, in support of intraoperative planning and adaptive replanning. Unlike standard back-projection methods, gIFPM avoids the need to match corresponding seed images on the projections. This algorithm also successfully reconstructs overlapping clustered and highly migrated seeds in the implant. The accuracy of better than 1 mm and 6 deg. demonstrates that gIFPM has the potential to support 2D Task Group 43 calculations in clinical practice.« less

Development of CPR security using impact analysis.

PubMed Central

Salazar-Kish, J.; Tate, D.; Hall, P. D.; Homa, K.

2000-01-01

The HIPAA regulations will require that institutions ensure the prevention of unauthorized access to electronically stored or transmitted patient records. This paper discusses a process for analyzing the impact of security mechanisms on users of computerized patient records through "behind the scenes" electronic access audits. In this way, those impacts can be assessed and refined to an acceptable standard prior to implementation. Through an iterative process of design and evaluation, we develop security algorithms that will protect electronic health information from improper access, alteration or loss, while minimally affecting the flow of work of the user population as a whole. PMID:11079984

An implicit iterative algorithm with a tuning parameter for Itô Lyapunov matrix equations

NASA Astrophysics Data System (ADS)

Zhang, Ying; Wu, Ai-Guo; Sun, Hui-Jie

2018-01-01

In this paper, an implicit iterative algorithm is proposed for solving a class of Lyapunov matrix equations arising in Itô stochastic linear systems. A tuning parameter is introduced in this algorithm, and thus the convergence rate of the algorithm can be changed. Some conditions are presented such that the developed algorithm is convergent. In addition, an explicit expression is also derived for the optimal tuning parameter, which guarantees that the obtained algorithm achieves its fastest convergence rate. Finally, numerical examples are employed to illustrate the effectiveness of the given algorithm.

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.

Advisory Algorithm for Scheduling Open Sectors, Operating Positions, and Workstations

NASA Technical Reports Server (NTRS)

Bloem, Michael; Drew, Michael; Lai, Chok Fung; Bilimoria, Karl D.

2012-01-01

Air traffic controller supervisors configure available sector, operating position, and work-station resources to safely and efficiently control air traffic in a region of airspace. In this paper, an algorithm for assisting supervisors with this task is described and demonstrated on two sample problem instances. The algorithm produces configuration schedule advisories that minimize a cost. The cost is a weighted sum of two competing costs: one penalizing mismatches between configurations and predicted air traffic demand and another penalizing the effort associated with changing configurations. The problem considered by the algorithm is a shortest path problem that is solved with a dynamic programming value iteration algorithm. The cost function contains numerous parameters. Default values for most of these are suggested based on descriptions of air traffic control procedures and subject-matter expert feedback. The parameter determining the relative importance of the two competing costs is tuned by comparing historical configurations with corresponding algorithm advisories. Two sample problem instances for which appropriate configuration advisories are obvious were designed to illustrate characteristics of the algorithm. Results demonstrate how the algorithm suggests advisories that appropriately utilize changes in airspace configurations and changes in the number of operating positions allocated to each open sector. The results also demonstrate how the advisories suggest appropriate times for configuration changes.

Emerging Techniques for Dose Optimization in Abdominal CT

PubMed Central

Platt, Joel F.; Goodsitt, Mitchell M.; Al-Hawary, Mahmoud M.; Maturen, Katherine E.; Wasnik, Ashish P.; Pandya, Amit

2014-01-01

Recent advances in computed tomographic (CT) scanning technique such as automated tube current modulation (ATCM), optimized x-ray tube voltage, and better use of iterative image reconstruction have allowed maintenance of good CT image quality with reduced radiation dose. ATCM varies the tube current during scanning to account for differences in patient attenuation, ensuring a more homogeneous image quality, although selection of the appropriate image quality parameter is essential for achieving optimal dose reduction. Reducing the x-ray tube voltage is best suited for evaluating iodinated structures, since the effective energy of the x-ray beam will be closer to the k-edge of iodine, resulting in a higher attenuation for the iodine. The optimal kilovoltage for a CT study should be chosen on the basis of imaging task and patient habitus. The aim of iterative image reconstruction is to identify factors that contribute to noise on CT images with use of statistical models of noise (statistical iterative reconstruction) and selective removal of noise to improve image quality. The degree of noise suppression achieved with statistical iterative reconstruction can be customized to minimize the effect of altered image quality on CT images. Unlike with statistical iterative reconstruction, model-based iterative reconstruction algorithms model both the statistical noise and the physical acquisition process, allowing CT to be performed with further reduction in radiation dose without an increase in image noise or loss of spatial resolution. Understanding these recently developed scanning techniques is essential for optimization of imaging protocols designed to achieve the desired image quality with a reduced dose. © RSNA, 2014 PMID:24428277

Iterative Neighbour-Information Gathering for Ranking Nodes in Complex Networks

NASA Astrophysics Data System (ADS)

Xu, Shuang; Wang, Pei; Lü, Jinhu

2017-01-01

Designing node influence ranking algorithms can provide insights into network dynamics, functions and structures. Increasingly evidences reveal that node’s spreading ability largely depends on its neighbours. We introduce an iterative neighbourinformation gathering (Ing) process with three parameters, including a transformation matrix, a priori information and an iteration time. The Ing process iteratively combines priori information from neighbours via the transformation matrix, and iteratively assigns an Ing score to each node to evaluate its influence. The algorithm appropriates for any types of networks, and includes some traditional centralities as special cases, such as degree, semi-local, LeaderRank. The Ing process converges in strongly connected networks with speed relying on the first two largest eigenvalues of the transformation matrix. Interestingly, the eigenvector centrality corresponds to a limit case of the algorithm. By comparing with eight renowned centralities, simulations of susceptible-infected-removed (SIR) model on real-world networks reveal that the Ing can offer more exact rankings, even without a priori information. We also observe that an optimal iteration time is always in existence to realize best characterizing of node influence. The proposed algorithms bridge the gaps among some existing measures, and may have potential applications in infectious disease control, designing of optimal information spreading strategies.

Conjugate gradient coupled with multigrid for an indefinite problem

NASA Technical Reports Server (NTRS)

Gozani, J.; Nachshon, A.; Turkel, E.

1984-01-01

An iterative algorithm for the Helmholtz equation is presented. This scheme was based on the preconditioned conjugate gradient method for the normal equations. The preconditioning is one cycle of a multigrid method for the discrete Laplacian. The smoothing algorithm is red-black Gauss-Seidel and is constructed so it is a symmetric operator. The total number of iterations needed by the algorithm is independent of h. By varying the number of grids, the number of iterations depends only weakly on k when k(3)h(2) is constant. Comparisons with a SSOR preconditioner are presented.

A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems.

PubMed

Gong, Pinghua; Zhang, Changshui; Lu, Zhaosong; Huang, Jianhua Z; Ye, Jieping

2013-01-01

Non-convex sparsity-inducing penalties have recently received considerable attentions in sparse learning. Recent theoretical investigations have demonstrated their superiority over the convex counterparts in several sparse learning settings. However, solving the non-convex optimization problems associated with non-convex penalties remains a big challenge. A commonly used approach is the Multi-Stage (MS) convex relaxation (or DC programming), which relaxes the original non-convex problem to a sequence of convex problems. This approach is usually not very practical for large-scale problems because its computational cost is a multiple of solving a single convex problem. In this paper, we propose a General Iterative Shrinkage and Thresholding (GIST) algorithm to solve the nonconvex optimization problem for a large class of non-convex penalties. The GIST algorithm iteratively solves a proximal operator problem, which in turn has a closed-form solution for many commonly used penalties. At each outer iteration of the algorithm, we use a line search initialized by the Barzilai-Borwein (BB) rule that allows finding an appropriate step size quickly. The paper also presents a detailed convergence analysis of the GIST algorithm. The efficiency of the proposed algorithm is demonstrated by extensive experiments on large-scale data sets.

Composition of Web Services Using Markov Decision Processes and Dynamic Programming

PubMed Central

Uc-Cetina, Víctor; Moo-Mena, Francisco; Hernandez-Ucan, Rafael

2015-01-01

We propose a Markov decision process model for solving the Web service composition (WSC) problem. Iterative policy evaluation, value iteration, and policy iteration algorithms are used to experimentally validate our approach, with artificial and real data. The experimental results show the reliability of the model and the methods employed, with policy iteration being the best one in terms of the minimum number of iterations needed to estimate an optimal policy, with the highest Quality of Service attributes. Our experimental work shows how the solution of a WSC problem involving a set of 100,000 individual Web services and where a valid composition requiring the selection of 1,000 services from the available set can be computed in the worst case in less than 200 seconds, using an Intel Core i5 computer with 6 GB RAM. Moreover, a real WSC problem involving only 7 individual Web services requires less than 0.08 seconds, using the same computational power. Finally, a comparison with two popular reinforcement learning algorithms, sarsa and Q-learning, shows that these algorithms require one or two orders of magnitude and more time than policy iteration, iterative policy evaluation, and value iteration to handle WSC problems of the same complexity. PMID:25874247

Iterative image reconstruction for PROPELLER-MRI using the nonuniform fast fourier transform.

PubMed

Tamhane, Ashish A; Anastasio, Mark A; Gui, Minzhi; Arfanakis, Konstantinos

2010-07-01

To investigate an iterative image reconstruction algorithm using the nonuniform fast Fourier transform (NUFFT) for PROPELLER (Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction) MRI. Numerical simulations, as well as experiments on a phantom and a healthy human subject were used to evaluate the performance of the iterative image reconstruction algorithm for PROPELLER, and compare it with that of conventional gridding. The trade-off between spatial resolution, signal to noise ratio, and image artifacts, was investigated for different values of the regularization parameter. The performance of the iterative image reconstruction algorithm in the presence of motion was also evaluated. It was demonstrated that, for a certain range of values of the regularization parameter, iterative reconstruction produced images with significantly increased signal to noise ratio, reduced artifacts, for similar spatial resolution, compared with gridding. Furthermore, the ability to reduce the effects of motion in PROPELLER-MRI was maintained when using the iterative reconstruction approach. An iterative image reconstruction technique based on the NUFFT was investigated for PROPELLER MRI. For a certain range of values of the regularization parameter, the new reconstruction technique may provide PROPELLER images with improved image quality compared with conventional gridding. (c) 2010 Wiley-Liss, Inc.

Iterative Image Reconstruction for PROPELLER-MRI using the NonUniform Fast Fourier Transform

PubMed Central

Tamhane, Ashish A.; Anastasio, Mark A.; Gui, Minzhi; Arfanakis, Konstantinos

2013-01-01

Purpose To investigate an iterative image reconstruction algorithm using the non-uniform fast Fourier transform (NUFFT) for PROPELLER (Periodically Rotated Overlapping parallEL Lines with Enhanced Reconstruction) MRI. Materials and Methods Numerical simulations, as well as experiments on a phantom and a healthy human subject were used to evaluate the performance of the iterative image reconstruction algorithm for PROPELLER, and compare it to that of conventional gridding. The trade-off between spatial resolution, signal to noise ratio, and image artifacts, was investigated for different values of the regularization parameter. The performance of the iterative image reconstruction algorithm in the presence of motion was also evaluated. Results It was demonstrated that, for a certain range of values of the regularization parameter, iterative reconstruction produced images with significantly increased SNR, reduced artifacts, for similar spatial resolution, compared to gridding. Furthermore, the ability to reduce the effects of motion in PROPELLER-MRI was maintained when using the iterative reconstruction approach. Conclusion An iterative image reconstruction technique based on the NUFFT was investigated for PROPELLER MRI. For a certain range of values of the regularization parameter the new reconstruction technique may provide PROPELLER images with improved image quality compared to conventional gridding. PMID:20578028

An iterated Laplacian based semi-supervised dimensionality reduction for classification of breast cancer on ultrasound images.

PubMed

Liu, Xiao; Shi, Jun; Zhou, Shichong; Lu, Minhua

2014-01-01

The dimensionality reduction is an important step in ultrasound image based computer-aided diagnosis (CAD) for breast cancer. A newly proposed l2,1 regularized correntropy algorithm for robust feature selection (CRFS) has achieved good performance for noise corrupted data. Therefore, it has the potential to reduce the dimensions of ultrasound image features. However, in clinical practice, the collection of labeled instances is usually expensive and time costing, while it is relatively easy to acquire the unlabeled or undetermined instances. Therefore, the semi-supervised learning is very suitable for clinical CAD. The iterated Laplacian regularization (Iter-LR) is a new regularization method, which has been proved to outperform the traditional graph Laplacian regularization in semi-supervised classification and ranking. In this study, to augment the classification accuracy of the breast ultrasound CAD based on texture feature, we propose an Iter-LR-based semi-supervised CRFS (Iter-LR-CRFS) algorithm, and then apply it to reduce the feature dimensions of ultrasound images for breast CAD. We compared the Iter-LR-CRFS with LR-CRFS, original supervised CRFS, and principal component analysis. The experimental results indicate that the proposed Iter-LR-CRFS significantly outperforms all other algorithms.

Regularization iteration imaging algorithm for electrical capacitance tomography

NASA Astrophysics Data System (ADS)

Tong, Guowei; Liu, Shi; Chen, Hongyan; Wang, Xueyao

2018-03-01

The image reconstruction method plays a crucial role in real-world applications of the electrical capacitance tomography technique. In this study, a new cost function that simultaneously considers the sparsity and low-rank properties of the imaging targets is proposed to improve the quality of the reconstruction images, in which the image reconstruction task is converted into an optimization problem. Within the framework of the split Bregman algorithm, an iterative scheme that splits a complicated optimization problem into several simpler sub-tasks is developed to solve the proposed cost function efficiently, in which the fast-iterative shrinkage thresholding algorithm is introduced to accelerate the convergence. Numerical experiment results verify the effectiveness of the proposed algorithm in improving the reconstruction precision and robustness.

A fast and robust iterative algorithm for prediction of RNA pseudoknotted secondary structures

PubMed Central

2014-01-01

Background Improving accuracy and efficiency of computational methods that predict pseudoknotted RNA secondary structures is an ongoing challenge. Existing methods based on free energy minimization tend to be very slow and are limited in the types of pseudoknots that they can predict. Incorporating known structural information can improve prediction accuracy; however, there are not many methods for prediction of pseudoknotted structures that can incorporate structural information as input. There is even less understanding of the relative robustness of these methods with respect to partial information. Results We present a new method, Iterative HFold, for pseudoknotted RNA secondary structure prediction. Iterative HFold takes as input a pseudoknot-free structure, and produces a possibly pseudoknotted structure whose energy is at least as low as that of any (density-2) pseudoknotted structure containing the input structure. Iterative HFold leverages strengths of earlier methods, namely the fast running time of HFold, a method that is based on the hierarchical folding hypothesis, and the energy parameters of HotKnots V2.0. Our experimental evaluation on a large data set shows that Iterative HFold is robust with respect to partial information, with average accuracy on pseudoknotted structures steadily increasing from roughly 54% to 79% as the user provides up to 40% of the input structure. Iterative HFold is much faster than HotKnots V2.0, while having comparable accuracy. Iterative HFold also has significantly better accuracy than IPknot on our HK-PK and IP-pk168 data sets. Conclusions Iterative HFold is a robust method for prediction of pseudoknotted RNA secondary structures, whose accuracy with more than 5% information about true pseudoknot-free structures is better than that of IPknot, and with about 35% information about true pseudoknot-free structures compares well with that of HotKnots V2.0 while being significantly faster. Iterative HFold and all data used in this work are freely available at http://www.cs.ubc.ca/~hjabbari/software.php. PMID:24884954

Tail Biting Trellis Representation of Codes: Decoding and Construction

NASA Technical Reports Server (NTRS)

Shao. Rose Y.; Lin, Shu; Fossorier, Marc

1999-01-01

This paper presents two new iterative algorithms for decoding linear codes based on their tail biting trellises, one is unidirectional and the other is bidirectional. Both algorithms are computationally efficient and achieves virtually optimum error performance with a small number of decoding iterations. They outperform all the previous suboptimal decoding algorithms. The bidirectional algorithm also reduces decoding delay. Also presented in the paper is a method for constructing tail biting trellises for linear block codes.

Single-step reinitialization and extending algorithms for level-set based multi-phase flow simulations

NASA Astrophysics Data System (ADS)

Fu, Lin; Hu, Xiangyu Y.; Adams, Nikolaus A.

2017-12-01

We propose efficient single-step formulations for reinitialization and extending algorithms, which are critical components of level-set based interface-tracking methods. The level-set field is reinitialized with a single-step (non iterative) "forward tracing" algorithm. A minimum set of cells is defined that describes the interface, and reinitialization employs only data from these cells. Fluid states are extrapolated or extended across the interface by a single-step "backward tracing" algorithm. Both algorithms, which are motivated by analogy to ray-tracing, avoid multiple block-boundary data exchanges that are inevitable for iterative reinitialization and extending approaches within a parallel-computing environment. The single-step algorithms are combined with a multi-resolution conservative sharp-interface method and validated by a wide range of benchmark test cases. We demonstrate that the proposed reinitialization method achieves second-order accuracy in conserving the volume of each phase. The interface location is invariant to reapplication of the single-step reinitialization. Generally, we observe smaller absolute errors than for standard iterative reinitialization on the same grid. The computational efficiency is higher than for the standard and typical high-order iterative reinitialization methods. We observe a 2- to 6-times efficiency improvement over the standard method for serial execution. The proposed single-step extending algorithm, which is commonly employed for assigning data to ghost cells with ghost-fluid or conservative interface interaction methods, shows about 10-times efficiency improvement over the standard method while maintaining same accuracy. Despite their simplicity, the proposed algorithms offer an efficient and robust alternative to iterative reinitialization and extending methods for level-set based multi-phase simulations.

Wideband dichroic-filter design for LED-phosphor beam-combining

DOEpatents

Falicoff, Waqidi

2010-12-28

A general method is disclosed of designing two-component dichroic short-pass filters operable for incidence angle distributions over the 0-30.degree. range, and specific preferred embodiments are listed. The method is based on computer optimization algorithms for an N-layer design, specifically the N-dimensional conjugate-gradient minimization of a merit function based on difference from a target transmission spectrum, as well as subsequent cycles of needle synthesis for increasing N. A key feature of the method is the initial filter design, upon which the algorithm proceeds to iterate successive design candidates with smaller merit functions. This initial design, with high-index material H and low-index L, is (0.75 H, 0.5 L, 0.75 H)^m, denoting m (20-30) repetitions of a three-layer motif, giving rise to a filter with N=2 m+1.

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

Possibilistic clustering for shape recognition

NASA Technical Reports Server (NTRS)

Keller, James M.; Krishnapuram, Raghu

1993-01-01

Clustering methods have been used extensively in computer vision and pattern recognition. Fuzzy clustering has been shown to be advantageous over crisp (or traditional) clustering in that total commitment of a vector to a given class is not required at each iteration. Recently fuzzy clustering methods have shown spectacular ability to detect not only hypervolume clusters, but also clusters which are actually 'thin shells', i.e., curves and surfaces. Most analytic fuzzy clustering approaches are derived from Bezdek's Fuzzy C-Means (FCM) algorithm. The FCM uses the probabilistic constraint that the memberships of a data point across classes sum to one. This constraint was used to generate the membership update equations for an iterative algorithm. Unfortunately, the memberships resulting from FCM and its derivatives do not correspond to the intuitive concept of degree of belonging, and moreover, the algorithms have considerable trouble in noisy environments. Recently, the clustering problem was cast into the framework of possibility theory. Our approach was radically different from the existing clustering methods in that the resulting partition of the data can be interpreted as a possibilistic partition, and the membership values may be interpreted as degrees of possibility of the points belonging to the classes. An appropriate objective function whose minimum will characterize a good possibilistic partition of the data was constructed, and the membership and prototype update equations from necessary conditions for minimization of our criterion function were derived. The ability of this approach to detect linear and quartic curves in the presence of considerable noise is shown.

Possibilistic clustering for shape recognition

NASA Technical Reports Server (NTRS)

Keller, James M.; Krishnapuram, Raghu

1992-01-01

Clustering methods have been used extensively in computer vision and pattern recognition. Fuzzy clustering has been shown to be advantageous over crisp (or traditional) clustering in that total commitment of a vector to a given class is not required at each iteration. Recently fuzzy clustering methods have shown spectacular ability to detect not only hypervolume clusters, but also clusters which are actually 'thin shells', i.e., curves and surfaces. Most analytic fuzzy clustering approaches are derived from Bezdek's Fuzzy C-Means (FCM) algorithm. The FCM uses the probabilistic constraint that the memberships of a data point across classes sum to one. This constraint was used to generate the membership update equations for an iterative algorithm. Unfortunately, the memberships resulting from FCM and its derivatives do not correspond to the intuitive concept of degree of belonging, and moreover, the algorithms have considerable trouble in noisy environments. Recently, we cast the clustering problem into the framework of possibility theory. Our approach was radically different from the existing clustering methods in that the resulting partition of the data can be interpreted as a possibilistic partition, and the membership values may be interpreted as degrees of possibility of the points belonging to the classes. We constructed an appropriate objective function whose minimum will characterize a good possibilistic partition of the data, and we derived the membership and prototype update equations from necessary conditions for minimization of our criterion function. In this paper, we show the ability of this approach to detect linear and quartic curves in the presence of considerable noise.

Design of Neural Networks for Fast Convergence and Accuracy

NASA Technical Reports Server (NTRS)

Maghami, Peiman G.; Sparks, Dean W., Jr.

1998-01-01

A novel procedure for the design and training of artificial neural networks, used for rapid and efficient controls and dynamics design and analysis for flexible space systems, has been developed. Artificial neural networks are employed to provide a means of evaluating the impact of design changes rapidly. Specifically, two-layer feedforward neural networks are designed to approximate the functional relationship between the component spacecraft design changes and measures of its performance. A training algorithm, based on statistical sampling theory, is presented, which guarantees that the trained networks provide a designer-specified degree of accuracy in mapping the functional relationship. Within each iteration of this statistical-based algorithm, a sequential design algorithm is used for the design and training of the feedforward network to provide rapid convergence to the network goals. Here, at each sequence a new network is trained to minimize the error of previous network. The design algorithm attempts to avoid the local minima phenomenon that hampers the traditional network training. A numerical example is performed on a spacecraft application in order to demonstrate the feasibility of the proposed approach.

On Deployment of Multiple Base Stations for Energy-Efficient Communication in Wireless Sensor Networks

DOE PAGES

Lin, Yunyue; Wu, Qishi; Cai, Xiaoshan; ...

2010-01-01

Data transmission from sensor nodes to a base station or a sink node often incurs significant energy consumption, which critically affects network lifetime. We generalize and solve the problem of deploying multiple base stations to maximize network lifetime in terms of two different metrics under one-hop and multihop communication models. In the one-hop communication model, the sensors far away from base stations always deplete their energy much faster than others. We propose an optimal solution and a heuristic approach based on the minimal enclosing circle algorithm to deploy a base station at the geometric center of each cluster. In themore » multihop communication model, both base station location and data routing mechanism need to be considered in maximizing network lifetime. We propose an iterative algorithm based on rigorous mathematical derivations and use linear programming to compute the optimal routing paths for data transmission. Simulation results show the distinguished performance of the proposed deployment algorithms in maximizing network lifetime.« less

Real-time Adaptive Control Using Neural Generalized Predictive Control

NASA Technical Reports Server (NTRS)

Haley, Pam; Soloway, Don; Gold, Brian

1999-01-01

The objective of this paper is to demonstrate the feasibility of a Nonlinear Generalized Predictive Control algorithm by showing real-time adaptive control on a plant with relatively fast time-constants. Generalized Predictive Control has classically been used in process control where linear control laws were formulated for plants with relatively slow time-constants. The plant of interest for this paper is a magnetic levitation device that is nonlinear and open-loop unstable. In this application, the reference model of the plant is a neural network that has an embedded nominal linear model in the network weights. The control based on the linear model provides initial stability at the beginning of network training. In using a neural network the control laws are nonlinear and online adaptation of the model is possible to capture unmodeled or time-varying dynamics. Newton-Raphson is the minimization algorithm. Newton-Raphson requires the calculation of the Hessian, but even with this computational expense the low iteration rate make this a viable algorithm for real-time control.

Efficient Compressed Sensing Based MRI Reconstruction using Nonconvex Total Variation Penalties

NASA Astrophysics Data System (ADS)

Lazzaro, D.; Loli Piccolomini, E.; Zama, F.

2016-10-01

This work addresses the problem of Magnetic Resonance Image Reconstruction from highly sub-sampled measurements in the Fourier domain. It is modeled as a constrained minimization problem, where the objective function is a non-convex function of the gradient of the unknown image and the constraints are given by the data fidelity term. We propose an algorithm, Fast Non Convex Reweighted (FNCR), where the constrained problem is solved by a reweighting scheme, as a strategy to overcome the non-convexity of the objective function, with an adaptive adjustment of the penalization parameter. We propose a fast iterative algorithm and we can prove that it converges to a local minimum because the constrained problem satisfies the Kurdyka-Lojasiewicz property. Moreover the adaptation of non convex l0 approximation and penalization parameters, by means of a continuation technique, allows us to obtain good quality solutions, avoiding to get stuck in unwanted local minima. Some numerical experiments performed on MRI sub-sampled data show the efficiency of the algorithm and the accuracy of the solution.

Effective dimensional reduction algorithm for eigenvalue problems for thin elastic structures: A paradigm in three dimensions

PubMed Central

Ovtchinnikov, Evgueni E.; Xanthis, Leonidas S.

2000-01-01

We present a methodology for the efficient numerical solution of eigenvalue problems of full three-dimensional elasticity for thin elastic structures, such as shells, plates and rods of arbitrary geometry, discretized by the finite element method. Such problems are solved by iterative methods, which, however, are known to suffer from slow convergence or even convergence failure, when the thickness is small. In this paper we show an effective way of resolving this difficulty by invoking a special preconditioning technique associated with the effective dimensional reduction algorithm (EDRA). As an example, we present an algorithm for computing the minimal eigenvalue of a thin elastic plate and we show both theoretically and numerically that it is robust with respect to both the thickness and discretization parameters, i.e. the convergence does not deteriorate with diminishing thickness or mesh refinement. This robustness is sine qua non for the efficient computation of large-scale eigenvalue problems for thin elastic structures. PMID:10655469

A novel hybrid genetic algorithm to solve the make-to-order sequence-dependent flow-shop scheduling problem

NASA Astrophysics Data System (ADS)

Mirabi, Mohammad; Fatemi Ghomi, S. M. T.; Jolai, F.

2014-04-01

Flow-shop scheduling problem (FSP) deals with the scheduling of a set of n jobs that visit a set of m machines in the same order. As the FSP is NP-hard, there is no efficient algorithm to reach the optimal solution of the problem. To minimize the holding, delay and setup costs of large permutation flow-shop scheduling problems with sequence-dependent setup times on each machine, this paper develops a novel hybrid genetic algorithm (HGA) with three genetic operators. Proposed HGA applies a modified approach to generate a pool of initial solutions, and also uses an improved heuristic called the iterated swap procedure to improve the initial solutions. We consider the make-to-order production approach that some sequences between jobs are assumed as tabu based on maximum allowable setup cost. In addition, the results are compared to some recently developed heuristics and computational experimental results show that the proposed HGA performs very competitively with respect to accuracy and efficiency of solution.

Stochastic Spectral Descent for Discrete Graphical Models

DOE PAGES

Carlson, David; Hsieh, Ya-Ping; Collins, Edo; ...

2015-12-14

Interest in deep probabilistic graphical models has in-creased in recent years, due to their state-of-the-art performance on many machine learning applications. Such models are typically trained with the stochastic gradient method, which can take a significant number of iterations to converge. Since the computational cost of gradient estimation is prohibitive even for modestly sized models, training becomes slow and practically usable models are kept small. In this paper we propose a new, largely tuning-free algorithm to address this problem. Our approach derives novel majorization bounds based on the Schatten- norm. Intriguingly, the minimizers of these bounds can be interpreted asmore » gradient methods in a non-Euclidean space. We thus propose using a stochastic gradient method in non-Euclidean space. We both provide simple conditions under which our algorithm is guaranteed to converge, and demonstrate empirically that our algorithm leads to dramatically faster training and improved predictive ability compared to stochastic gradient descent for both directed and undirected graphical models.« less

Algorithms for bioluminescence tomography incorporating anatomical information and reconstruction of tissue optical properties

PubMed Central

Naser, Mohamed A.; Patterson, Michael S.

2010-01-01

Reconstruction algorithms are presented for a two-step solution of the bioluminescence tomography (BLT) problem. In the first step, a priori anatomical information provided by x-ray computed tomography or by other methods is used to solve the continuous wave (cw) diffuse optical tomography (DOT) problem. A Taylor series expansion approximates the light fluence rate dependence on the optical properties of each region where first and second order direct derivatives of the light fluence rate with respect to scattering and absorption coefficients are obtained and used for the reconstruction. In the second step, the reconstructed optical properties at different wavelengths are used to calculate the Green’s function of the system. Then an iterative minimization solution based on the L1 norm shrinks the permissible regions where the sources are allowed by selecting points with higher probability to contribute to the source distribution. This provides an efficient BLT reconstruction algorithm with the ability to determine relative source magnitudes and positions in the presence of noise. PMID:21258486

Blind One-Bit Compressive Sampling

DTIC Science & Technology

2013-01-17

14] Q. Li, C. A. Micchelli, L. Shen, and Y. Xu, A proximity algorithm accelerated by Gauss - Seidel iterations for L1/TV denoising models, Inverse...methods for nonconvex optimization on the unit sphere and has a provable convergence guarantees. Binary iterative hard thresholding (BIHT) algorithms were... Convergence analysis of the algorithm is presented. Our approach is to obtain a sequence of optimization problems by successively approximating the ℓ0

Iterative Importance Sampling Algorithms for Parameter Estimation

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

Grout, Ray W; Morzfeld, Matthias; Day, Marcus S.

In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov chain Monte Carlo (MCMC) is often used for the numerical solution of such problems. An alternative to MCMC is importance sampling, which can exhibit near perfect scaling with the number of cores on high performance computing systems because samples are drawn independently. However, finding a suitable proposal distribution is a challenging task. Several sampling algorithms have been proposed over the past years that take an iterative approach to constructing a proposal distribution. We investigate the applicabilitymore » of such algorithms by applying them to two realistic and challenging test problems, one in subsurface flow, and one in combustion modeling. More specifically, we implement importance sampling algorithms that iterate over the mean and covariance matrix of Gaussian or multivariate t-proposal distributions. Our implementation leverages massively parallel computers, and we present strategies to initialize the iterations using 'coarse' MCMC runs or Gaussian mixture models.« less

Iterative cross section sequence graph for handwritten character segmentation.

PubMed

Dawoud, Amer

2007-08-01

The iterative cross section sequence graph (ICSSG) is an algorithm for handwritten character segmentation. It expands the cross section sequence graph concept by applying it iteratively at equally spaced thresholds. The iterative thresholding reduces the effect of information loss associated with image binarization. ICSSG preserves the characters' skeletal structure by preventing the interference of pixels that causes flooding of adjacent characters' segments. Improving the structural quality of the characters' skeleton facilitates better feature extraction and classification, which improves the overall performance of optical character recognition (OCR). Experimental results showed significant improvements in OCR recognition rates compared to other well-established segmentation algorithms.

Accurate low-dose iterative CT reconstruction from few projections by Generalized Anisotropic Total Variation minimization for industrial CT.

PubMed

Debatin, Maurice; Hesser, Jürgen

2015-01-01

Reducing the amount of time for data acquisition and reconstruction in industrial CT decreases the operation time of the X-ray machine and therefore increases the sales. This can be achieved by reducing both, the dose and the pulse length of the CT system and the number of projections for the reconstruction, respectively. In this paper, a novel generalized Anisotropic Total Variation regularization for under-sampled, low-dose iterative CT reconstruction is discussed and compared to the standard methods, Total Variation, Adaptive weighted Total Variation and Filtered Backprojection. The novel regularization function uses a priori information about the Gradient Magnitude Distribution of the scanned object for the reconstruction. We provide a general parameterization scheme and evaluate the efficiency of our new algorithm for different noise levels and different number of projection views. When noise is not present, error-free reconstructions are achievable for AwTV and GATV from 40 projections. In cases where noise is simulated, our strategy achieves a Relative Root Mean Square Error that is up to 11 times lower than Total Variation-based and up to 4 times lower than AwTV-based iterative statistical reconstruction (e.g. for a SNR of 223 and 40 projections). To obtain the same reconstruction quality as achieved by Total Variation, the projection number and the pulse length, and the acquisition time and the dose respectively can be reduced by a factor of approximately 3.5, when AwTV is used and a factor of approximately 6.7, when our proposed algorithm is used.

Quantitative X-ray fluorescence computed tomography for low-Z samples using an iterative absorption correction algorithm

NASA Astrophysics Data System (ADS)

Huang, Rong; Limburg, Karin; Rohtla, Mehis

2017-05-01

X-ray fluorescence computed tomography is often used to measure trace element distributions within low-Z samples, using algorithms capable of X-ray absorption correction when sample self-absorption is not negligible. Its reconstruction is more complicated compared to transmission tomography, and therefore not widely used. We describe in this paper a very practical iterative method that uses widely available transmission tomography reconstruction software for fluorescence tomography. With this method, sample self-absorption can be corrected not only for the absorption within the measured layer but also for the absorption by material beyond that layer. By combining tomography with analysis for scanning X-ray fluorescence microscopy, absolute concentrations of trace elements can be obtained. By using widely shared software, we not only minimized the coding, took advantage of computing efficiency of fast Fourier transform in transmission tomography software, but also thereby accessed well-developed data processing tools coming with well-known and reliable software packages. The convergence of the iterations was also carefully studied for fluorescence of different attenuation lengths. As an example, fish eye lenses could provide valuable information about fish life-history and endured environmental conditions. Given the lens's spherical shape and sometimes the short distance from sample to detector for detecting low concentration trace elements, its tomography data are affected by absorption related to material beyond the measured layer but can be reconstructed well with our method. Fish eye lens tomography results are compared with sliced lens 2D fluorescence mapping with good agreement, and with tomography providing better spatial resolution.

Seismic tomography of the southern California crust based on spectral-element and adjoint methods

NASA Astrophysics Data System (ADS)

Tape, Carl; Liu, Qinya; Maggi, Alessia; Tromp, Jeroen

2010-01-01

We iteratively improve a 3-D tomographic model of the southern California crust using numerical simulations of seismic wave propagation based on a spectral-element method (SEM) in combination with an adjoint method. The initial 3-D model is provided by the Southern California Earthquake Center. The data set comprises three-component seismic waveforms (i.e. both body and surface waves), filtered over the period range 2-30 s, from 143 local earthquakes recorded by a network of 203 stations. Time windows for measurements are automatically selected by the FLEXWIN algorithm. The misfit function in the tomographic inversion is based on frequency-dependent multitaper traveltime differences. The gradient of the misfit function and related finite-frequency sensitivity kernels for each earthquake are computed using an adjoint technique. The kernels are combined using a source subspace projection method to compute a model update at each iteration of a gradient-based minimization algorithm. The inversion involved 16 iterations, which required 6800 wavefield simulations. The new crustal model, m16, is described in terms of independent shear (VS) and bulk-sound (VB) wave speed variations. It exhibits strong heterogeneity, including local changes of +/-30 per cent with respect to the initial 3-D model. The model reveals several features that relate to geological observations, such as sedimentary basins, exhumed batholiths, and contrasting lithologies across faults. The quality of the new model is validated by quantifying waveform misfits of full-length seismograms from 91 earthquakes that were not used in the tomographic inversion. The new model provides more accurate synthetic seismograms that will benefit seismic hazard assessment.

Adjoint Tomography of the Southern California Crust (Invited) (Invited)

NASA Astrophysics Data System (ADS)

Tape, C.; Liu, Q.; Maggi, A.; Tromp, J.

2009-12-01

We iteratively improve a three-dimensional tomographic model of the southern California crust using numerical simulations of seismic wave propagation based on a spectral-element method (SEM) in combination with an adjoint method. The initial 3D model is provided by the Southern California Earthquake Center. The dataset comprises three-component seismic waveforms (i.e. both body and surface waves), filtered over the period range 2-30 s, from 143 local earthquakes recorded by a network of 203 stations. Time windows for measurements are automatically selected by the FLEXWIN algorithm. The misfit function in the tomographic inversion is based on frequency-dependent multitaper traveltime differences. The gradient of the misfit function and related finite-frequency sensitivity kernels for each earthquake are computed using an adjoint technique. The kernels are combined using a source subspace projection method to compute a model update at each iteration of a gradient-based minimization algorithm. The inversion involved 16 iterations, which required 6800 wavefield simulations and a total of 0.8 million CPU hours. The new crustal model, m16, is described in terms of independent shear (Vs) and bulk-sound (Vb) wavespeed variations. It exhibits strong heterogeneity, including local changes of ±30% with respect to the initial 3D model. The model reveals several features that relate to geologic observations, such as sedimentary basins, exhumed batholiths, and contrasting lithologies across faults. The quality of the new model is validated by quantifying waveform misfits of full-length seismograms from 91 earthquakes that were not used in the tomographic inversion. The new model provides more accurate synthetic seismograms that will benefit seismic hazard assessment.

Performance analysis of improved iterated cubature Kalman filter and its application to GNSS/INS.

PubMed

Cui, Bingbo; Chen, Xiyuan; Xu, Yuan; Huang, Haoqian; Liu, Xiao

2017-01-01

In order to improve the accuracy and robustness of GNSS/INS navigation system, an improved iterated cubature Kalman filter (IICKF) is proposed by considering the state-dependent noise and system uncertainty. First, a simplified framework of iterated Gaussian filter is derived by using damped Newton-Raphson algorithm and online noise estimator. Then the effect of state-dependent noise coming from iterated update is analyzed theoretically, and an augmented form of CKF algorithm is applied to improve the estimation accuracy. The performance of IICKF is verified by field test and numerical simulation, and results reveal that, compared with non-iterated filter, iterated filter is less sensitive to the system uncertainty, and IICKF improves the accuracy of yaw, roll and pitch by 48.9%, 73.1% and 83.3%, respectively, compared with traditional iterated KF. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

a Weighted Closed-Form Solution for Rgb-D Data Registration

NASA Astrophysics Data System (ADS)

Vestena, K. M.; Dos Santos, D. R.; Oilveira, E. M., Jr.; Pavan, N. L.; Khoshelham, K.

2016-06-01

Existing 3D indoor mapping of RGB-D data are prominently point-based and feature-based methods. In most cases iterative closest point (ICP) and its variants are generally used for pairwise registration process. Considering that the ICP algorithm requires an relatively accurate initial transformation and high overlap a weighted closed-form solution for RGB-D data registration is proposed. In this solution, we weighted and normalized the 3D points based on the theoretical random errors and the dual-number quaternions are used to represent the 3D rigid body motion. Basically, dual-number quaternions provide a closed-form solution by minimizing a cost function. The most important advantage of the closed-form solution is that it provides the optimal transformation in one-step, it does not need to calculate good initial estimates and expressively decreases the demand for computer resources in contrast to the iterative method. Basically, first our method exploits RGB information. We employed a scale invariant feature transformation (SIFT) for extracting, detecting, and matching features. It is able to detect and describe local features that are invariant to scaling and rotation. To detect and filter outliers, we used random sample consensus (RANSAC) algorithm, jointly with an statistical dispersion called interquartile range (IQR). After, a new RGB-D loop-closure solution is implemented based on the volumetric information between pair of point clouds and the dispersion of the random errors. The loop-closure consists to recognize when the sensor revisits some region. Finally, a globally consistent map is created to minimize the registration errors via a graph-based optimization. The effectiveness of the proposed method is demonstrated with a Kinect dataset. The experimental results show that the proposed method can properly map the indoor environment with an absolute accuracy around 1.5% of the travel of a trajectory.

Histogram-driven cupping correction (HDCC) in CT

NASA Astrophysics Data System (ADS)

Kyriakou, Y.; Meyer, M.; Lapp, R.; Kalender, W. A.

2010-04-01

Typical cupping correction methods are pre-processing methods which require either pre-calibration measurements or simulations of standard objects to approximate and correct for beam hardening and scatter. Some of them require the knowledge of spectra, detector characteristics, etc. The aim of this work was to develop a practical histogram-driven cupping correction (HDCC) method to post-process the reconstructed images. We use a polynomial representation of the raw-data generated by forward projection of the reconstructed images; forward and backprojection are performed on graphics processing units (GPU). The coefficients of the polynomial are optimized using a simplex minimization of the joint entropy of the CT image and its gradient. The algorithm was evaluated using simulations and measurements of homogeneous and inhomogeneous phantoms. For the measurements a C-arm flat-detector CT (FD-CT) system with a 30×40 cm2 detector, a kilovoltage on board imager (radiation therapy simulator) and a micro-CT system were used. The algorithm reduced cupping artifacts both in simulations and measurements using a fourth-order polynomial and was in good agreement to the reference. The minimization algorithm required less than 70 iterations to adjust the coefficients only performing a linear combination of basis images, thus executing without time consuming operations. HDCC reduced cupping artifacts without the necessity of pre-calibration or other scan information enabling a retrospective improvement of CT image homogeneity. However, the method can work with other cupping correction algorithms or in a calibration manner, as well.

Plenoptic Image Motion Deblurring.

PubMed

Chandramouli, Paramanand; Jin, Meiguang; Perrone, Daniele; Favaro, Paolo

2018-04-01

We propose a method to remove motion blur in a single light field captured with a moving plenoptic camera. Since motion is unknown, we resort to a blind deconvolution formulation, where one aims to identify both the blur point spread function and the latent sharp image. Even in the absence of motion, light field images captured by a plenoptic camera are affected by a non-trivial combination of both aliasing and defocus, which depends on the 3D geometry of the scene. Therefore, motion deblurring algorithms designed for standard cameras are not directly applicable. Moreover, many state of the art blind deconvolution algorithms are based on iterative schemes, where blurry images are synthesized through the imaging model. However, current imaging models for plenoptic images are impractical due to their high dimensionality. We observe that plenoptic cameras introduce periodic patterns that can be exploited to obtain highly parallelizable numerical schemes to synthesize images. These schemes allow extremely efficient GPU implementations that enable the use of iterative methods. We can then cast blind deconvolution of a blurry light field image as a regularized energy minimization to recover a sharp high-resolution scene texture and the camera motion. Furthermore, the proposed formulation can handle non-uniform motion blur due to camera shake as demonstrated on both synthetic and real light field data.

Robust non-rigid registration algorithm based on local affine registration

NASA Astrophysics Data System (ADS)

Wu, Liyang; Xiong, Lei; Du, Shaoyi; Bi, Duyan; Fang, Ting; Liu, Kun; Wu, Dongpeng

2018-04-01

Aiming at the problem that the traditional point set non-rigid registration algorithm has low precision and slow convergence speed for complex local deformation data, this paper proposes a robust non-rigid registration algorithm based on local affine registration. The algorithm uses a hierarchical iterative method to complete the point set non-rigid registration from coarse to fine. In each iteration, the sub data point sets and sub model point sets are divided and the shape control points of each sub point set are updated. Then we use the control point guided affine ICP algorithm to solve the local affine transformation between the corresponding sub point sets. Next, the local affine transformation obtained by the previous step is used to update the sub data point sets and their shape control point sets. When the algorithm reaches the maximum iteration layer K, the loop ends and outputs the updated sub data point sets. Experimental results demonstrate that the accuracy and convergence of our algorithm are greatly improved compared with the traditional point set non-rigid registration algorithms.

Modeling design iteration in product design and development and its solution by a novel artificial bee colony algorithm.

PubMed

Chen, Tinggui; Xiao, Renbin

2014-01-01

Due to fierce market competition, how to improve product quality and reduce development cost determines the core competitiveness of enterprises. However, design iteration generally causes increases of product cost and delays of development time as well, so how to identify and model couplings among tasks in product design and development has become an important issue for enterprises to settle. In this paper, the shortcomings existing in WTM model are discussed and tearing approach as well as inner iteration method is used to complement the classic WTM model. In addition, the ABC algorithm is also introduced to find out the optimal decoupling schemes. In this paper, firstly, tearing approach and inner iteration method are analyzed for solving coupled sets. Secondly, a hybrid iteration model combining these two technologies is set up. Thirdly, a high-performance swarm intelligence algorithm, artificial bee colony, is adopted to realize problem-solving. Finally, an engineering design of a chemical processing system is given in order to verify its reasonability and effectiveness.

Adaptive Dynamic Programming for Discrete-Time Zero-Sum Games.

PubMed

Wei, Qinglai; Liu, Derong; Lin, Qiao; Song, Ruizhuo

2018-04-01

In this paper, a novel adaptive dynamic programming (ADP) algorithm, called "iterative zero-sum ADP algorithm," is developed to solve infinite-horizon discrete-time two-player zero-sum games of nonlinear systems. The present iterative zero-sum ADP algorithm permits arbitrary positive semidefinite functions to initialize the upper and lower iterations. A novel convergence analysis is developed to guarantee the upper and lower iterative value functions to converge to the upper and lower optimums, respectively. When the saddle-point equilibrium exists, it is emphasized that both the upper and lower iterative value functions are proved to converge to the optimal solution of the zero-sum game, where the existence criteria of the saddle-point equilibrium are not required. If the saddle-point equilibrium does not exist, the upper and lower optimal performance index functions are obtained, respectively, where the upper and lower performance index functions are proved to be not equivalent. Finally, simulation results and comparisons are shown to illustrate the performance of the present method.

Effective channel estimation and efficient symbol detection for multi-input multi-output underwater acoustic communications

NASA Astrophysics Data System (ADS)

Ling, Jun

Achieving reliable underwater acoustic communications (UAC) has long been recognized as a challenging problem owing to the scarce bandwidth available and the reverberant spread in both time and frequency domains. To pursue high data rates, we consider a multi-input multi-output (MIMO) UAC system, and our focus is placed on two main issues regarding a MIMO UAC system: (1) channel estimation, which involves the design of the training sequences and the development of a reliable channel estimation algorithm, and (2) symbol detection, which requires interference cancelation schemes due to simultaneous transmission from multiple transducers. To enhance channel estimation performance, we present a cyclic approach for designing training sequences with good auto- and cross-correlation properties, and a channel estimation algorithm called the iterative adaptive approach (IAA). Sparse channel estimates can be obtained by combining IAA with the Bayesian information criterion (BIC). Moreover, we present sparse learning via iterative minimization (SLIM) and demonstrate that SLIM gives similar performance to IAA but at a much lower computational cost. Furthermore, an extension of the SLIM algorithm is introduced to estimate the sparse and frequency modulated acoustic channels. The extended algorithm is referred to as generalization of SLIM (GoSLIM). Regarding symbol detection, a linear minimum mean-squared error based detection scheme, called RELAX-BLAST, which is a combination of vertical Bell Labs layered space-time (V-BLAST) algorithm and the cyclic principle of the RELAX algorithm, is presented and it is shown that RELAX-BLAST outperforms V-BLAST. We show that RELAX-BLAST can be implemented efficiently by making use of the conjugate gradient method and diagonalization properties of circulant matrices. This fast implementation approach requires only simple fast Fourier transform operations and facilitates parallel implementations. The effectiveness of the proposed MIMO schemes is verified by both computer simulations and experimental results obtained by analyzing the measurements acquired in multiple in-water experiments.

A promising limited angular computed tomography reconstruction via segmentation based regional enhancement and total variation minimization

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

Zhang, Wenkun; Zhang, Hanming; Li, Lei

2016-08-15

X-ray computed tomography (CT) is a powerful and common inspection technique used for the industrial non-destructive testing. However, large-sized and heavily absorbing objects cause the formation of artifacts because of either the lack of specimen penetration in specific directions or the acquisition of data from only a limited angular range of views. Although the sparse optimization-based methods, such as the total variation (TV) minimization method, can suppress artifacts to some extent, reconstructing the images such that they converge to accurate values remains difficult because of the deficiency in continuous angular data and inconsistency in the projections. To address this problem,more » we use the idea of regional enhancement of the true values and suppression of the illusory artifacts outside the region to develop an efficient iterative algorithm. This algorithm is based on the combination of regional enhancement of the true values and TV minimization for the limited angular reconstruction. In this algorithm, the segmentation approach is introduced to distinguish the regions of different image knowledge and generate the support mask of the image. A new regularization term, which contains the support knowledge to enhance the true values of the image, is incorporated into the objective function. Then, the proposed optimization model is solved by variable splitting and the alternating direction method efficiently. A compensation approach is also designed to extract useful information from the initial projections and thus reduce false segmentation result and correct the segmentation support and the segmented image. The results obtained from comparing both simulation studies and real CT data set reconstructions indicate that the proposed algorithm generates a more accurate image than do the other reconstruction methods. The experimental results show that this algorithm can produce high-quality reconstructed images for the limited angular reconstruction and suppress the illusory artifacts caused by the deficiency in valid data.« less

A promising limited angular computed tomography reconstruction via segmentation based regional enhancement and total variation minimization

NASA Astrophysics Data System (ADS)

Zhang, Wenkun; Zhang, Hanming; Li, Lei; Wang, Linyuan; Cai, Ailong; Li, Zhongguo; Yan, Bin

2016-08-01

X-ray computed tomography (CT) is a powerful and common inspection technique used for the industrial non-destructive testing. However, large-sized and heavily absorbing objects cause the formation of artifacts because of either the lack of specimen penetration in specific directions or the acquisition of data from only a limited angular range of views. Although the sparse optimization-based methods, such as the total variation (TV) minimization method, can suppress artifacts to some extent, reconstructing the images such that they converge to accurate values remains difficult because of the deficiency in continuous angular data and inconsistency in the projections. To address this problem, we use the idea of regional enhancement of the true values and suppression of the illusory artifacts outside the region to develop an efficient iterative algorithm. This algorithm is based on the combination of regional enhancement of the true values and TV minimization for the limited angular reconstruction. In this algorithm, the segmentation approach is introduced to distinguish the regions of different image knowledge and generate the support mask of the image. A new regularization term, which contains the support knowledge to enhance the true values of the image, is incorporated into the objective function. Then, the proposed optimization model is solved by variable splitting and the alternating direction method efficiently. A compensation approach is also designed to extract useful information from the initial projections and thus reduce false segmentation result and correct the segmentation support and the segmented image. The results obtained from comparing both simulation studies and real CT data set reconstructions indicate that the proposed algorithm generates a more accurate image than do the other reconstruction methods. The experimental results show that this algorithm can produce high-quality reconstructed images for the limited angular reconstruction and suppress the illusory artifacts caused by the deficiency in valid data.

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes

NASA Technical Reports Server (NTRS)

Lin, Shu

1998-01-01

A code trellis is a graphical representation of a code, block or convolutional, in which every path represents a codeword (or a code sequence for a convolutional code). This representation makes it possible to implement Maximum Likelihood Decoding (MLD) of a code with reduced decoding complexity. The most well known trellis-based MLD algorithm is the Viterbi algorithm. The trellis representation was first introduced and used for convolutional codes [23]. This representation, together with the Viterbi decoding algorithm, has resulted in a wide range of applications of convolutional codes for error control in digital communications over the last two decades. There are two major reasons for this inactive period of research in this area. First, most coding theorists at that time believed that block codes did not have simple trellis structure like convolutional codes and maximum likelihood decoding of linear block codes using the Viterbi algorithm was practically impossible, except for very short block codes. Second, since almost all of the linear block codes are constructed algebraically or based on finite geometries, it was the belief of many coding theorists that algebraic decoding was the only way to decode these codes. These two reasons seriously hindered the development of efficient soft-decision decoding methods for linear block codes and their applications to error control in digital communications. This led to a general belief that block codes are inferior to convolutional codes and hence, that they were not useful. Chapter 2 gives a brief review of linear block codes. The goal is to provide the essential background material for the development of trellis structure and trellis-based decoding algorithms for linear block codes in the later chapters. Chapters 3 through 6 present the fundamental concepts, finite-state machine model, state space formulation, basic structural properties, state labeling, construction procedures, complexity, minimality, and sectionalization of trellises. Chapter 7 discusses trellis decomposition and subtrellises for low-weight codewords. Chapter 8 first presents well known methods for constructing long powerful codes from short component codes or component codes of smaller dimensions, and then provides methods for constructing their trellises which include Shannon and Cartesian product techniques. Chapter 9 deals with convolutional codes, puncturing, zero-tail termination and tail-biting.Chapters 10 through 13 present various trellis-based decoding algorithms, old and new. Chapter 10 first discusses the application of the well known Viterbi decoding algorithm to linear block codes, optimum sectionalization of a code trellis to minimize computation complexity, and design issues for IC (integrated circuit) implementation of a Viterbi decoder. Then it presents a new decoding algorithm for convolutional codes, named Differential Trellis Decoding (DTD) algorithm. Chapter 12 presents a suboptimum reliability-based iterative decoding algorithm with a low-weight trellis search for the most likely codeword. This decoding algorithm provides a good trade-off between error performance and decoding complexity. All the decoding algorithms presented in Chapters 10 through 12 are devised to minimize word error probability. Chapter 13 presents decoding algorithms that minimize bit error probability and provide the corresponding soft (reliability) information at the output of the decoder. Decoding algorithms presented are the MAP (maximum a posteriori probability) decoding algorithm and the Soft-Output Viterbi Algorithm (SOVA) algorithm. Finally, the minimization of bit error probability in trellis-based MLD is discussed.

A multiresolution approach to iterative reconstruction algorithms in X-ray computed tomography.

PubMed

De Witte, Yoni; Vlassenbroeck, Jelle; Van Hoorebeke, Luc

2010-09-01

In computed tomography, the application of iterative reconstruction methods in practical situations is impeded by their high computational demands. Especially in high resolution X-ray computed tomography, where reconstruction volumes contain a high number of volume elements (several giga voxels), this computational burden prevents their actual breakthrough. Besides the large amount of calculations, iterative algorithms require the entire volume to be kept in memory during reconstruction, which quickly becomes cumbersome for large data sets. To overcome this obstacle, we present a novel multiresolution reconstruction, which greatly reduces the required amount of memory without significantly affecting the reconstructed image quality. It is shown that, combined with an efficient implementation on a graphical processing unit, the multiresolution approach enables the application of iterative algorithms in the reconstruction of large volumes at an acceptable speed using only limited resources.

Spectral Regularization Algorithms for Learning Large Incomplete Matrices.

PubMed

Mazumder, Rahul; Hastie, Trevor; Tibshirani, Robert

2010-03-01

We use convex relaxation techniques to provide a sequence of regularized low-rank solutions for large-scale matrix completion problems. Using the nuclear norm as a regularizer, we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the nuclear norm. Our algorithm Soft-Impute iteratively replaces the missing elements with those obtained from a soft-thresholded SVD. With warm starts this allows us to efficiently compute an entire regularization path of solutions on a grid of values of the regularization parameter. The computationally intensive part of our algorithm is in computing a low-rank SVD of a dense matrix. Exploiting the problem structure, we show that the task can be performed with a complexity linear in the matrix dimensions. Our semidefinite-programming algorithm is readily scalable to large matrices: for example it can obtain a rank-80 approximation of a 10(6) × 10(6) incomplete matrix with 10(5) observed entries in 2.5 hours, and can fit a rank 40 approximation to the full Netflix training set in 6.6 hours. Our methods show very good performance both in training and test error when compared to other competitive state-of-the art techniques.

Spectral Regularization Algorithms for Learning Large Incomplete Matrices

PubMed Central

Mazumder, Rahul; Hastie, Trevor; Tibshirani, Robert

2010-01-01

We use convex relaxation techniques to provide a sequence of regularized low-rank solutions for large-scale matrix completion problems. Using the nuclear norm as a regularizer, we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the nuclear norm. Our algorithm Soft-Impute iteratively replaces the missing elements with those obtained from a soft-thresholded SVD. With warm starts this allows us to efficiently compute an entire regularization path of solutions on a grid of values of the regularization parameter. The computationally intensive part of our algorithm is in computing a low-rank SVD of a dense matrix. Exploiting the problem structure, we show that the task can be performed with a complexity linear in the matrix dimensions. Our semidefinite-programming algorithm is readily scalable to large matrices: for example it can obtain a rank-80 approximation of a 106 × 106 incomplete matrix with 105 observed entries in 2.5 hours, and can fit a rank 40 approximation to the full Netflix training set in 6.6 hours. Our methods show very good performance both in training and test error when compared to other competitive state-of-the art techniques. PMID:21552465

Stokes space modulation format classification based on non-iterative clustering algorithm for coherent optical receivers.

PubMed

Mai, Xiaofeng; Liu, Jie; Wu, Xiong; Zhang, Qun; Guo, Changjian; Yang, Yanfu; Li, Zhaohui

2017-02-06

A Stokes-space modulation format classification (MFC) technique is proposed for coherent optical receivers by using a non-iterative clustering algorithm. In the clustering algorithm, two simple parameters are calculated to help find the density peaks of the data points in Stokes space and no iteration is required. Correct MFC can be realized in numerical simulations among PM-QPSK, PM-8QAM, PM-16QAM, PM-32QAM and PM-64QAM signals within practical optical signal-to-noise ratio (OSNR) ranges. The performance of the proposed MFC algorithm is also compared with those of other schemes based on clustering algorithms. The simulation results show that good classification performance can be achieved using the proposed MFC scheme with moderate time complexity. Proof-of-concept experiments are finally implemented to demonstrate MFC among PM-QPSK/16QAM/64QAM signals, which confirm the feasibility of our proposed MFC scheme.

Self-adaptive predictor-corrector algorithm for static nonlinear structural analysis

NASA Technical Reports Server (NTRS)

Padovan, J.

1981-01-01

A multiphase selfadaptive predictor corrector type algorithm was developed. This algorithm enables the solution of highly nonlinear structural responses including kinematic, kinetic and material effects as well as pro/post buckling behavior. The strategy involves three main phases: (1) the use of a warpable hyperelliptic constraint surface which serves to upperbound dependent iterate excursions during successive incremental Newton Ramphson (INR) type iterations; (20 uses an energy constraint to scale the generation of successive iterates so as to maintain the appropriate form of local convergence behavior; (3) the use of quality of convergence checks which enable various self adaptive modifications of the algorithmic structure when necessary. The restructuring is achieved by tightening various conditioning parameters as well as switch to different algorithmic levels to improve the convergence process. The capabilities of the procedure to handle various types of static nonlinear structural behavior are illustrated.

Multi-limit unsymmetrical MLIBD image restoration algorithm

NASA Astrophysics Data System (ADS)

Yang, Yang; Cheng, Yiping; Chen, Zai-wang; Bo, Chen

2012-11-01

A novel multi-limit unsymmetrical iterative blind deconvolution(MLIBD) algorithm was presented to enhance the performance of adaptive optics image restoration.The algorithm enhances the reliability of iterative blind deconvolution by introducing the bandwidth limit into the frequency domain of point spread(PSF),and adopts the PSF dynamic support region estimation to improve the convergence speed.The unsymmetrical factor is automatically computed to advance its adaptivity.Image deconvolution comparing experiments between Richardson-Lucy IBD and MLIBD were done,and the result indicates that the iteration number is reduced by 22.4% and the peak signal-to-noise ratio is improved by 10.18dB with MLIBD method. The performance of MLIBD algorithm is outstanding in the images restoration the FK5-857 adaptive optics and the double-star adaptive optics.

Richardson-Lucy/maximum likelihood image restoration algorithm for fluorescence microscopy: further testing.

PubMed

Holmes, T J; Liu, Y H

1989-11-15

A maximum likelihood based iterative algorithm adapted from nuclear medicine imaging for noncoherent optical imaging was presented in a previous publication with some initial computer-simulation testing. This algorithm is identical in form to that previously derived in a different way by W. H. Richardson "Bayesian-Based Iterative Method of Image Restoration," J. Opt. Soc. Am. 62, 55-59 (1972) and L. B. Lucy "An Iterative Technique for the Rectification of Observed Distributions," Astron. J. 79, 745-765 (1974). Foreseen applications include superresolution and 3-D fluorescence microscopy. This paper presents further simulation testing of this algorithm and a preliminary experiment with a defocused camera. The simulations show quantified resolution improvement as a function of iteration number, and they show qualitatively the trend in limitations on restored resolution when noise is present in the data. Also shown are results of a simulation in restoring missing-cone information for 3-D imaging. Conclusions are in support of the feasibility of using these methods with real systems, while computational cost and timing estimates indicate that it should be realistic to implement these methods. Itis suggested in the Appendix that future extensions to the maximum likelihood based derivation of this algorithm will address some of the limitations that are experienced with the nonextended form of the algorithm presented here.

A fast iterative recursive least squares algorithm for Wiener model identification of highly nonlinear systems.

PubMed

Kazemi, Mahdi; Arefi, Mohammad Mehdi

2017-03-01

In this paper, an online identification algorithm is presented for nonlinear systems in the presence of output colored noise. The proposed method is based on extended recursive least squares (ERLS) algorithm, where the identified system is in polynomial Wiener form. To this end, an unknown intermediate signal is estimated by using an inner iterative algorithm. The iterative recursive algorithm adaptively modifies the vector of parameters of the presented Wiener model when the system parameters vary. In addition, to increase the robustness of the proposed method against variations, a robust RLS algorithm is applied to the model. Simulation results are provided to show the effectiveness of the proposed approach. Results confirm that the proposed method has fast convergence rate with robust characteristics, which increases the efficiency of the proposed model and identification approach. For instance, the FIT criterion will be achieved 92% in CSTR process where about 400 data is used. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

A New Pivoting and Iterative Text Detection Algorithm for Biomedical Images

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

Xu, Songhua; Krauthammer, Prof. Michael

2010-01-01

There is interest to expand the reach of literature mining to include the analysis of biomedical images, which often contain a paper's key findings. Examples include recent studies that use Optical Character Recognition (OCR) to extract image text, which is used to boost biomedical image retrieval and classification. Such studies rely on the robust identification of text elements in biomedical images, which is a non-trivial task. In this work, we introduce a new text detection algorithm for biomedical images based on iterative projection histograms. We study the effectiveness of our algorithm by evaluating the performance on a set of manuallymore » labeled random biomedical images, and compare the performance against other state-of-the-art text detection algorithms. We demonstrate that our projection histogram-based text detection approach is well suited for text detection in biomedical images, and that the iterative application of the algorithm boosts performance to an F score of .60. We provide a C++ implementation of our algorithm freely available for academic use.« less

High-speed parallel implementation of a modified PBR algorithm on DSP-based EH topology

NASA Astrophysics Data System (ADS)

Rajan, K.; Patnaik, L. M.; Ramakrishna, J.

1997-08-01

Algebraic Reconstruction Technique (ART) is an age-old method used for solving the problem of three-dimensional (3-D) reconstruction from projections in electron microscopy and radiology. In medical applications, direct 3-D reconstruction is at the forefront of investigation. The simultaneous iterative reconstruction technique (SIRT) is an ART-type algorithm with the potential of generating in a few iterations tomographic images of a quality comparable to that of convolution backprojection (CBP) methods. Pixel-based reconstruction (PBR) is similar to SIRT reconstruction, and it has been shown that PBR algorithms give better quality pictures compared to those produced by SIRT algorithms. In this work, we propose a few modifications to the PBR algorithms. The modified algorithms are shown to give better quality pictures compared to PBR algorithms. The PBR algorithm and the modified PBR algorithms are highly compute intensive, Not many attempts have been made to reconstruct objects in the true 3-D sense because of the high computational overhead. In this study, we have developed parallel two-dimensional (2-D) and 3-D reconstruction algorithms based on modified PBR. We attempt to solve the two problems encountered by the PBR and modified PBR algorithms, i.e., the long computational time and the large memory requirements, by parallelizing the algorithm on a multiprocessor system. We investigate the possible task and data partitioning schemes by exploiting the potential parallelism in the PBR algorithm subject to minimizing the memory requirement. We have implemented an extended hypercube (EH) architecture for the high-speed execution of the 3-D reconstruction algorithm using the commercially available fast floating point digital signal processor (DSP) chips as the processing elements (PEs) and dual-port random access memories (DPR) as channels between the PEs. We discuss and compare the performances of the PBR algorithm on an IBM 6000 RISC workstation, on a Silicon Graphics Indigo 2 workstation, and on an EH system. The results show that an EH(3,1) using DSP chips as PEs executes the modified PBR algorithm about 100 times faster than an LBM 6000 RISC workstation. We have executed the algorithms on a 4-node IBM SP2 parallel computer. The results show that execution time of the algorithm on an EH(3,1) is better than that of a 4-node IBM SP2 system. The speed-up of an EH(3,1) system with eight PEs and one network controller is approximately 7.85.

Sparse Adaptive Iteratively-Weighted Thresholding Algorithm (SAITA) for Lp-Regularization Using the Multiple Sub-Dictionary Representation

PubMed Central

Zhang, Jie; Fan, Shangang; Xiong, Jian; Cheng, Xiefeng; Sari, Hikmet; Adachi, Fumiyuki

2017-01-01

Both L1/2 and L2/3 are two typical non-convex regularizations of Lp (0

Sparse Adaptive Iteratively-Weighted Thresholding Algorithm (SAITA) for Lp-Regularization Using the Multiple Sub-Dictionary Representation.

PubMed

Li, Yunyi; Zhang, Jie; Fan, Shangang; Yang, Jie; Xiong, Jian; Cheng, Xiefeng; Sari, Hikmet; Adachi, Fumiyuki; Gui, Guan

2017-12-15

Both L 1/2 and L 2/3 are two typical non-convex regularizations of L p (0

Space shuttle propulsion parameter estimation using optimal estimation techniques

NASA Technical Reports Server (NTRS)

1983-01-01

The first twelve system state variables are presented with the necessary mathematical developments for incorporating them into the filter/smoother algorithm. Other state variables, i.e., aerodynamic coefficients can be easily incorporated into the estimation algorithm, representing uncertain parameters, but for initial checkout purposes are treated as known quantities. An approach for incorporating the NASA propulsion predictive model results into the optimal estimation algorithm was identified. This approach utilizes numerical derivatives and nominal predictions within the algorithm with global iterations of the algorithm. The iterative process is terminated when the quality of the estimates provided no longer significantly improves.

Exact exchange potential evaluated from occupied Kohn-Sham and Hartree-Fock solutions

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

Cinal, M.; Holas, A.

2011-06-15

The reported algorithm determines the exact exchange potential v{sub x} in an iterative way using energy shifts (ESs) and orbital shifts (OSs) obtained with finite-difference formulas from the solutions (occupied orbitals and their energies) of the Hartree-Fock-like equation and the Kohn-Sham-like equation, the former used for the initial approximation to v{sub x} and the latter for increments of ES and OS due to subsequent changes of v{sub x}. Thus, the need for solution of the differential equations for OSs, used by Kuemmel and Perdew [Phys. Rev. Lett. 90, 043004 (2003)], is bypassed. The iterated exchange potential, expressed in terms ofmore » ESs and OSs, is improved by modifying ESs at odd iteration steps and OSs at even steps. The modification formulas are related to the optimized-effective-potential equation (satisfied at convergence) written as the condition of vanishing density shift (DS). They are obtained, respectively, by enforcing its satisfaction through corrections to approximate OSs and by determining the optimal ESs that minimize the DS norm. The proposed method, successfully tested for several closed-(sub)shell atoms, from Be to Kr, within the density functional theory exchange-only approximation, proves highly efficient. The calculations using the pseudospectral method for representing orbitals give iterative sequences of approximate exchange potentials (starting with the Krieger-Li-Iafrate approximation) that rapidly approach the exact v{sub x} so that, for Ne, Ar, and Zn, the corresponding DS norm becomes less than 10{sup -6} after 13, 13, and 9 iteration steps for a given electron density. In self-consistent density calculations, orbital energies of 10{sup -4} hartree accuracy are obtained for these atoms after, respectively, 9, 12, and 12 density iteration steps, each involving just two steps of v{sub x} iteration, while the accuracy limit of 10{sup -6} to 10{sup -7} hartree is reached after 20 density iterations.« less

Exact exchange potential evaluated from occupied Kohn-Sham and Hartree-Fock solutions

NASA Astrophysics Data System (ADS)

Cinal, M.; Holas, A.

2011-06-01

The reported algorithm determines the exact exchange potential vx in an iterative way using energy shifts (ESs) and orbital shifts (OSs) obtained with finite-difference formulas from the solutions (occupied orbitals and their energies) of the Hartree-Fock-like equation and the Kohn-Sham-like equation, the former used for the initial approximation to vx and the latter for increments of ES and OS due to subsequent changes of vx. Thus, the need for solution of the differential equations for OSs, used by Kümmel and Perdew [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.90.043004 90, 043004 (2003)], is bypassed. The iterated exchange potential, expressed in terms of ESs and OSs, is improved by modifying ESs at odd iteration steps and OSs at even steps. The modification formulas are related to the optimized-effective-potential equation (satisfied at convergence) written as the condition of vanishing density shift (DS). They are obtained, respectively, by enforcing its satisfaction through corrections to approximate OSs and by determining the optimal ESs that minimize the DS norm. The proposed method, successfully tested for several closed-(sub)shell atoms, from Be to Kr, within the density functional theory exchange-only approximation, proves highly efficient. The calculations using the pseudospectral method for representing orbitals give iterative sequences of approximate exchange potentials (starting with the Krieger-Li-Iafrate approximation) that rapidly approach the exact vx so that, for Ne, Ar, and Zn, the corresponding DS norm becomes less than 10-6 after 13, 13, and 9 iteration steps for a given electron density. In self-consistent density calculations, orbital energies of 10-4 hartree accuracy are obtained for these atoms after, respectively, 9, 12, and 12 density iteration steps, each involving just two steps of vx iteration, while the accuracy limit of 10-6 to 10-7 hartree is reached after 20 density iterations.

Iterative inversion of deformation vector fields with feedback control.

PubMed

Dubey, Abhishek; Iliopoulos, Alexandros-Stavros; Sun, Xiaobai; Yin, Fang-Fang; Ren, Lei

2018-05-14

Often, the inverse deformation vector field (DVF) is needed together with the corresponding forward DVF in four-dimesional (4D) reconstruction and dose calculation, adaptive radiation therapy, and simultaneous deformable registration. This study aims at improving both accuracy and efficiency of iterative algorithms for DVF inversion, and advancing our understanding of divergence and latency conditions. We introduce a framework of fixed-point iteration algorithms with active feedback control for DVF inversion. Based on rigorous convergence analysis, we design control mechanisms for modulating the inverse consistency (IC) residual of the current iterate, to be used as feedback into the next iterate. The control is designed adaptively to the input DVF with the objective to enlarge the convergence area and expedite convergence. Three particular settings of feedback control are introduced: constant value over the domain throughout the iteration; alternating values between iteration steps; and spatially variant values. We also introduce three spectral measures of the displacement Jacobian for characterizing a DVF. These measures reveal the critical role of what we term the nontranslational displacement component (NTDC) of the DVF. We carry out inversion experiments with an analytical DVF pair, and with DVFs associated with thoracic CT images of six patients at end of expiration and end of inspiration. The NTDC-adaptive iterations are shown to attain a larger convergence region at a faster pace compared to previous nonadaptive DVF inversion iteration algorithms. By our numerical experiments, alternating control yields smaller IC residuals and inversion errors than constant control. Spatially variant control renders smaller residuals and errors by at least an order of magnitude, compared to other schemes, in no more than 10 steps. Inversion results also show remarkable quantitative agreement with analysis-based predictions. Our analysis captures properties of DVF data associated with clinical CT images, and provides new understanding of iterative DVF inversion algorithms with a simple residual feedback control. Adaptive control is necessary and highly effective in the presence of nonsmall NTDCs. The adaptive iterations or the spectral measures, or both, may potentially be incorporated into deformable image registration methods. © 2018 American Association of Physicists in Medicine.

Robust Transceiver Design for Multiuser MIMO Downlink with Channel Uncertainties

NASA Astrophysics Data System (ADS)

Miao, Wei; Li, Yunzhou; Chen, Xiang; Zhou, Shidong; Wang, Jing

This letter addresses the problem of robust transceiver design for the multiuser multiple-input-multiple-output (MIMO) downlink where the channel state information at the base station (BS) is imperfect. A stochastic approach which minimizes the expectation of the total mean square error (MSE) of the downlink conditioned on the channel estimates under a total transmit power constraint is adopted. The iterative algorithm reported in [2] is improved to handle the proposed robust optimization problem. Simulation results show that our proposed robust scheme effectively reduces the performance loss due to channel uncertainties and outperforms existing methods, especially when the channel errors of the users are different.

Integrating atlas and graph cut methods for right ventricle blood-pool segmentation from cardiac cine MRI

NASA Astrophysics Data System (ADS)

Dangi, Shusil; Linte, Cristian A.

2017-03-01

Segmentation of right ventricle from cardiac MRI images can be used to build pre-operative anatomical heart models to precisely identify regions of interest during minimally invasive therapy. Furthermore, many functional parameters of right heart such as right ventricular volume, ejection fraction, myocardial mass and thickness can also be assessed from the segmented images. To obtain an accurate and computationally efficient segmentation of right ventricle from cardiac cine MRI, we propose a segmentation algorithm formulated as an energy minimization problem in a graph. Shape prior obtained by propagating label from an average atlas using affine registration is incorporated into the graph framework to overcome problems in ill-defined image regions. The optimal segmentation corresponding to the labeling with minimum energy configuration of the graph is obtained via graph-cuts and is iteratively refined to produce the final right ventricle blood pool segmentation. We quantitatively compare the segmentation results obtained from our algorithm to the provided gold-standard expert manual segmentation for 16 cine-MRI datasets available through the MICCAI 2012 Cardiac MR Right Ventricle Segmentation Challenge according to several similarity metrics, including Dice coefficient, Jaccard coefficient, Hausdorff distance, and Mean absolute distance error.

A new approach to blind deconvolution of astronomical images

NASA Astrophysics Data System (ADS)

Vorontsov, S. V.; Jefferies, S. M.

2017-05-01

We readdress the strategy of finding approximate regularized solutions to the blind deconvolution problem, when both the object and the point-spread function (PSF) have finite support. Our approach consists in addressing fixed points of an iteration in which both the object x and the PSF y are approximated in an alternating manner, discarding the previous approximation for x when updating x (similarly for y), and considering the resultant fixed points as candidates for a sensible solution. Alternating approximations are performed by truncated iterative least-squares descents. The number of descents in the object- and in the PSF-space play a role of two regularization parameters. Selection of appropriate fixed points (which may not be unique) is performed by relaxing the regularization gradually, using the previous fixed point as an initial guess for finding the next one, which brings an approximation of better spatial resolution. We report the results of artificial experiments with noise-free data, targeted at examining the potential capability of the technique to deconvolve images of high complexity. We also show the results obtained with two sets of satellite images acquired using ground-based telescopes with and without adaptive optics compensation. The new approach brings much better results when compared with an alternating minimization technique based on positivity-constrained conjugate gradients, where the iterations stagnate when addressing data of high complexity. In the alternating-approximation step, we examine the performance of three different non-blind iterative deconvolution algorithms. The best results are provided by the non-negativity-constrained successive over-relaxation technique (+SOR) supplemented with an adaptive scheduling of the relaxation parameter. Results of comparable quality are obtained with steepest descents modified by imposing the non-negativity constraint, at the expense of higher numerical costs. The Richardson-Lucy (or expectation-maximization) algorithm fails to locate stable fixed points in our experiments, due apparently to inappropriate regularization properties.

Joint design of large-tip-angle parallel RF pulses and blipped gradient trajectories.

PubMed

Cao, Zhipeng; Donahue, Manus J; Ma, Jun; Grissom, William A

2016-03-01

To design multichannel large-tip-angle kT-points and spokes radiofrequency (RF) pulses and gradient waveforms for transmit field inhomogeneity compensation in high field magnetic resonance imaging. An algorithm to design RF subpulse weights and gradient blip areas is proposed to minimize a magnitude least-squares cost function that measures the difference between realized and desired state parameters in the spin domain, and penalizes integrated RF power. The minimization problem is solved iteratively with interleaved target phase updates, RF subpulse weights updates using the conjugate gradient method with optimal control-based derivatives, and gradient blip area updates using the conjugate gradient method. Two-channel parallel transmit simulations and experiments were conducted in phantoms and human subjects at 7 T to demonstrate the method and compare it to small-tip-angle-designed pulses and circularly polarized excitations. The proposed algorithm designed more homogeneous and accurate 180° inversion and refocusing pulses than other methods. It also designed large-tip-angle pulses on multiple frequency bands with independent and joint phase relaxation. Pulses designed by the method improved specificity and contrast-to-noise ratio in a finger-tapping spin echo blood oxygen level dependent functional magnetic resonance imaging study, compared with circularly polarized mode refocusing. A joint RF and gradient waveform design algorithm was proposed and validated to improve large-tip-angle inversion and refocusing at ultrahigh field. © 2015 Wiley Periodicals, Inc.

Limited data tomographic image reconstruction via dual formulation of total variation minimization

NASA Astrophysics Data System (ADS)

Jang, Kwang Eun; Sung, Younghun; Lee, Kangeui; Lee, Jongha; Cho, Seungryong

2011-03-01

The X-ray mammography is the primary imaging modality for breast cancer screening. For the dense breast, however, the mammogram is usually difficult to read due to tissue overlap problem caused by the superposition of normal tissues. The digital breast tomosynthesis (DBT) that measures several low dose projections over a limited angle range may be an alternative modality for breast imaging, since it allows the visualization of the cross-sectional information of breast. The DBT, however, may suffer from the aliasing artifact and the severe noise corruption. To overcome these problems, a total variation (TV) regularized statistical reconstruction algorithm is presented. Inspired by the dual formulation of TV minimization in denoising and deblurring problems, we derived a gradient-type algorithm based on statistical model of X-ray tomography. The objective function is comprised of a data fidelity term derived from the statistical model and a TV regularization term. The gradient of the objective function can be easily calculated using simple operations in terms of auxiliary variables. After a descending step, the data fidelity term is renewed in each iteration. Since the proposed algorithm can be implemented without sophisticated operations such as matrix inverse, it provides an efficient way to include the TV regularization in the statistical reconstruction method, which results in a fast and robust estimation for low dose projections over the limited angle range. Initial tests with an experimental DBT system confirmed our finding.

Combinatorial therapy discovery using mixed integer linear programming.

PubMed

Pang, Kaifang; Wan, Ying-Wooi; Choi, William T; Donehower, Lawrence A; Sun, Jingchun; Pant, Dhruv; Liu, Zhandong

2014-05-15

Combinatorial therapies play increasingly important roles in combating complex diseases. Owing to the huge cost associated with experimental methods in identifying optimal drug combinations, computational approaches can provide a guide to limit the search space and reduce cost. However, few computational approaches have been developed for this purpose, and thus there is a great need of new algorithms for drug combination prediction. Here we proposed to formulate the optimal combinatorial therapy problem into two complementary mathematical algorithms, Balanced Target Set Cover (BTSC) and Minimum Off-Target Set Cover (MOTSC). Given a disease gene set, BTSC seeks a balanced solution that maximizes the coverage on the disease genes and minimizes the off-target hits at the same time. MOTSC seeks a full coverage on the disease gene set while minimizing the off-target set. Through simulation, both BTSC and MOTSC demonstrated a much faster running time over exhaustive search with the same accuracy. When applied to real disease gene sets, our algorithms not only identified known drug combinations, but also predicted novel drug combinations that are worth further testing. In addition, we developed a web-based tool to allow users to iteratively search for optimal drug combinations given a user-defined gene set. Our tool is freely available for noncommercial use at http://www.drug.liuzlab.org/. zhandong.liu@bcm.edu Supplementary data are available at Bioinformatics online.

A Double-difference Earthquake location algorithm: Method and application to the Northern Hayward Fault, California

USGS Publications Warehouse

Waldhauser, F.; Ellsworth, W.L.

2000-01-01

We have developed an efficient method to determine high-resolution hypocenter locations over large distances. The location method incorporates ordinary absolute travel-time measurements and/or cross-correlation P-and S-wave differential travel-time measurements. Residuals between observed and theoretical travel-time differences (or double-differences) are minimized for pairs of earthquakes at each station while linking together all observed event-station pairs. A least-squares solution is found by iteratively adjusting the vector difference between hypocentral pairs. The double-difference algorithm minimizes errors due to unmodeled velocity structure without the use of station corrections. Because catalog and cross-correlation data are combined into one system of equations, interevent distances within multiplets are determined to the accuracy of the cross-correlation data, while the relative locations between multiplets and uncorrelated events are simultaneously determined to the accuracy of the absolute travel-time data. Statistical resampling methods are used to estimate data accuracy and location errors. Uncertainties in double-difference locations are improved by more than an order of magnitude compared to catalog locations. The algorithm is tested, and its performance is demonstrated on two clusters of earthquakes located on the northern Hayward fault, California. There it colapses the diffuse catalog locations into sharp images of seismicity and reveals horizontal lineations of hypocenter that define the narrow regions on the fault where stress is released by brittle failure.

An efficient iteration strategy for the solution of the Euler equations

NASA Technical Reports Server (NTRS)

Walters, R. W.; Dwoyer, D. L.

1985-01-01

A line Gauss-Seidel (LGS) relaxation algorithm in conjunction with a one-parameter family of upwind discretizations of the Euler equations in two-dimensions is described. The basic algorithm has the property that convergence to the steady-state is quadratic for fully supersonic flows and linear otherwise. This is in contrast to the block ADI methods (either central or upwind differenced) and the upwind biased relaxation schemes, all of which converge linearly, independent of the flow regime. Moreover, the algorithm presented here is easily enhanced to detect regions of subsonic flow embedded in supersonic flow. This allows marching by lines in the supersonic regions, converging each line quadratically, and iterating in the subsonic regions, thus yielding a very efficient iteration strategy. Numerical results are presented for two-dimensional supersonic and transonic flows containing both oblique and normal shock waves which confirm the efficiency of the iteration strategy.

Further investigation on "A multiplicative regularization for force reconstruction"

NASA Astrophysics Data System (ADS)

Aucejo, M.; De Smet, O.

2018-05-01

We have recently proposed a multiplicative regularization to reconstruct mechanical forces acting on a structure from vibration measurements. This method does not require any selection procedure for choosing the regularization parameter, since the amount of regularization is automatically adjusted throughout an iterative resolution process. The proposed iterative algorithm has been developed with performance and efficiency in mind, but it is actually a simplified version of a full iterative procedure not described in the original paper. The present paper aims at introducing the full resolution algorithm and comparing it with its simplified version in terms of computational efficiency and solution accuracy. In particular, it is shown that both algorithms lead to very similar identified solutions.

A Multiuser Detector Based on Artificial Bee Colony Algorithm for DS-UWB Systems

PubMed Central

Liu, Xiaohui

2013-01-01

Artificial Bee Colony (ABC) algorithm is an optimization algorithm based on the intelligent behavior of honey bee swarm. The ABC algorithm was developed to solve optimizing numerical problems and revealed premising results in processing time and solution quality. In ABC, a colony of artificial bees search for rich artificial food sources; the optimizing numerical problems are converted to the problem of finding the best parameter which minimizes an objective function. Then, the artificial bees randomly discover a population of initial solutions and then iteratively improve them by employing the behavior: moving towards better solutions by means of a neighbor search mechanism while abandoning poor solutions. In this paper, an efficient multiuser detector based on a suboptimal code mapping multiuser detector and artificial bee colony algorithm (SCM-ABC-MUD) is proposed and implemented in direct-sequence ultra-wideband (DS-UWB) systems under the additive white Gaussian noise (AWGN) channel. The simulation results demonstrate that the BER and the near-far effect resistance performances of this proposed algorithm are quite close to those of the optimum multiuser detector (OMD) while its computational complexity is much lower than that of OMD. Furthermore, the BER performance of SCM-ABC-MUD is not sensitive to the number of active users and can obtain a large system capacity. PMID:23983638

A fast 4D cone beam CT reconstruction method based on the OSC-TV algorithm.

PubMed

Mascolo-Fortin, Julia; Matenine, Dmitri; Archambault, Louis; Després, Philippe

2018-01-01

Four-dimensional cone beam computed tomography allows for temporally resolved imaging with useful applications in radiotherapy, but raises particular challenges in terms of image quality and computation time. The purpose of this work is to develop a fast and accurate 4D algorithm by adapting a GPU-accelerated ordered subsets convex algorithm (OSC), combined with the total variation minimization regularization technique (TV). Different initialization schemes were studied to adapt the OSC-TV algorithm to 4D reconstruction: each respiratory phase was initialized either with a 3D reconstruction or a blank image. Reconstruction algorithms were tested on a dynamic numerical phantom and on a clinical dataset. 4D iterations were implemented for a cluster of 8 GPUs. All developed methods allowed for an adequate visualization of the respiratory movement and compared favorably to the McKinnon-Bates and adaptive steepest descent projection onto convex sets algorithms, while the 4D reconstructions initialized from a prior 3D reconstruction led to better overall image quality. The most suitable adaptation of OSC-TV to 4D CBCT was found to be a combination of a prior FDK reconstruction and a 4D OSC-TV reconstruction with a reconstruction time of 4.5 minutes. This relatively short reconstruction time could facilitate a clinical use.

Optimal spiral phase modulation in Gerchberg-Saxton algorithm for wavefront reconstruction and correction

NASA Astrophysics Data System (ADS)

Baránek, M.; Běhal, J.; Bouchal, Z.

2018-01-01

In the phase retrieval applications, the Gerchberg-Saxton (GS) algorithm is widely used for the simplicity of implementation. This iterative process can advantageously be deployed in the combination with a spatial light modulator (SLM) enabling simultaneous correction of optical aberrations. As recently demonstrated, the accuracy and efficiency of the aberration correction using the GS algorithm can be significantly enhanced by a vortex image spot used as the target intensity pattern in the iterative process. Here we present an optimization of the spiral phase modulation incorporated into the GS algorithm.

Reducing Memory Cost of Exact Diagonalization using Singular Value Decomposition

NASA Astrophysics Data System (ADS)

Weinstein, Marvin; Chandra, Ravi; Auerbach, Assa

2012-02-01

We present a modified Lanczos algorithm to diagonalize lattice Hamiltonians with dramatically reduced memory requirements. In contrast to variational approaches and most implementations of DMRG, Lanczos rotations towards the ground state do not involve incremental minimizations, (e.g. sweeping procedures) which may get stuck in false local minima. The lattice of size N is partitioned into two subclusters. At each iteration the rotating Lanczos vector is compressed into two sets of nsvd small subcluster vectors using singular value decomposition. For low entanglement entropy See, (satisfied by short range Hamiltonians), the truncation error is bounded by (-nsvd^1/See). Convergence is tested for the Heisenberg model on Kagom'e clusters of 24, 30 and 36 sites, with no lattice symmetries exploited, using less than 15GB of dynamical memory. Generalization of the Lanczos-SVD algorithm to multiple partitioning is discussed, and comparisons to other techniques are given. Reference: arXiv:1105.0007

Mixed-Strategy Chance Constrained Optimal Control

NASA Technical Reports Server (NTRS)

Ono, Masahiro; Kuwata, Yoshiaki; Balaram, J.

2013-01-01

This paper presents a novel chance constrained optimal control (CCOC) algorithm that chooses a control action probabilistically. A CCOC problem is to find a control input that minimizes the expected cost while guaranteeing that the probability of violating a set of constraints is below a user-specified threshold. We show that a probabilistic control approach, which we refer to as a mixed control strategy, enables us to obtain a cost that is better than what deterministic control strategies can achieve when the CCOC problem is nonconvex. The resulting mixed-strategy CCOC problem turns out to be a convexification of the original nonconvex CCOC problem. Furthermore, we also show that a mixed control strategy only needs to "mix" up to two deterministic control actions in order to achieve optimality. Building upon an iterative dual optimization, the proposed algorithm quickly converges to the optimal mixed control strategy with a user-specified tolerance.

An Interactive Image Segmentation Method in Hand Gesture Recognition

PubMed Central

Chen, Disi; Li, Gongfa; Sun, Ying; Kong, Jianyi; Jiang, Guozhang; Tang, Heng; Ju, Zhaojie; Yu, Hui; Liu, Honghai

2017-01-01

In order to improve the recognition rate of hand gestures a new interactive image segmentation method for hand gesture recognition is presented, and popular methods, e.g., Graph cut, Random walker, Interactive image segmentation using geodesic star convexity, are studied in this article. The Gaussian Mixture Model was employed for image modelling and the iteration of Expectation Maximum algorithm learns the parameters of Gaussian Mixture Model. We apply a Gibbs random field to the image segmentation and minimize the Gibbs Energy using Min-cut theorem to find the optimal segmentation. The segmentation result of our method is tested on an image dataset and compared with other methods by estimating the region accuracy and boundary accuracy. Finally five kinds of hand gestures in different backgrounds are tested on our experimental platform, and the sparse representation algorithm is used, proving that the segmentation of hand gesture images helps to improve the recognition accuracy. PMID:28134818

Layout optimization with algebraic multigrid methods

NASA Technical Reports Server (NTRS)

Regler, Hans; Ruede, Ulrich

1993-01-01

Finding the optimal position for the individual cells (also called functional modules) on the chip surface is an important and difficult step in the design of integrated circuits. This paper deals with the problem of relative placement, that is the minimization of a quadratic functional with a large, sparse, positive definite system matrix. The basic optimization problem must be augmented by constraints to inhibit solutions where cells overlap. Besides classical iterative methods, based on conjugate gradients (CG), we show that algebraic multigrid methods (AMG) provide an interesting alternative. For moderately sized examples with about 10000 cells, AMG is already competitive with CG and is expected to be superior for larger problems. Besides the classical 'multiplicative' AMG algorithm where the levels are visited sequentially, we propose an 'additive' variant of AMG where levels may be treated in parallel and that is suitable as a preconditioner in the CG algorithm.

Online Updating of Statistical Inference in the Big Data Setting.

PubMed

Schifano, Elizabeth D; Wu, Jing; Wang, Chun; Yan, Jun; Chen, Ming-Hui

2016-01-01

We present statistical methods for big data arising from online analytical processing, where large amounts of data arrive in streams and require fast analysis without storage/access to the historical data. In particular, we develop iterative estimating algorithms and statistical inferences for linear models and estimating equations that update as new data arrive. These algorithms are computationally efficient, minimally storage-intensive, and allow for possible rank deficiencies in the subset design matrices due to rare-event covariates. Within the linear model setting, the proposed online-updating framework leads to predictive residual tests that can be used to assess the goodness-of-fit of the hypothesized model. We also propose a new online-updating estimator under the estimating equation setting. Theoretical properties of the goodness-of-fit tests and proposed estimators are examined in detail. In simulation studies and real data applications, our estimator compares favorably with competing approaches under the estimating equation setting.

A compressed sensing based approach on Discrete Algebraic Reconstruction Technique.

PubMed

Demircan-Tureyen, Ezgi; Kamasak, Mustafa E

2015-01-01

Discrete tomography (DT) techniques are capable of computing better results, even using less number of projections than the continuous tomography techniques. Discrete Algebraic Reconstruction Technique (DART) is an iterative reconstruction method proposed to achieve this goal by exploiting a prior knowledge on the gray levels and assuming that the scanned object is composed from a few different densities. In this paper, DART method is combined with an initial total variation minimization (TvMin) phase to ensure a better initial guess and extended with a segmentation procedure in which the threshold values are estimated from a finite set of candidates to minimize both the projection error and the total variation (TV) simultaneously. The accuracy and the robustness of the algorithm is compared with the original DART by the simulation experiments which are done under (1) limited number of projections, (2) limited view problem and (3) noisy projections conditions.

Iterative updating of model error for Bayesian inversion

NASA Astrophysics Data System (ADS)

Calvetti, Daniela; Dunlop, Matthew; Somersalo, Erkki; Stuart, Andrew

2018-02-01

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when optimization algorithms are used to find a single estimate, or to speed up Markov chain Monte Carlo (MCMC) calculations in the Bayesian framework. The use of an approximate model introduces a discrepancy, or modeling error, that may have a detrimental effect on the solution of the ill-posed inverse problem, or it may severely distort the estimate of the posterior distribution. In the Bayesian paradigm, the modeling error can be considered as a random variable, and by using an estimate of the probability distribution of the unknown, one may estimate the probability distribution of the modeling error and incorporate it into the inversion. We introduce an algorithm which iterates this idea to update the distribution of the model error, leading to a sequence of posterior distributions that are demonstrated empirically to capture the underlying truth with increasing accuracy. Since the algorithm is not based on rejections, it requires only limited full model evaluations. We show analytically that, in the linear Gaussian case, the algorithm converges geometrically fast with respect to the number of iterations when the data is finite dimensional. For more general models, we introduce particle approximations of the iteratively generated sequence of distributions; we also prove that each element of the sequence converges in the large particle limit under a simplifying assumption. We show numerically that, as in the linear case, rapid convergence occurs with respect to the number of iterations. Additionally, we show through computed examples that point estimates obtained from this iterative algorithm are superior to those obtained by neglecting the model error.

Deconvolution of interferometric data using interior point iterative algorithms

NASA Astrophysics Data System (ADS)

Theys, C.; Lantéri, H.; Aime, C.

2016-09-01

We address the problem of deconvolution of astronomical images that could be obtained with future large interferometers in space. The presentation is made in two complementary parts. The first part gives an introduction to the image deconvolution with linear and nonlinear algorithms. The emphasis is made on nonlinear iterative algorithms that verify the constraints of non-negativity and constant flux. The Richardson-Lucy algorithm appears there as a special case for photon counting conditions. More generally, the algorithm published recently by Lanteri et al. (2015) is based on scale invariant divergences without assumption on the statistic model of the data. The two proposed algorithms are interior-point algorithms, the latter being more efficient in terms of speed of calculation. These algorithms are applied to the deconvolution of simulated images corresponding to an interferometric system of 16 diluted telescopes in space. Two non-redundant configurations, one disposed around a circle and the other on an hexagonal lattice, are compared for their effectiveness on a simple astronomical object. The comparison is made in the direct and Fourier spaces. Raw "dirty" images have many artifacts due to replicas of the original object. Linear methods cannot remove these replicas while iterative methods clearly show their efficacy in these examples.

Adaptive dynamic programming for discrete-time linear quadratic regulation based on multirate generalised policy iteration

NASA Astrophysics Data System (ADS)

Chun, Tae Yoon; Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho

2018-06-01

In this paper, we propose two multirate generalised policy iteration (GPI) algorithms applied to discrete-time linear quadratic regulation problems. The proposed algorithms are extensions of the existing GPI algorithm that consists of the approximate policy evaluation and policy improvement steps. The two proposed schemes, named heuristic dynamic programming (HDP) and dual HDP (DHP), based on multirate GPI, use multi-step estimation (M-step Bellman equation) at the approximate policy evaluation step for estimating the value function and its gradient called costate, respectively. Then, we show that these two methods with the same update horizon can be considered equivalent in the iteration domain. Furthermore, monotonically increasing and decreasing convergences, so called value iteration (VI)-mode and policy iteration (PI)-mode convergences, are proved to hold for the proposed multirate GPIs. Further, general convergence properties in terms of eigenvalues are also studied. The data-driven online implementation methods for the proposed HDP and DHP are demonstrated and finally, we present the results of numerical simulations performed to verify the effectiveness of the proposed methods.

Modeling Design Iteration in Product Design and Development and Its Solution by a Novel Artificial Bee Colony Algorithm

PubMed Central

2014-01-01

Due to fierce market competition, how to improve product quality and reduce development cost determines the core competitiveness of enterprises. However, design iteration generally causes increases of product cost and delays of development time as well, so how to identify and model couplings among tasks in product design and development has become an important issue for enterprises to settle. In this paper, the shortcomings existing in WTM model are discussed and tearing approach as well as inner iteration method is used to complement the classic WTM model. In addition, the ABC algorithm is also introduced to find out the optimal decoupling schemes. In this paper, firstly, tearing approach and inner iteration method are analyzed for solving coupled sets. Secondly, a hybrid iteration model combining these two technologies is set up. Thirdly, a high-performance swarm intelligence algorithm, artificial bee colony, is adopted to realize problem-solving. Finally, an engineering design of a chemical processing system is given in order to verify its reasonability and effectiveness. PMID:25431584

Block Iterative Methods for Elliptic and Parabolic Difference Equations.

DTIC Science & Technology

1981-09-01

S V PARTER, M STEUERWALT N0OO14-7A-C-0341 UNCLASSIFIED CSTR -447 NL ENN.EEEEEN LLf SCOMPUTER SCIENCES c~DEPARTMENT SUniversity of Wisconsin- SMadison...suggests that iterative algorithms that solve for several points at once will converge more rapidly than point algorithms . The Gaussian elimination... algorithm is seen in this light to converge in one step. Frankel [14], Young [34], Arms, Gates, and Zondek [1], and Varga [32], using the algebraic structure

Semiannual Report, April 1, 1989 through September 30, 1989 (Institute for Computer Applications in Science and Engineering)

DTIC Science & Technology

1990-02-01

noise. Tobias B. Orloff Work began on developing a high quality rendering algorithm based on the radiosity method. The algorithm is similar to...previous progressive radiosity algorithms except for the following improvements: 1. At each iteration vertex radiosities are computed using a modified scan...line approach, thus eliminating the quadratic cost associated with a ray tracing computation of vortex radiosities . 2. At each iteration the scene is

Increasing feasibility of the field-programmable gate array implementation of an iterative image registration using a kernel-warping algorithm

NASA Astrophysics Data System (ADS)

Nguyen, An Hung; Guillemette, Thomas; Lambert, Andrew J.; Pickering, Mark R.; Garratt, Matthew A.

2017-09-01

Image registration is a fundamental image processing technique. It is used to spatially align two or more images that have been captured at different times, from different sensors, or from different viewpoints. There have been many algorithms proposed for this task. The most common of these being the well-known Lucas-Kanade (LK) and Horn-Schunck approaches. However, the main limitation of these approaches is the computational complexity required to implement the large number of iterations necessary for successful alignment of the images. Previously, a multi-pass image interpolation algorithm (MP-I2A) was developed to considerably reduce the number of iterations required for successful registration compared with the LK algorithm. This paper develops a kernel-warping algorithm (KWA), a modified version of the MP-I2A, which requires fewer iterations to successfully register two images and less memory space for the field-programmable gate array (FPGA) implementation than the MP-I2A. These reductions increase feasibility of the implementation of the proposed algorithm on FPGAs with very limited memory space and other hardware resources. A two-FPGA system rather than single FPGA system is successfully developed to implement the KWA in order to compensate insufficiency of hardware resources supported by one FPGA, and increase parallel processing ability and scalability of the system.

A multi-level solution algorithm for steady-state Markov chains

NASA Technical Reports Server (NTRS)

Horton, Graham; Leutenegger, Scott T.

1993-01-01

A new iterative algorithm, the multi-level algorithm, for the numerical solution of steady state Markov chains is presented. The method utilizes a set of recursively coarsened representations of the original system to achieve accelerated convergence. It is motivated by multigrid methods, which are widely used for fast solution of partial differential equations. Initial results of numerical experiments are reported, showing significant reductions in computation time, often an order of magnitude or more, relative to the Gauss-Seidel and optimal SOR algorithms for a variety of test problems. The multi-level method is compared and contrasted with the iterative aggregation-disaggregation algorithm of Takahashi.

The optimal algorithm for Multi-source RS image fusion.

PubMed

Fu, Wei; Huang, Shui-Guang; Li, Zeng-Shun; Shen, Hao; Li, Jun-Shuai; Wang, Peng-Yuan

2016-01-01

In order to solve the issue which the fusion rules cannot be self-adaptively adjusted by using available fusion methods according to the subsequent processing requirements of Remote Sensing (RS) image, this paper puts forward GSDA (genetic-iterative self-organizing data analysis algorithm) by integrating the merit of genetic arithmetic together with the advantage of iterative self-organizing data analysis algorithm for multi-source RS image fusion. The proposed algorithm considers the wavelet transform of the translation invariance as the model operator, also regards the contrast pyramid conversion as the observed operator. The algorithm then designs the objective function by taking use of the weighted sum of evaluation indices, and optimizes the objective function by employing GSDA so as to get a higher resolution of RS image. As discussed above, the bullet points of the text are summarized as follows.•The contribution proposes the iterative self-organizing data analysis algorithm for multi-source RS image fusion.•This article presents GSDA algorithm for the self-adaptively adjustment of the fusion rules.•This text comes up with the model operator and the observed operator as the fusion scheme of RS image based on GSDA. The proposed algorithm opens up a novel algorithmic pathway for multi-source RS image fusion by means of GSDA.

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.

WE-FG-207B-05: Iterative Reconstruction Via Prior Image Constrained Total Generalized Variation for Spectral CT

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

Niu, S; Zhang, Y; Ma, J

Purpose: To investigate iterative reconstruction via prior image constrained total generalized variation (PICTGV) for spectral computed tomography (CT) using fewer projections while achieving greater image quality. Methods: The proposed PICTGV method is formulated as an optimization problem, which balances the data fidelity and prior image constrained total generalized variation of reconstructed images in one framework. The PICTGV method is based on structure correlations among images in the energy domain and high-quality images to guide the reconstruction of energy-specific images. In PICTGV method, the high-quality image is reconstructed from all detector-collected X-ray signals and is referred as the broad-spectrum image. Distinctmore » from the existing reconstruction methods applied on the images with first order derivative, the higher order derivative of the images is incorporated into the PICTGV method. An alternating optimization algorithm is used to minimize the PICTGV objective function. We evaluate the performance of PICTGV on noise and artifacts suppressing using phantom studies and compare the method with the conventional filtered back-projection method as well as TGV based method without prior image. Results: On the digital phantom, the proposed method outperforms the existing TGV method in terms of the noise reduction, artifacts suppression, and edge detail preservation. Compared to that obtained by the TGV based method without prior image, the relative root mean square error in the images reconstructed by the proposed method is reduced by over 20%. Conclusion: The authors propose an iterative reconstruction via prior image constrained total generalize variation for spectral CT. Also, we have developed an alternating optimization algorithm and numerically demonstrated the merits of our approach. Results show that the proposed PICTGV method outperforms the TGV method for spectral CT.« less

A new pivoting and iterative text detection algorithm for biomedical images.

PubMed

Xu, Songhua; Krauthammer, Michael

2010-12-01

There is interest to expand the reach of literature mining to include the analysis of biomedical images, which often contain a paper's key findings. Examples include recent studies that use Optical Character Recognition (OCR) to extract image text, which is used to boost biomedical image retrieval and classification. Such studies rely on the robust identification of text elements in biomedical images, which is a non-trivial task. In this work, we introduce a new text detection algorithm for biomedical images based on iterative projection histograms. We study the effectiveness of our algorithm by evaluating the performance on a set of manually labeled random biomedical images, and compare the performance against other state-of-the-art text detection algorithms. We demonstrate that our projection histogram-based text detection approach is well suited for text detection in biomedical images, and that the iterative application of the algorithm boosts performance to an F score of .60. We provide a C++ implementation of our algorithm freely available for academic use. Copyright © 2010 Elsevier Inc. All rights reserved.

Robust iterative closest point algorithm based on global reference point for rotation invariant registration.

PubMed

Du, Shaoyi; Xu, Yiting; Wan, Teng; Hu, Huaizhong; Zhang, Sirui; Xu, Guanglin; Zhang, Xuetao

2017-01-01

The iterative closest point (ICP) algorithm is efficient and accurate for rigid registration but it needs the good initial parameters. It is easily failed when the rotation angle between two point sets is large. To deal with this problem, a new objective function is proposed by introducing a rotation invariant feature based on the Euclidean distance between each point and a global reference point, where the global reference point is a rotation invariant. After that, this optimization problem is solved by a variant of ICP algorithm, which is an iterative method. Firstly, the accurate correspondence is established by using the weighted rotation invariant feature distance and position distance together. Secondly, the rigid transformation is solved by the singular value decomposition method. Thirdly, the weight is adjusted to control the relative contribution of the positions and features. Finally this new algorithm accomplishes the registration by a coarse-to-fine way whatever the initial rotation angle is, which is demonstrated to converge monotonically. The experimental results validate that the proposed algorithm is more accurate and robust compared with the original ICP algorithm.

Robust iterative closest point algorithm based on global reference point for rotation invariant registration

PubMed Central

Du, Shaoyi; Xu, Yiting; Wan, Teng; Zhang, Sirui; Xu, Guanglin; Zhang, Xuetao

2017-01-01

The iterative closest point (ICP) algorithm is efficient and accurate for rigid registration but it needs the good initial parameters. It is easily failed when the rotation angle between two point sets is large. To deal with this problem, a new objective function is proposed by introducing a rotation invariant feature based on the Euclidean distance between each point and a global reference point, where the global reference point is a rotation invariant. After that, this optimization problem is solved by a variant of ICP algorithm, which is an iterative method. Firstly, the accurate correspondence is established by using the weighted rotation invariant feature distance and position distance together. Secondly, the rigid transformation is solved by the singular value decomposition method. Thirdly, the weight is adjusted to control the relative contribution of the positions and features. Finally this new algorithm accomplishes the registration by a coarse-to-fine way whatever the initial rotation angle is, which is demonstrated to converge monotonically. The experimental results validate that the proposed algorithm is more accurate and robust compared with the original ICP algorithm. PMID:29176780

An image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm

NASA Astrophysics Data System (ADS)

Zhang, B.; Sang, Jun; Alam, Mohammad S.

2013-03-01

An image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm was proposed. Firstly, the original secret image was encrypted into two phase-only masks M1 and M2 via cascaded iterative Fourier transform (CIFT) algorithm. Then, the public-key encryption algorithm RSA was adopted to encrypt M2 into M2' . Finally, a host image was enlarged by extending one pixel into 2×2 pixels and each element in M1 and M2' was multiplied with a superimposition coefficient and added to or subtracted from two different elements in the 2×2 pixels of the enlarged host image. To recover the secret image from the stego-image, the two masks were extracted from the stego-image without the original host image. By applying public-key encryption algorithm, the key distribution was facilitated, and also compared with the image hiding method based on optical interference, the proposed method may reach higher robustness by employing the characteristics of the CIFT algorithm. Computer simulations show that this method has good robustness against image processing.

Design and FPGA Implementation of a Universal Chaotic Signal Generator Based on the Verilog HDL Fixed-Point Algorithm and State Machine Control

NASA Astrophysics Data System (ADS)

Qiu, Mo; Yu, Simin; Wen, Yuqiong; Lü, Jinhu; He, Jianbin; Lin, Zhuosheng

In this paper, a novel design methodology and its FPGA hardware implementation for a universal chaotic signal generator is proposed via the Verilog HDL fixed-point algorithm and state machine control. According to continuous-time or discrete-time chaotic equations, a Verilog HDL fixed-point algorithm and its corresponding digital system are first designed. In the FPGA hardware platform, each operation step of Verilog HDL fixed-point algorithm is then controlled by a state machine. The generality of this method is that, for any given chaotic equation, it can be decomposed into four basic operation procedures, i.e. nonlinear function calculation, iterative sequence operation, iterative values right shifting and ceiling, and chaotic iterative sequences output, each of which corresponds to only a state via state machine control. Compared with the Verilog HDL floating-point algorithm, the Verilog HDL fixed-point algorithm can save the FPGA hardware resources and improve the operation efficiency. FPGA-based hardware experimental results validate the feasibility and reliability of the proposed approach.

Multidirectional hybrid algorithm for the split common fixed point problem and application to the split common null point problem.

PubMed

Li, Xia; Guo, Meifang; Su, Yongfu

2016-01-01

In this article, a new multidirectional monotone hybrid iteration algorithm for finding a solution to the split common fixed point problem is presented for two countable families of quasi-nonexpansive mappings in Banach spaces. Strong convergence theorems are proved. The application of the result is to consider the split common null point problem of maximal monotone operators in Banach spaces. Strong convergence theorems for finding a solution of the split common null point problem are derived. This iteration algorithm can accelerate the convergence speed of iterative sequence. The results of this paper improve and extend the recent results of Takahashi and Yao (Fixed Point Theory Appl 2015:87, 2015) and many others .

Solution algorithms for nonlinear transient heat conduction analysis employing element-by-element iterative strategies

NASA Technical Reports Server (NTRS)

Winget, J. M.; Hughes, T. J. R.

1985-01-01

The particular problems investigated in the present study arise from nonlinear transient heat conduction. One of two types of nonlinearities considered is related to a material temperature dependence which is frequently needed to accurately model behavior over the range of temperature of engineering interest. The second nonlinearity is introduced by radiation boundary conditions. The finite element equations arising from the solution of nonlinear transient heat conduction problems are formulated. The finite element matrix equations are temporally discretized, and a nonlinear iterative solution algorithm is proposed. Algorithms for solving the linear problem are discussed, taking into account the form of the matrix equations, Gaussian elimination, cost, and iterative techniques. Attention is also given to approximate factorization, implementational aspects, and numerical results.

On improving the iterative convergence properties of an implicit approximate-factorization finite difference algorithm. [considering transonic flow

NASA Technical Reports Server (NTRS)

Desideri, J. A.; Steger, J. L.; Tannehill, J. C.

1978-01-01

The iterative convergence properties of an approximate-factorization implicit finite-difference algorithm are analyzed both theoretically and numerically. Modifications to the base algorithm were made to remove the inconsistency in the original implementation of artificial dissipation. In this way, the steady-state solution became independent of the time-step, and much larger time-steps can be used stably. To accelerate the iterative convergence, large time-steps and a cyclic sequence of time-steps were used. For a model transonic flow problem governed by the Euler equations, convergence was achieved with 10 times fewer time-steps using the modified differencing scheme. A particular form of instability due to variable coefficients is also analyzed.

Rescheduling with iterative repair

NASA Technical Reports Server (NTRS)

Zweben, Monte; Davis, Eugene; Daun, Brian; Deale, Michael

1992-01-01

This paper presents a new approach to rescheduling called constraint-based iterative repair. This approach gives our system the ability to satisfy domain constraints, address optimization concerns, minimize perturbation to the original schedule, and produce modified schedules quickly. The system begins with an initial, flawed schedule and then iteratively repairs constraint violations until a conflict-free schedule is produced. In an empirical demonstration, we vary the importance of minimizing perturbation and report how fast the system is able to resolve conflicts in a given time bound. These experiments were performed within the domain of Space Shuttle ground processing.

Diagonalization of complex symmetric matrices: Generalized Householder reflections, iterative deflation and implicit shifts

NASA Astrophysics Data System (ADS)

Noble, J. H.; Lubasch, M.; Stevens, J.; Jentschura, U. D.

2017-12-01

We describe a matrix diagonalization algorithm for complex symmetric (not Hermitian) matrices, A ̲ =A̲T, which is based on a two-step algorithm involving generalized Householder reflections based on the indefinite inner product 〈 u ̲ , v ̲ 〉 ∗ =∑iuivi. This inner product is linear in both arguments and avoids complex conjugation. The complex symmetric input matrix is transformed to tridiagonal form using generalized Householder transformations (first step). An iterative, generalized QL decomposition of the tridiagonal matrix employing an implicit shift converges toward diagonal form (second step). The QL algorithm employs iterative deflation techniques when a machine-precision zero is encountered "prematurely" on the super-/sub-diagonal. The algorithm allows for a reliable and computationally efficient computation of resonance and antiresonance energies which emerge from complex-scaled Hamiltonians, and for the numerical determination of the real energy eigenvalues of pseudo-Hermitian and PT-symmetric Hamilton matrices. Numerical reference values are provided.

Routing and spectrum assignment based on ant colony optimization of minimum consecutiveness loss in elastic optical networks

NASA Astrophysics Data System (ADS)

Wang, Fu; Liu, Bo; Zhang, Lijia; Xin, Xiangjun; Tian, Qinghua; Zhang, Qi; Rao, Lan; Tian, Feng; Luo, Biao; Liu, Yingjun; Tang, Bao

2016-10-01

Elastic Optical Networks are considered to be a promising technology for future high-speed network. In this paper, we propose a RSA algorithm based on the ant colony optimization of minimum consecutiveness loss (ACO-MCL). Based on the effect of the spectrum consecutiveness loss on the pheromone in the ant colony optimization, the path and spectrum of the minimal impact on the network are selected for the service request. When an ant arrives at the destination node from the source node along a path, we assume that this path is selected for the request. We calculate the consecutiveness loss of candidate-neighbor link pairs along this path after the routing and spectrum assignment. Then, the networks update the pheromone according to the value of the consecutiveness loss. We save the path with the smallest value. After multiple iterations of the ant colony optimization, the final selection of the path is assigned for the request. The algorithms are simulated in different networks. The results show that ACO-MCL algorithm performs better in blocking probability and spectrum efficiency than other algorithms. Moreover, the ACO-MCL algorithm can effectively decrease spectrum fragmentation and enhance available spectrum consecutiveness. Compared with other algorithms, the ACO-MCL algorithm can reduce the blocking rate by at least 5.9% in heavy load.

Continuous analog of multiplicative algebraic reconstruction technique for computed tomography

NASA Astrophysics Data System (ADS)

Tateishi, Kiyoko; Yamaguchi, Yusaku; Abou Al-Ola, Omar M.; Kojima, Takeshi; Yoshinaga, Tetsuya

2016-03-01

We propose a hybrid dynamical system as a continuous analog to the block-iterative multiplicative algebraic reconstruction technique (BI-MART), which is a well-known iterative image reconstruction algorithm for computed tomography. The hybrid system is described by a switched nonlinear system with a piecewise smooth vector field or differential equation and, for consistent inverse problems, the convergence of non-negatively constrained solutions to a globally stable equilibrium is guaranteed by the Lyapunov theorem. Namely, we can prove theoretically that a weighted Kullback-Leibler divergence measure can be a common Lyapunov function for the switched system. We show that discretizing the differential equation by using the first-order approximation (Euler's method) based on the geometric multiplicative calculus leads to the same iterative formula of the BI-MART with the scaling parameter as a time-step of numerical discretization. The present paper is the first to reveal that a kind of iterative image reconstruction algorithm is constructed by the discretization of a continuous-time dynamical system for solving tomographic inverse problems. Iterative algorithms with not only the Euler method but also the Runge-Kutta methods of lower-orders applied for discretizing the continuous-time system can be used for image reconstruction. A numerical example showing the characteristics of the discretized iterative methods is presented.

Globally Deghosting for Marine Streamer with Alternating Minimization Approach in Frequency-slowness Domain

NASA Astrophysics Data System (ADS)

Wang, C.; Zhu, Z.; Gu, H.; Liu, C.; Liu, Z.; Jiao, Z.

2017-12-01

The ghost effects of the sea surface can generate notch in marine towed-streamer data, which results in narrow bandwidth of seismic data. Currently, deghosting is widely utilized to increase the bandwidth of the seismic data or the images. However, most of the conventional deghosting algorithms havenot considered the error of streamer depth causing a biased ghost-delay time (τ) with respect to primary reflection and amplitude difference coefficient (r) between ghost and primary reflection varies with offset due to rugged seabed and target depth variation. We proposed a ghost filtering operator considering the protentional biases within the ghost-delay time (τ) and the amplitude difference coefficient (r). The up-going wavefield (u), ghost-delay time (τ) and amplitude difference coefficient (r) can be obtained by utilizing alternating minimization approach for minimizing the difference between actual wavefield and theoretical wavefield in frequency-slowness domain. The main idea is to alternatively updating u, τ and r in each iteration: we update u by least-squares when we keep τ and r constant; and we then keep u constant and optimize over τ and r with a closed-form solution which is closely related to matched filtering. The convergence of the proposed algorithm is guaranteed since we have closed-form solutions for each stage. The experiments on synthetic record confirmed the reliability of the proposed algorithm. We also demonstrate our proposed method in marine VDS shot acquisition. After migration stack processing, our ghosting method significantly increases the bandwidth of the average amplitude, amplitude energy of the medium and high frequency spectrum, improving resolution of medium and deep reflection and providing higher signal-to-noise ratio with clear break point. This research is funded by China Important National Science & Technology Specific Projects (2016ZX05026001-001).

Algorithms for the optimization of RBE-weighted dose in particle therapy.

PubMed

Horcicka, M; Meyer, C; Buschbacher, A; Durante, M; Krämer, M

2013-01-21

We report on various algorithms used for the nonlinear optimization of RBE-weighted dose in particle therapy. Concerning the dose calculation carbon ions are considered and biological effects are calculated by the Local Effect Model. Taking biological effects fully into account requires iterative methods to solve the optimization problem. We implemented several additional algorithms into GSI's treatment planning system TRiP98, like the BFGS-algorithm and the method of conjugated gradients, in order to investigate their computational performance. We modified textbook iteration procedures to improve the convergence speed. The performance of the algorithms is presented by convergence in terms of iterations and computation time. We found that the Fletcher-Reeves variant of the method of conjugated gradients is the algorithm with the best computational performance. With this algorithm we could speed up computation times by a factor of 4 compared to the method of steepest descent, which was used before. With our new methods it is possible to optimize complex treatment plans in a few minutes leading to good dose distributions. At the end we discuss future goals concerning dose optimization issues in particle therapy which might benefit from fast optimization solvers.

Algorithms for the optimization of RBE-weighted dose in particle therapy

NASA Astrophysics Data System (ADS)

Horcicka, M.; Meyer, C.; Buschbacher, A.; Durante, M.; Krämer, M.

2013-01-01

We report on various algorithms used for the nonlinear optimization of RBE-weighted dose in particle therapy. Concerning the dose calculation carbon ions are considered and biological effects are calculated by the Local Effect Model. Taking biological effects fully into account requires iterative methods to solve the optimization problem. We implemented several additional algorithms into GSI's treatment planning system TRiP98, like the BFGS-algorithm and the method of conjugated gradients, in order to investigate their computational performance. We modified textbook iteration procedures to improve the convergence speed. The performance of the algorithms is presented by convergence in terms of iterations and computation time. We found that the Fletcher-Reeves variant of the method of conjugated gradients is the algorithm with the best computational performance. With this algorithm we could speed up computation times by a factor of 4 compared to the method of steepest descent, which was used before. With our new methods it is possible to optimize complex treatment plans in a few minutes leading to good dose distributions. At the end we discuss future goals concerning dose optimization issues in particle therapy which might benefit from fast optimization solvers.

Seismic waveform tomography with shot-encoding using a restarted L-BFGS algorithm.

PubMed

Rao, Ying; Wang, Yanghua

2017-08-17

In seismic waveform tomography, or full-waveform inversion (FWI), one effective strategy used to reduce the computational cost is shot-encoding, which encodes all shots randomly and sums them into one super shot to significantly reduce the number of wavefield simulations in the inversion. However, this process will induce instability in the iterative inversion regardless of whether it uses a robust limited-memory BFGS (L-BFGS) algorithm. The restarted L-BFGS algorithm proposed here is both stable and efficient. This breakthrough ensures, for the first time, the applicability of advanced FWI methods to three-dimensional seismic field data. In a standard L-BFGS algorithm, if the shot-encoding remains unchanged, it will generate a crosstalk effect between different shots. This crosstalk effect can only be suppressed by employing sufficient randomness in the shot-encoding. Therefore, the implementation of the L-BFGS algorithm is restarted at every segment. Each segment consists of a number of iterations; the first few iterations use an invariant encoding, while the remainder use random re-coding. This restarted L-BFGS algorithm balances the computational efficiency of shot-encoding, the convergence stability of the L-BFGS algorithm, and the inversion quality characteristic of random encoding in FWI.

Compressed sensing with gradient total variation for low-dose CBCT reconstruction

NASA Astrophysics Data System (ADS)

Seo, Chang-Woo; Cha, Bo Kyung; Jeon, Seongchae; Huh, Young; Park, Justin C.; Lee, Byeonghun; Baek, Junghee; Kim, Eunyoung

2015-06-01

This paper describes the improvement of convergence speed with gradient total variation (GTV) in compressed sensing (CS) for low-dose cone-beam computed tomography (CBCT) reconstruction. We derive a fast algorithm for the constrained total variation (TV)-based a minimum number of noisy projections. To achieve this task we combine the GTV with a TV-norm regularization term to promote an accelerated sparsity in the X-ray attenuation characteristics of the human body. The GTV is derived from a TV and enforces more efficient computationally and faster in convergence until a desired solution is achieved. The numerical algorithm is simple and derives relatively fast convergence. We apply a gradient projection algorithm that seeks a solution iteratively in the direction of the projected gradient while enforcing a non-negatively of the found solution. In comparison with the Feldkamp, Davis, and Kress (FDK) and conventional TV algorithms, the proposed GTV algorithm showed convergence in ≤18 iterations, whereas the original TV algorithm needs at least 34 iterations in reducing 50% of the projections compared with the FDK algorithm in order to reconstruct the chest phantom images. Future investigation includes improving imaging quality, particularly regarding X-ray cone-beam scatter, and motion artifacts of CBCT reconstruction.

An Evaluation of an Algorithm for Linear Inequalities and Its Applications

NASA Technical Reports Server (NTRS)

Jurgensen, J.

1973-01-01

An algorithm is presented for obtaining a solution alpha to a set of inequalities (A alpha) 0 where A is an N x m-matrix and alpha is an m-vector. If the set of inequalities is consistant, then the algorithm is guaranteed to arrive at a solution in a finite number of steps. Also, if in the iteration, a negative vector is obtained, then the initial set of inequalities is inconsistant, and the iteration is terminated.

Learning control system design based on 2-D theory - An application to parallel link manipulator

NASA Technical Reports Server (NTRS)

Geng, Z.; Carroll, R. L.; Lee, J. D.; Haynes, L. H.

1990-01-01

An approach to iterative learning control system design based on two-dimensional system theory is presented. A two-dimensional model for the iterative learning control system which reveals the connections between learning control systems and two-dimensional system theory is established. A learning control algorithm is proposed, and the convergence of learning using this algorithm is guaranteed by two-dimensional stability. The learning algorithm is applied successfully to the trajectory tracking control problem for a parallel link robot manipulator. The excellent performance of this learning algorithm is demonstrated by the computer simulation results.

Minimization of required model runs in the Random Mixing approach to inverse groundwater flow and transport modeling

NASA Astrophysics Data System (ADS)

Hoerning, Sebastian; Bardossy, Andras; du Plessis, Jaco

2017-04-01

Most geostatistical inverse groundwater flow and transport modelling approaches utilize a numerical solver to minimize the discrepancy between observed and simulated hydraulic heads and/or hydraulic concentration values. The optimization procedure often requires many model runs, which for complex models lead to long run times. Random Mixing is a promising new geostatistical technique for inverse modelling. The method is an extension of the gradual deformation approach. It works by finding a field which preserves the covariance structure and maintains observed hydraulic conductivities. This field is perturbed by mixing it with new fields that fulfill the homogeneous conditions. This mixing is expressed as an optimization problem which aims to minimize the difference between the observed and simulated hydraulic heads and/or concentration values. To preserve the spatial structure, the mixing weights must lie on the unit hyper-sphere. We present a modification to the Random Mixing algorithm which significantly reduces the number of model runs required. The approach involves taking n equally spaced points on the unit circle as weights for mixing conditional random fields. Each of these mixtures provides a solution to the forward model at the conditioning locations. For each of the locations the solutions are then interpolated around the circle to provide solutions for additional mixing weights at very low computational cost. The interpolated solutions are used to search for a mixture which maximally reduces the objective function. This is in contrast to other approaches which evaluate the objective function for the n mixtures and then interpolate the obtained values. Keeping the mixture on the unit circle makes it easy to generate equidistant sampling points in the space; however, this means that only two fields are mixed at a time. Once the optimal mixture for two fields has been found, they are combined to form the input to the next iteration of the algorithm. This process is repeated until a threshold in the objective function is met or insufficient changes are produced in successive iterations.

Iterative wave-front reconstruction in the Fourier domain.

PubMed

Bond, Charlotte Z; Correia, Carlos M; Sauvage, Jean-François; Neichel, Benoit; Fusco, Thierry

2017-05-15

The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data set which conform to specific boundary requirements, whereas wave-front sensor data is typically defined over a circular domain (the telescope pupil). Here we present an iterative Gerchberg routine modified for the purposes of discrete wave-front reconstruction which adapts the measurement data (wave-front sensor slopes) for Fourier analysis, fulfilling the requirements of the fast Fourier transform (FFT) and providing accurate reconstruction. The routine is used in the adaptation step only and can be coupled to any other Wiener-like or least-squares method. We compare simulations using this method with previous Fourier methods and show an increase in performance in terms of Strehl ratio and a reduction in noise propagation for a 40×40 SPHERE-like adaptive optics system. For closed loop operation with minimal iterations the Gerchberg method provides an improvement in Strehl, from 95.4% to 96.9% in K-band. This corresponds to ~ 40 nm improvement in rms, and avoids the high spatial frequency errors present in other methods, providing an increase in contrast towards the edge of the correctable band.

Volumetric quantification of lung nodules in CT with iterative reconstruction (ASiR and MBIR).

PubMed

Chen, Baiyu; Barnhart, Huiman; Richard, Samuel; Robins, Marthony; Colsher, James; Samei, Ehsan

2013-11-01

Volume quantifications of lung nodules with multidetector computed tomography (CT) images provide useful information for monitoring nodule developments. The accuracy and precision of the volume quantification, however, can be impacted by imaging and reconstruction parameters. This study aimed to investigate the impact of iterative reconstruction algorithms on the accuracy and precision of volume quantification with dose and slice thickness as additional variables. Repeated CT images were acquired from an anthropomorphic chest phantom with synthetic nodules (9.5 and 4.8 mm) at six dose levels, and reconstructed with three reconstruction algorithms [filtered backprojection (FBP), adaptive statistical iterative reconstruction (ASiR), and model based iterative reconstruction (MBIR)] into three slice thicknesses. The nodule volumes were measured with two clinical software (A: Lung VCAR, B: iNtuition), and analyzed for accuracy and precision. Precision was found to be generally comparable between FBP and iterative reconstruction with no statistically significant difference noted for different dose levels, slice thickness, and segmentation software. Accuracy was found to be more variable. For large nodules, the accuracy was significantly different between ASiR and FBP for all slice thicknesses with both software, and significantly different between MBIR and FBP for 0.625 mm slice thickness with Software A and for all slice thicknesses with Software B. For small nodules, the accuracy was more similar between FBP and iterative reconstruction, with the exception of ASIR vs FBP at 1.25 mm with Software A and MBIR vs FBP at 0.625 mm with Software A. The systematic difference between the accuracy of FBP and iterative reconstructions highlights the importance of extending current segmentation software to accommodate the image characteristics of iterative reconstructions. In addition, a calibration process may help reduce the dependency of accuracy on reconstruction algorithms, such that volumes quantified from scans of different reconstruction algorithms can be compared. The little difference found between the precision of FBP and iterative reconstructions could be a result of both iterative reconstruction's diminished noise reduction at the edge of the nodules as well as the loss of resolution at high noise levels with iterative reconstruction. The findings do not rule out potential advantage of IR that might be evident in a study that uses a larger number of nodules or repeated scans.

Soft-output decoding algorithms in iterative decoding of turbo codes

NASA Technical Reports Server (NTRS)

Benedetto, S.; Montorsi, G.; Divsalar, D.; Pollara, F.

1996-01-01

In this article, we present two versions of a simplified maximum a posteriori decoding algorithm. The algorithms work in a sliding window form, like the Viterbi algorithm, and can thus be used to decode continuously transmitted sequences obtained by parallel concatenated codes, without requiring code trellis termination. A heuristic explanation is also given of how to embed the maximum a posteriori algorithms into the iterative decoding of parallel concatenated codes (turbo codes). The performances of the two algorithms are compared on the basis of a powerful rate 1/3 parallel concatenated code. Basic circuits to implement the simplified a posteriori decoding algorithm using lookup tables, and two further approximations (linear and threshold), with a very small penalty, to eliminate the need for lookup tables are proposed.

Mean-variance analysis of block-iterative reconstruction algorithms modeling 3D detector response in SPECT

NASA Astrophysics Data System (ADS)

Lalush, D. S.; Tsui, B. M. W.

1998-06-01

We study the statistical convergence properties of two fast iterative reconstruction algorithms, the rescaled block-iterative (RBI) and ordered subset (OS) EM algorithms, in the context of cardiac SPECT with 3D detector response modeling. The Monte Carlo method was used to generate nearly noise-free projection data modeling the effects of attenuation, detector response, and scatter from the MCAT phantom. One thousand noise realizations were generated with an average count level approximating a typical T1-201 cardiac study. Each noise realization was reconstructed using the RBI and OS algorithms for cases with and without detector response modeling. For each iteration up to twenty, we generated mean and variance images, as well as covariance images for six specific locations. Both OS and RBI converged in the mean to results that were close to the noise-free ML-EM result using the same projection model. When detector response was not modeled in the reconstruction, RBI exhibited considerably lower noise variance than OS for the same resolution. When 3D detector response was modeled, the RBI-EM provided a small improvement in the tradeoff between noise level and resolution recovery, primarily in the axial direction, while OS required about half the number of iterations of RBI to reach the same resolution. We conclude that OS is faster than RBI, but may be sensitive to errors in the projection model. Both OS-EM and RBI-EM are effective alternatives to the EVIL-EM algorithm, but noise level and speed of convergence depend on the projection model used.

Using a latent variable model with non-constant factor loadings to examine PM2.5 constituents related to secondary inorganic aerosols.

PubMed

Zhang, Zhenzhen; O'Neill, Marie S; Sánchez, Brisa N

2016-04-01

Factor analysis is a commonly used method of modelling correlated multivariate exposure data. Typically, the measurement model is assumed to have constant factor loadings. However, from our preliminary analyses of the Environmental Protection Agency's (EPA's) PM 2.5 fine speciation data, we have observed that the factor loadings for four constituents change considerably in stratified analyses. Since invariance of factor loadings is a prerequisite for valid comparison of the underlying latent variables, we propose a factor model that includes non-constant factor loadings that change over time and space using P-spline penalized with the generalized cross-validation (GCV) criterion. The model is implemented using the Expectation-Maximization (EM) algorithm and we select the multiple spline smoothing parameters by minimizing the GCV criterion with Newton's method during each iteration of the EM algorithm. The algorithm is applied to a one-factor model that includes four constituents. Through bootstrap confidence bands, we find that the factor loading for total nitrate changes across seasons and geographic regions.

Independent tasks scheduling in cloud computing via improved estimation of distribution algorithm

NASA Astrophysics Data System (ADS)

Sun, Haisheng; Xu, Rui; Chen, Huaping

2018-04-01

To minimize makespan for scheduling independent tasks in cloud computing, an improved estimation of distribution algorithm (IEDA) is proposed to tackle the investigated problem in this paper. Considering that the problem is concerned with multi-dimensional discrete problems, an improved population-based incremental learning (PBIL) algorithm is applied, which the parameter for each component is independent with other components in PBIL. In order to improve the performance of PBIL, on the one hand, the integer encoding scheme is used and the method of probability calculation of PBIL is improved by using the task average processing time; on the other hand, an effective adaptive learning rate function that related to the number of iterations is constructed to trade off the exploration and exploitation of IEDA. In addition, both enhanced Max-Min and Min-Min algorithms are properly introduced to form two initial individuals. In the proposed IEDA, an improved genetic algorithm (IGA) is applied to generate partial initial population by evolving two initial individuals and the rest of initial individuals are generated at random. Finally, the sampling process is divided into two parts including sampling by probabilistic model and IGA respectively. The experiment results show that the proposed IEDA not only gets better solution, but also has faster convergence speed.

Artificial Neural Network Approach in Laboratory Test Reporting:  Learning Algorithms.

PubMed

Demirci, Ferhat; Akan, Pinar; Kume, Tuncay; Sisman, Ali Riza; Erbayraktar, Zubeyde; Sevinc, Suleyman

2016-08-01

In the field of laboratory medicine, minimizing errors and establishing standardization is only possible by predefined processes. The aim of this study was to build an experimental decision algorithm model open to improvement that would efficiently and rapidly evaluate the results of biochemical tests with critical values by evaluating multiple factors concurrently. The experimental model was built by Weka software (Weka, Waikato, New Zealand) based on the artificial neural network method. Data were received from Dokuz Eylül University Central Laboratory. "Training sets" were developed for our experimental model to teach the evaluation criteria. After training the system, "test sets" developed for different conditions were used to statistically assess the validity of the model. After developing the decision algorithm with three iterations of training, no result was verified that was refused by the laboratory specialist. The sensitivity of the model was 91% and specificity was 100%. The estimated κ score was 0.950. This is the first study based on an artificial neural network to build an experimental assessment and decision algorithm model. By integrating our trained algorithm model into a laboratory information system, it may be possible to reduce employees' workload without compromising patient safety. © American Society for Clinical Pathology, 2016. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

A depth-first search algorithm to compute elementary flux modes by linear programming.

PubMed

Quek, Lake-Ee; Nielsen, Lars K

2014-07-30

The decomposition of complex metabolic networks into elementary flux modes (EFMs) provides a useful framework for exploring reaction interactions systematically. Generating a complete set of EFMs for large-scale models, however, is near impossible. Even for moderately-sized models (<400 reactions), existing approaches based on the Double Description method must iterate through a large number of combinatorial candidates, thus imposing an immense processor and memory demand. Based on an alternative elementarity test, we developed a depth-first search algorithm using linear programming (LP) to enumerate EFMs in an exhaustive fashion. Constraints can be introduced to directly generate a subset of EFMs satisfying the set of constraints. The depth-first search algorithm has a constant memory overhead. Using flux constraints, a large LP problem can be massively divided and parallelized into independent sub-jobs for deployment into computing clusters. Since the sub-jobs do not overlap, the approach scales to utilize all available computing nodes with minimal coordination overhead or memory limitations. The speed of the algorithm was comparable to efmtool, a mainstream Double Description method, when enumerating all EFMs; the attrition power gained from performing flux feasibility tests offsets the increased computational demand of running an LP solver. Unlike the Double Description method, the algorithm enables accelerated enumeration of all EFMs satisfying a set of constraints.

Spectral Diffusion: An Algorithm for Robust Material Decomposition of Spectral CT Data

PubMed Central

Clark, Darin P.; Badea, Cristian T.

2014-01-01

Clinical successes with dual energy CT, aggressive development of energy discriminating x-ray detectors, and novel, target-specific, nanoparticle contrast agents promise to establish spectral CT as a powerful functional imaging modality. Common to all of these applications is the need for a material decomposition algorithm which is robust in the presence of noise. Here, we develop such an algorithm which uses spectrally joint, piece-wise constant kernel regression and the split Bregman method to iteratively solve for a material decomposition which is gradient sparse, quantitatively accurate, and minimally biased. We call this algorithm spectral diffusion because it integrates structural information from multiple spectral channels and their corresponding material decompositions within the framework of diffusion-like denoising algorithms (e.g. anisotropic diffusion, total variation, bilateral filtration). Using a 3D, digital bar phantom and a material sensitivity matrix calibrated for use with a polychromatic x-ray source, we quantify the limits of detectability (CNR = 5) afforded by spectral diffusion in the triple-energy material decomposition of iodine (3.1 mg/mL), gold (0.9 mg/mL), and gadolinium (2.9 mg/mL) concentrations. We then apply spectral diffusion to the in vivo separation of these three materials in the mouse kidneys, liver, and spleen. PMID:25296173

Spectral diffusion: an algorithm for robust material decomposition of spectral CT data.

PubMed

Clark, Darin P; Badea, Cristian T

2014-11-07

Clinical successes with dual energy CT, aggressive development of energy discriminating x-ray detectors, and novel, target-specific, nanoparticle contrast agents promise to establish spectral CT as a powerful functional imaging modality. Common to all of these applications is the need for a material decomposition algorithm which is robust in the presence of noise. Here, we develop such an algorithm which uses spectrally joint, piecewise constant kernel regression and the split Bregman method to iteratively solve for a material decomposition which is gradient sparse, quantitatively accurate, and minimally biased. We call this algorithm spectral diffusion because it integrates structural information from multiple spectral channels and their corresponding material decompositions within the framework of diffusion-like denoising algorithms (e.g. anisotropic diffusion, total variation, bilateral filtration). Using a 3D, digital bar phantom and a material sensitivity matrix calibrated for use with a polychromatic x-ray source, we quantify the limits of detectability (CNR = 5) afforded by spectral diffusion in the triple-energy material decomposition of iodine (3.1 mg mL(-1)), gold (0.9 mg mL(-1)), and gadolinium (2.9 mg mL(-1)) concentrations. We then apply spectral diffusion to the in vivo separation of these three materials in the mouse kidneys, liver, and spleen.

Hessian-based norm regularization for image restoration with biomedical applications.

PubMed

Lefkimmiatis, Stamatios; Bourquard, Aurélien; Unser, Michael

2012-03-01

We present nonquadratic Hessian-based regularization methods that can be effectively used for image restoration problems in a variational framework. Motivated by the great success of the total-variation (TV) functional, we extend it to also include second-order differential operators. Specifically, we derive second-order regularizers that involve matrix norms of the Hessian operator. The definition of these functionals is based on an alternative interpretation of TV that relies on mixed norms of directional derivatives. We show that the resulting regularizers retain some of the most favorable properties of TV, i.e., convexity, homogeneity, rotation, and translation invariance, while dealing effectively with the staircase effect. We further develop an efficient minimization scheme for the corresponding objective functions. The proposed algorithm is of the iteratively reweighted least-square type and results from a majorization-minimization approach. It relies on a problem-specific preconditioned conjugate gradient method, which makes the overall minimization scheme very attractive since it can be applied effectively to large images in a reasonable computational time. We validate the overall proposed regularization framework through deblurring experiments under additive Gaussian noise on standard and biomedical images.

CLAss-Specific Subspace Kernel Representations and Adaptive Margin Slack Minimization for Large Scale Classification.

PubMed

Yu, Yinan; Diamantaras, Konstantinos I; McKelvey, Tomas; Kung, Sun-Yuan

2018-02-01

In kernel-based classification models, given limited computational power and storage capacity, operations over the full kernel matrix becomes prohibitive. In this paper, we propose a new supervised learning framework using kernel models for sequential data processing. The framework is based on two components that both aim at enhancing the classification capability with a subset selection scheme. The first part is a subspace projection technique in the reproducing kernel Hilbert space using a CLAss-specific Subspace Kernel representation for kernel approximation. In the second part, we propose a novel structural risk minimization algorithm called the adaptive margin slack minimization to iteratively improve the classification accuracy by an adaptive data selection. We motivate each part separately, and then integrate them into learning frameworks for large scale data. We propose two such frameworks: the memory efficient sequential processing for sequential data processing and the parallelized sequential processing for distributed computing with sequential data acquisition. We test our methods on several benchmark data sets and compared with the state-of-the-art techniques to verify the validity of the proposed techniques.

Comparison of different eigensolvers for calculating vibrational spectra using low-rank, sum-of-product basis functions

NASA Astrophysics Data System (ADS)

Leclerc, Arnaud; Thomas, Phillip S.; Carrington, Tucker

2017-08-01

Vibrational spectra and wavefunctions of polyatomic molecules can be calculated at low memory cost using low-rank sum-of-product (SOP) decompositions to represent basis functions generated using an iterative eigensolver. Using a SOP tensor format does not determine the iterative eigensolver. The choice of the interative eigensolver is limited by the need to restrict the rank of the SOP basis functions at every stage of the calculation. We have adapted, implemented and compared different reduced-rank algorithms based on standard iterative methods (block-Davidson algorithm, Chebyshev iteration) to calculate vibrational energy levels and wavefunctions of the 12-dimensional acetonitrile molecule. The effect of using low-rank SOP basis functions on the different methods is analysed and the numerical results are compared with those obtained with the reduced rank block power method. Relative merits of the different algorithms are presented, showing that the advantage of using a more sophisticated method, although mitigated by the use of reduced-rank SOP functions, is noticeable in terms of CPU time.

Q-Learning-Based Adjustable Fixed-Phase Quantum Grover Search Algorithm

NASA Astrophysics Data System (ADS)

Guo, Ying; Shi, Wensha; Wang, Yijun; Hu, Jiankun

2017-02-01

We demonstrate that the rotation phase can be suitably chosen to increase the efficiency of the phase-based quantum search algorithm, leading to a dynamic balance between iterations and success probabilities of the fixed-phase quantum Grover search algorithm with Q-learning for a given number of solutions. In this search algorithm, the proposed Q-learning algorithm, which is a model-free reinforcement learning strategy in essence, is used for performing a matching algorithm based on the fraction of marked items λ and the rotation phase α. After establishing the policy function α = π(λ), we complete the fixed-phase Grover algorithm, where the phase parameter is selected via the learned policy. Simulation results show that the Q-learning-based Grover search algorithm (QLGA) enables fewer iterations and gives birth to higher success probabilities. Compared with the conventional Grover algorithms, it avoids the optimal local situations, thereby enabling success probabilities to approach one.

New matrix bounds and iterative algorithms for the discrete coupled algebraic Riccati equation

NASA Astrophysics Data System (ADS)

Liu, Jianzhou; Wang, Li; Zhang, Juan

2017-11-01

The discrete coupled algebraic Riccati equation (DCARE) has wide applications in control theory and linear system. In general, for the DCARE, one discusses every term of the coupled term, respectively. In this paper, we consider the coupled term as a whole, which is different from the recent results. When applying eigenvalue inequalities to discuss the coupled term, our method has less error. In terms of the properties of special matrices and eigenvalue inequalities, we propose several upper and lower matrix bounds for the solution of DCARE. Further, we discuss the iterative algorithms for the solution of the DCARE. In the fixed point iterative algorithms, the scope of Lipschitz factor is wider than the recent results. Finally, we offer corresponding numerical examples to illustrate the effectiveness of the derived results.

A fast reconstruction algorithm for fluorescence optical diffusion tomography based on preiteration.

PubMed

Song, Xiaolei; Xiong, Xiaoyun; Bai, Jing

2007-01-01

Fluorescence optical diffusion tomography in the near-infrared (NIR) bandwidth is considered to be one of the most promising ways for noninvasive molecular-based imaging. Many reconstructive approaches to it utilize iterative methods for data inversion. However, they are time-consuming and they are far from meeting the real-time imaging demands. In this work, a fast preiteration algorithm based on the generalized inverse matrix is proposed. This method needs only one step of matrix-vector multiplication online, by pushing the iteration process to be executed offline. In the preiteration process, the second-order iterative format is employed to exponentially accelerate the convergence. Simulations based on an analytical diffusion model show that the distribution of fluorescent yield can be well estimated by this algorithm and the reconstructed speed is remarkably increased.

Improving the efficiency of molecular replacement by utilizing a new iterative transform phasing algorithm

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

He, Hongxing; Fang, Hengrui; Miller, Mitchell D.

2016-07-15

An iterative transform algorithm is proposed to improve the conventional molecular-replacement method for solving the phase problem in X-ray crystallography. Several examples of successful trial calculations carried out with real diffraction data are presented. An iterative transform method proposed previously for direct phasing of high-solvent-content protein crystals is employed for enhancing the molecular-replacement (MR) algorithm in protein crystallography. Target structures that are resistant to conventional MR due to insufficient similarity between the template and target structures might be tractable with this modified phasing method. Trial calculations involving three different structures are described to test and illustrate the methodology. The relationshipmore » of the approach to PHENIX Phaser-MR and MR-Rosetta is discussed.« less

Noise removal in extended depth of field microscope images through nonlinear signal processing.

PubMed

Zahreddine, Ramzi N; Cormack, Robert H; Cogswell, Carol J

2013-04-01

Extended depth of field (EDF) microscopy, achieved through computational optics, allows for real-time 3D imaging of live cell dynamics. EDF is achieved through a combination of point spread function engineering and digital image processing. A linear Wiener filter has been conventionally used to deconvolve the image, but it suffers from high frequency noise amplification and processing artifacts. A nonlinear processing scheme is proposed which extends the depth of field while minimizing background noise. The nonlinear filter is generated via a training algorithm and an iterative optimizer. Biological microscope images processed with the nonlinear filter show a significant improvement in image quality and signal-to-noise ratio over the conventional linear filter.

Iterated oversampled filter banks and wavelet frames

NASA Astrophysics Data System (ADS)

Selesnick, Ivan W.; Sendur, Levent

2000-12-01

This paper takes up the design of wavelet tight frames that are analogous to Daubechies orthonormal wavelets - that is, the design of minimal length wavelet filters satisfying certain polynomial properties, but now in the oversampled case. The oversampled dyadic DWT considered in this paper is based on a single scaling function and tow distinct wavelets. Having more wavelets than necessary gives a closer spacing between adjacent wavelets within the same scale. As a result, the transform is nearly shift-invariant, and can be used to improve denoising. Because the associated time- frequency lattice preserves the dyadic structure of the critically sampled DWT it can be used with tree-based denoising algorithms that exploit parent-child correlation.

An iterative algorithm for L1-TV constrained regularization in image restoration

NASA Astrophysics Data System (ADS)

Chen, K.; Loli Piccolomini, E.; Zama, F.

2015-11-01

We consider the problem of restoring blurred images affected by impulsive noise. The adopted method restores the images by solving a sequence of constrained minimization problems where the data fidelity function is the ℓ1 norm of the residual and the constraint, chosen as the image Total Variation, is automatically adapted to improve the quality of the restored images. Although this approach is general, we report here the case of vectorial images where the blurring model involves contributions from the different image channels (cross channel blur). A computationally convenient extension of the Total Variation function to vectorial images is used and the results reported show that this approach is efficient for recovering nearly optimal images.

Simultaneous deblurring and iterative reconstruction of CBCT for image guided brain radiosurgery.

PubMed

Hashemi, SayedMasoud; Song, William Y; Sahgal, Arjun; Lee, Young; Huynh, Christopher; Grouza, Vladimir; Nordström, Håkan; Eriksson, Markus; Dorenlot, Antoine; Régis, Jean Marie; Mainprize, James G; Ruschin, Mark

2017-04-07

One of the limiting factors in cone-beam CT (CBCT) image quality is system blur, caused by detector response, x-ray source focal spot size, azimuthal blurring, and reconstruction algorithm. In this work, we develop a novel iterative reconstruction algorithm that improves spatial resolution by explicitly accounting for image unsharpness caused by different factors in the reconstruction formulation. While the model-based iterative reconstruction techniques use prior information about the detector response and x-ray source, our proposed technique uses a simple measurable blurring model. In our reconstruction algorithm, denoted as simultaneous deblurring and iterative reconstruction (SDIR), the blur kernel can be estimated using the modulation transfer function (MTF) slice of the CatPhan phantom or any other MTF phantom, such as wire phantoms. The proposed image reconstruction formulation includes two regularization terms: (1) total variation (TV) and (2) nonlocal regularization, solved with a split Bregman augmented Lagrangian iterative method. The SDIR formulation preserves edges, eases the parameter adjustments to achieve both high spatial resolution and low noise variances, and reduces the staircase effect caused by regular TV-penalized iterative algorithms. The proposed algorithm is optimized for a point-of-care head CBCT unit for image-guided radiosurgery and is tested with CatPhan phantom, an anthropomorphic head phantom, and 6 clinical brain stereotactic radiosurgery cases. Our experiments indicate that SDIR outperforms the conventional filtered back projection and TV penalized simultaneous algebraic reconstruction technique methods (represented by adaptive steepest-descent POCS algorithm, ASD-POCS) in terms of MTF and line pair resolution, and retains the favorable properties of the standard TV-based iterative reconstruction algorithms in improving the contrast and reducing the reconstruction artifacts. It improves the visibility of the high contrast details in bony areas and the brain soft-tissue. For example, the results show the ventricles and some brain folds become visible in SDIR reconstructed images and the contrast of the visible lesions is effectively improved. The line-pair resolution was improved from 12 line-pair/cm in FBP to 14 line-pair/cm in SDIR. Adjusting the parameters of the ASD-POCS to achieve 14 line-pair/cm caused the noise variance to be higher than the SDIR. Using these parameters for ASD-POCS, the MTF of FBP and ASD-POCS were very close and equal to 0.7 mm -1 which was increased to 1.2 mm -1 by SDIR, at half maximum.

Simultaneous deblurring and iterative reconstruction of CBCT for image guided brain radiosurgery

NASA Astrophysics Data System (ADS)

Hashemi, SayedMasoud; Song, William Y.; Sahgal, Arjun; Lee, Young; Huynh, Christopher; Grouza, Vladimir; Nordström, Håkan; Eriksson, Markus; Dorenlot, Antoine; Régis, Jean Marie; Mainprize, James G.; Ruschin, Mark

2017-04-01

One of the limiting factors in cone-beam CT (CBCT) image quality is system blur, caused by detector response, x-ray source focal spot size, azimuthal blurring, and reconstruction algorithm. In this work, we develop a novel iterative reconstruction algorithm that improves spatial resolution by explicitly accounting for image unsharpness caused by different factors in the reconstruction formulation. While the model-based iterative reconstruction techniques use prior information about the detector response and x-ray source, our proposed technique uses a simple measurable blurring model. In our reconstruction algorithm, denoted as simultaneous deblurring and iterative reconstruction (SDIR), the blur kernel can be estimated using the modulation transfer function (MTF) slice of the CatPhan phantom or any other MTF phantom, such as wire phantoms. The proposed image reconstruction formulation includes two regularization terms: (1) total variation (TV) and (2) nonlocal regularization, solved with a split Bregman augmented Lagrangian iterative method. The SDIR formulation preserves edges, eases the parameter adjustments to achieve both high spatial resolution and low noise variances, and reduces the staircase effect caused by regular TV-penalized iterative algorithms. The proposed algorithm is optimized for a point-of-care head CBCT unit for image-guided radiosurgery and is tested with CatPhan phantom, an anthropomorphic head phantom, and 6 clinical brain stereotactic radiosurgery cases. Our experiments indicate that SDIR outperforms the conventional filtered back projection and TV penalized simultaneous algebraic reconstruction technique methods (represented by adaptive steepest-descent POCS algorithm, ASD-POCS) in terms of MTF and line pair resolution, and retains the favorable properties of the standard TV-based iterative reconstruction algorithms in improving the contrast and reducing the reconstruction artifacts. It improves the visibility of the high contrast details in bony areas and the brain soft-tissue. For example, the results show the ventricles and some brain folds become visible in SDIR reconstructed images and the contrast of the visible lesions is effectively improved. The line-pair resolution was improved from 12 line-pair/cm in FBP to 14 line-pair/cm in SDIR. Adjusting the parameters of the ASD-POCS to achieve 14 line-pair/cm caused the noise variance to be higher than the SDIR. Using these parameters for ASD-POCS, the MTF of FBP and ASD-POCS were very close and equal to 0.7 mm-1 which was increased to 1.2 mm-1 by SDIR, at half maximum.

Noise reduction for low-dose helical CT by 3D penalized weighted least-squares sinogram smoothing

NASA Astrophysics Data System (ADS)

Wang, Jing; Li, Tianfang; Lu, Hongbing; Liang, Zhengrong

2006-03-01

Helical computed tomography (HCT) has several advantages over conventional step-and-shoot CT for imaging a relatively large object, especially for dynamic studies. However, HCT may increase X-ray exposure significantly to the patient. This work aims to reduce the radiation by lowering the X-ray tube current (mA) and filtering the low-mA (or dose) sinogram noise. Based on the noise properties of HCT sinogram, a three-dimensional (3D) penalized weighted least-squares (PWLS) objective function was constructed and an optimal sinogram was estimated by minimizing the objective function. To consider the difference of signal correlation among different direction of the HCT sinogram, an anisotropic Markov random filed (MRF) Gibbs function was designed as the penalty. The minimization of the objection function was performed by iterative Gauss-Seidel updating strategy. The effectiveness of the 3D-PWLS sinogram smoothing for low-dose HCT was demonstrated by a 3D Shepp-Logan head phantom study. Comparison studies with our previously developed KL domain PWLS sinogram smoothing algorithm indicate that the KL+2D-PWLS algorithm shows better performance on in-plane noise-resolution trade-off while the 3D-PLWS shows better performance on z-axis noise-resolution trade-off. Receiver operating characteristic (ROC) studies by using channelized Hotelling observer (CHO) shows that 3D-PWLS and KL+2DPWLS algorithms have similar performance on detectability in low-contrast environment.

Model-based minimization algorithm of a supercritical helium loop consumption subject to operational constraints

NASA Astrophysics Data System (ADS)

Bonne, F.; Bonnay, P.; Girard, A.; Hoa, C.; Lacroix, B.; Le Coz, Q.; Nicollet, S.; Poncet, J.-M.; Zani, L.

2017-12-01

Supercritical helium loops at 4.2 K are the baseline cooling strategy of tokamaks superconducting magnets (JT-60SA, ITER, DEMO, etc.). This loops work with cryogenic circulators that force a supercritical helium flow through the superconducting magnets in order that the temperature stay below the working range all along their length. This paper shows that a supercritical helium loop associated with a saturated liquid helium bath can satisfy temperature constraints in different ways (playing on bath temperature and on the supercritical flow), but that only one is optimal from an energy point of view (every Watt consumed at 4.2 K consumes at least 220 W of electrical power). To find the optimal operational conditions, an algorithm capable of minimizing an objective function (energy consumption at 5 bar, 5 K) subject to constraints has been written. This algorithm works with a supercritical loop model realized with the Simcryogenics [2] library. This article describes the model used and the results of constrained optimization. It will be possible to see that the changes in operating point on the temperature of the magnet (e.g. in case of a change in the plasma configuration) involves large changes on the cryodistribution optimal operating point. Recommendations will be made to ensure that the energetic consumption is kept as low as possible despite the changing operating point. This work is partially supported by EUROfusion Consortium through the Euratom Research and Training Program 20142018 under Grant 633053.

A biological phantom for evaluation of CT image reconstruction algorithms

NASA Astrophysics Data System (ADS)

Cammin, J.; Fung, G. S. K.; Fishman, E. K.; Siewerdsen, J. H.; Stayman, J. W.; Taguchi, K.

2014-03-01

In recent years, iterative algorithms have become popular in diagnostic CT imaging to reduce noise or radiation dose to the patient. The non-linear nature of these algorithms leads to non-linearities in the imaging chain. However, the methods to assess the performance of CT imaging systems were developed assuming the linear process of filtered backprojection (FBP). Those methods may not be suitable any longer when applied to non-linear systems. In order to evaluate the imaging performance, a phantom is typically scanned and the image quality is measured using various indices. For reasons of practicality, cost, and durability, those phantoms often consist of simple water containers with uniform cylinder inserts. However, these phantoms do not represent the rich structure and patterns of real tissue accurately. As a result, the measured image quality or detectability performance for lesions may not reflect the performance on clinical images. The discrepancy between estimated and real performance may be even larger for iterative methods which sometimes produce "plastic-like", patchy images with homogeneous patterns. Consequently, more realistic phantoms should be used to assess the performance of iterative algorithms. We designed and constructed a biological phantom consisting of porcine organs and tissue that models a human abdomen, including liver lesions. We scanned the phantom on a clinical CT scanner and compared basic image quality indices between filtered backprojection and an iterative reconstruction algorithm.

Iterative Transform Phase Diversity: An Image-Based Object and Wavefront Recovery

NASA Technical Reports Server (NTRS)

Smith, Jeffrey

2012-01-01

The Iterative Transform Phase Diversity algorithm is designed to solve the problem of recovering the wavefront in the exit pupil of an optical system and the object being imaged. This algorithm builds upon the robust convergence capability of Variable Sampling Mapping (VSM), in combination with the known success of various deconvolution algorithms. VSM is an alternative method for enforcing the amplitude constraints of a Misell-Gerchberg-Saxton (MGS) algorithm. When provided the object and additional optical parameters, VSM can accurately recover the exit pupil wavefront. By combining VSM and deconvolution, one is able to simultaneously recover the wavefront and the object.

Optimal Decentralized Protocol for Electric Vehicle Charging

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

Gan, LW; Topcu, U; Low, SH

We propose a decentralized algorithm to optimally schedule electric vehicle (EV) charging. The algorithm exploits the elasticity of electric vehicle loads to fill the valleys in electric load profiles. We first formulate the EV charging scheduling problem as an optimal control problem, whose objective is to impose a generalized notion of valley-filling, and study properties of optimal charging profiles. We then give a decentralized algorithm to iteratively solve the optimal control problem. In each iteration, EVs update their charging profiles according to the control signal broadcast by the utility company, and the utility company alters the control signal to guidemore » their updates. The algorithm converges to optimal charging profiles (that are as "flat" as they can possibly be) irrespective of the specifications (e.g., maximum charging rate and deadline) of EVs, even if EVs do not necessarily update their charging profiles in every iteration, and use potentially outdated control signal when they update. Moreover, the algorithm only requires each EV solving its local problem, hence its implementation requires low computation capability. We also extend the algorithm to track a given load profile and to real-time implementation.« less

A New Pivoting and Iterative Text Detection Algorithm for Biomedical Images

PubMed Central

Xu, Songhua; Krauthammer, Michael

2010-01-01

There is interest to expand the reach of literature mining to include the analysis of biomedical images, which often contain a paper’s key findings. Examples include recent studies that use Optical Character Recognition (OCR) to extract image text, which is used to boost biomedical image retrieval and classification. Such studies rely on the robust identification of text elements in biomedical images, which is a non-trivial task. In this work, we introduce a new text detection algorithm for biomedical images based on iterative projection histograms. We study the effectiveness of our algorithm by evaluating the performance on a set of manually labeled random biomedical images, and compare the performance against other state-of-the-art text detection algorithms. In this paper, we demonstrate that a projection histogram-based text detection approach is well suited for text detection in biomedical images, with a performance of F score of .60. The approach performs better than comparable approaches for text detection. Further, we show that the iterative application of the algorithm is boosting overall detection performance. A C++ implementation of our algorithm is freely available through email request for academic use. PMID:20887803

Marginal Consistency: Upper-Bounding Partition Functions over Commutative Semirings.

PubMed

Werner, Tomás

2015-07-01

Many inference tasks in pattern recognition and artificial intelligence lead to partition functions in which addition and multiplication are abstract binary operations forming a commutative semiring. By generalizing max-sum diffusion (one of convergent message passing algorithms for approximate MAP inference in graphical models), we propose an iterative algorithm to upper bound such partition functions over commutative semirings. The iteration of the algorithm is remarkably simple: change any two factors of the partition function such that their product remains the same and their overlapping marginals become equal. In many commutative semirings, repeating this iteration for different pairs of factors converges to a fixed point when the overlapping marginals of every pair of factors coincide. We call this state marginal consistency. During that, an upper bound on the partition function monotonically decreases. This abstract algorithm unifies several existing algorithms, including max-sum diffusion and basic constraint propagation (or local consistency) algorithms in constraint programming. We further construct a hierarchy of marginal consistencies of increasingly higher levels and show than any such level can be enforced by adding identity factors of higher arity (order). Finally, we discuss instances of the framework for several semirings, including the distributive lattice and the max-sum and sum-product semirings.

Efficient convex-elastic net algorithm to solve the Euclidean traveling salesman problem.

PubMed

Al-Mulhem, M; Al-Maghrabi, T

1998-01-01

This paper describes a hybrid algorithm that combines an adaptive-type neural network algorithm and a nondeterministic iterative algorithm to solve the Euclidean traveling salesman problem (E-TSP). It begins with a brief introduction to the TSP and the E-TSP. Then, it presents the proposed algorithm with its two major components: the convex-elastic net (CEN) algorithm and the nondeterministic iterative improvement (NII) algorithm. These two algorithms are combined into the efficient convex-elastic net (ECEN) algorithm. The CEN algorithm integrates the convex-hull property and elastic net algorithm to generate an initial tour for the E-TSP. The NII algorithm uses two rearrangement operators to improve the initial tour given by the CEN algorithm. The paper presents simulation results for two instances of E-TSP: randomly generated tours and tours for well-known problems in the literature. Experimental results are given to show that the proposed algorithm ran find the nearly optimal solution for the E-TSP that outperform many similar algorithms reported in the literature. The paper concludes with the advantages of the new algorithm and possible extensions.

A Novel Particle Swarm Optimization Algorithm for Global Optimization

PubMed Central

Wang, Chun-Feng; Liu, Kui

2016-01-01

Particle Swarm Optimization (PSO) is a recently developed optimization method, which has attracted interest of researchers in various areas due to its simplicity and effectiveness, and many variants have been proposed. In this paper, a novel Particle Swarm Optimization algorithm is presented, in which the information of the best neighbor of each particle and the best particle of the entire population in the current iteration is considered. Meanwhile, to avoid premature, an abandoned mechanism is used. Furthermore, for improving the global convergence speed of our algorithm, a chaotic search is adopted in the best solution of the current iteration. To verify the performance of our algorithm, standard test functions have been employed. The experimental results show that the algorithm is much more robust and efficient than some existing Particle Swarm Optimization algorithms. PMID:26955387

Guided particle swarm optimization method to solve general nonlinear optimization problems

NASA Astrophysics Data System (ADS)

Abdelhalim, Alyaa; Nakata, Kazuhide; El-Alem, Mahmoud; Eltawil, Amr

2018-04-01

The development of hybrid algorithms is becoming an important topic in the global optimization research area. This article proposes a new technique in hybridizing the particle swarm optimization (PSO) algorithm and the Nelder-Mead (NM) simplex search algorithm to solve general nonlinear unconstrained optimization problems. Unlike traditional hybrid methods, the proposed method hybridizes the NM algorithm inside the PSO to improve the velocities and positions of the particles iteratively. The new hybridization considers the PSO algorithm and NM algorithm as one heuristic, not in a sequential or hierarchical manner. The NM algorithm is applied to improve the initial random solution of the PSO algorithm and iteratively in every step to improve the overall performance of the method. The performance of the proposed method was tested over 20 optimization test functions with varying dimensions. Comprehensive comparisons with other methods in the literature indicate that the proposed solution method is promising and competitive.

A proximity algorithm accelerated by Gauss-Seidel iterations for L1/TV denoising models

NASA Astrophysics Data System (ADS)

Li, Qia; Micchelli, Charles A.; Shen, Lixin; Xu, Yuesheng

2012-09-01

Our goal in this paper is to improve the computational performance of the proximity algorithms for the L1/TV denoising model. This leads us to a new characterization of all solutions to the L1/TV model via fixed-point equations expressed in terms of the proximity operators. Based upon this observation we develop an algorithm for solving the model and establish its convergence. Furthermore, we demonstrate that the proposed algorithm can be accelerated through the use of the componentwise Gauss-Seidel iteration so that the CPU time consumed is significantly reduced. Numerical experiments using the proposed algorithm for impulsive noise removal are included, with a comparison to three recently developed algorithms. The numerical results show that while the proposed algorithm enjoys a high quality of the restored images, as the other three known algorithms do, it performs significantly better in terms of computational efficiency measured in the CPU time consumed.

Accuracy Improvement for Light-Emitting-Diode-Based Colorimeter by Iterative Algorithm

NASA Astrophysics Data System (ADS)

Yang, Pao-Keng

2011-09-01

We present a simple algorithm, combining an interpolating method with an iterative calculation, to enhance the resolution of spectral reflectance by removing the spectral broadening effect due to the finite bandwidth of the light-emitting diode (LED) from it. The proposed algorithm can be used to improve the accuracy of a reflective colorimeter using multicolor LEDs as probing light sources and is also applicable to the case when the probing LEDs have different bandwidths in different spectral ranges, to which the powerful deconvolution method cannot be applied.

Language Evolution by Iterated Learning with Bayesian Agents

ERIC Educational Resources Information Center

Griffiths, Thomas L.; Kalish, Michael L.

2007-01-01

Languages are transmitted from person to person and generation to generation via a process of iterated learning: people learn a language from other people who once learned that language themselves. We analyze the consequences of iterated learning for learning algorithms based on the principles of Bayesian inference, assuming that learners compute…

Wireless Power Transfer for Distributed Estimation in Sensor Networks

NASA Astrophysics Data System (ADS)

Mai, Vien V.; Shin, Won-Yong; Ishibashi, Koji

2017-04-01

This paper studies power allocation for distributed estimation of an unknown scalar random source in sensor networks with a multiple-antenna fusion center (FC), where wireless sensors are equipped with radio-frequency based energy harvesting technology. The sensors' observation is locally processed by using an uncoded amplify-and-forward scheme. The processed signals are then sent to the FC, and are coherently combined at the FC, at which the best linear unbiased estimator (BLUE) is adopted for reliable estimation. We aim to solve the following two power allocation problems: 1) minimizing distortion under various power constraints; and 2) minimizing total transmit power under distortion constraints, where the distortion is measured in terms of mean-squared error of the BLUE. Two iterative algorithms are developed to solve the non-convex problems, which converge at least to a local optimum. In particular, the above algorithms are designed to jointly optimize the amplification coefficients, energy beamforming, and receive filtering. For each problem, a suboptimal design, a single-antenna FC scenario, and a common harvester deployment for colocated sensors, are also studied. Using the powerful semidefinite relaxation framework, our result is shown to be valid for any number of sensors, each with different noise power, and for an arbitrarily number of antennas at the FC.

Exact and approximate Fourier rebinning algorithms for the solution of the data truncation problem in 3-D PET.

PubMed

Bouallègue, Fayçal Ben; Crouzet, Jean-François; Comtat, Claude; Fourcade, Marjolaine; Mohammadi, Bijan; Mariano-Goulart, Denis

2007-07-01

This paper presents an extended 3-D exact rebinning formula in the Fourier space that leads to an iterative reprojection algorithm (iterative FOREPROJ), which enables the estimation of unmeasured oblique projection data on the basis of the whole set of measured data. In first approximation, this analytical formula also leads to an extended Fourier rebinning equation that is the basis for an approximate reprojection algorithm (extended FORE). These algorithms were evaluated on numerically simulated 3-D positron emission tomography (PET) data for the solution of the truncation problem, i.e., the estimation of the missing portions in the oblique projection data, before the application of algorithms that require complete projection data such as some rebinning methods (FOREX) or 3-D reconstruction algorithms (3DRP or direct Fourier methods). By taking advantage of all the 3-D data statistics, the iterative FOREPROJ reprojection provides a reliable alternative to the classical FOREPROJ method, which only exploits the low-statistics nonoblique data. It significantly improves the quality of the external reconstructed slices without loss of spatial resolution. As for the approximate extended FORE algorithm, it clearly exhibits limitations due to axial interpolations, but will require clinical studies with more realistic measured data in order to decide on its pertinence.

The Normalized-Rate Iterative Algorithm: A Practical Dynamic Spectrum Management Method for DSL

NASA Astrophysics Data System (ADS)

Statovci, Driton; Nordström, Tomas; Nilsson, Rickard

2006-12-01

We present a practical solution for dynamic spectrum management (DSM) in digital subscriber line systems: the normalized-rate iterative algorithm (NRIA). Supported by a novel optimization problem formulation, the NRIA is the only DSM algorithm that jointly addresses spectrum balancing for frequency division duplexing systems and power allocation for the users sharing a common cable bundle. With a focus on being implementable rather than obtaining the highest possible theoretical performance, the NRIA is designed to efficiently solve the DSM optimization problem with the operators' business models in mind. This is achieved with the help of two types of parameters: the desired network asymmetry and the desired user priorities. The NRIA is a centralized DSM algorithm based on the iterative water-filling algorithm (IWFA) for finding efficient power allocations, but extends the IWFA by finding the achievable bitrates and by optimizing the bandplan. It is compared with three other DSM proposals: the IWFA, the optimal spectrum balancing algorithm (OSBA), and the bidirectional IWFA (bi-IWFA). We show that the NRIA achieves better bitrate performance than the IWFA and the bi-IWFA. It can even achieve performance almost as good as the OSBA, but with dramatically lower requirements on complexity. Additionally, the NRIA can achieve bitrate combinations that cannot be supported by any other DSM algorithm.

On the assessment of spatial resolution of PET systems with iterative image reconstruction

NASA Astrophysics Data System (ADS)

Gong, Kuang; Cherry, Simon R.; Qi, Jinyi

2016-03-01

Spatial resolution is an important metric for performance characterization in PET systems. Measuring spatial resolution is straightforward with a linear reconstruction algorithm, such as filtered backprojection, and can be performed by reconstructing a point source scan and calculating the full-width-at-half-maximum (FWHM) along the principal directions. With the widespread adoption of iterative reconstruction methods, it is desirable to quantify the spatial resolution using an iterative reconstruction algorithm. However, the task can be difficult because the reconstruction algorithms are nonlinear and the non-negativity constraint can artificially enhance the apparent spatial resolution if a point source image is reconstructed without any background. Thus, it was recommended that a background should be added to the point source data before reconstruction for resolution measurement. However, there has been no detailed study on the effect of the point source contrast on the measured spatial resolution. Here we use point source scans from a preclinical PET scanner to investigate the relationship between measured spatial resolution and the point source contrast. We also evaluate whether the reconstruction of an isolated point source is predictive of the ability of the system to resolve two adjacent point sources. Our results indicate that when the point source contrast is below a certain threshold, the measured FWHM remains stable. Once the contrast is above the threshold, the measured FWHM monotonically decreases with increasing point source contrast. In addition, the measured FWHM also monotonically decreases with iteration number for maximum likelihood estimate. Therefore, when measuring system resolution with an iterative reconstruction algorithm, we recommend using a low-contrast point source and a fixed number of iterations.

A Survey of the Use of Iterative Reconstruction Algorithms in Electron Microscopy

PubMed Central

Otón, J.; Vilas, J. L.; Kazemi, M.; Melero, R.; del Caño, L.; Cuenca, J.; Conesa, P.; Gómez-Blanco, J.; Marabini, R.; Carazo, J. M.

2017-01-01

One of the key steps in Electron Microscopy is the tomographic reconstruction of a three-dimensional (3D) map of the specimen being studied from a set of two-dimensional (2D) projections acquired at the microscope. This tomographic reconstruction may be performed with different reconstruction algorithms that can be grouped into several large families: direct Fourier inversion methods, back-projection methods, Radon methods, or iterative algorithms. In this review, we focus on the latter family of algorithms, explaining the mathematical rationale behind the different algorithms in this family as they have been introduced in the field of Electron Microscopy. We cover their use in Single Particle Analysis (SPA) as well as in Electron Tomography (ET). PMID:29312997

The MHOST finite element program: 3-D inelastic analysis methods for hot section components. Volume 1: Theoretical manual

NASA Technical Reports Server (NTRS)

Nakazawa, Shohei

1991-01-01

Formulations and algorithms implemented in the MHOST finite element program are discussed. The code uses a novel concept of the mixed iterative solution technique for the efficient 3-D computations of turbine engine hot section components. The general framework of variational formulation and solution algorithms are discussed which were derived from the mixed three field Hu-Washizu principle. This formulation enables the use of nodal interpolation for coordinates, displacements, strains, and stresses. Algorithmic description of the mixed iterative method includes variations for the quasi static, transient dynamic and buckling analyses. The global-local analysis procedure referred to as the subelement refinement is developed in the framework of the mixed iterative solution, of which the detail is presented. The numerically integrated isoparametric elements implemented in the framework is discussed. Methods to filter certain parts of strain and project the element discontinuous quantities to the nodes are developed for a family of linear elements. Integration algorithms are described for linear and nonlinear equations included in MHOST program.

Numerical evaluation of mobile robot navigation in static indoor environment via EGAOR Iteration

NASA Astrophysics Data System (ADS)

Dahalan, A. A.; Saudi, A.; Sulaiman, J.; Din, W. R. W.

2017-09-01

One of the key issues in mobile robot navigation is the ability for the robot to move from an arbitrary start location to a specified goal location without colliding with any obstacles while traveling, also known as mobile robot path planning problem. In this paper, however, we examined the performance of a robust searching algorithm that relies on the use of harmonic potentials of the environment to generate smooth and safe path for mobile robot navigation in a static known indoor environment. The harmonic potentials will be discretized by using Laplacian’s operator to form a system of algebraic approximation equations. This algebraic linear system will be computed via 4-Point Explicit Group Accelerated Over-Relaxation (4-EGAOR) iterative method for rapid computation. The performance of the proposed algorithm will then be compared and analyzed against the existing algorithms in terms of number of iterations and execution time. The result shows that the proposed algorithm performed better than the existing methods.

Iterative Most-Likely Point Registration (IMLP): A Robust Algorithm for Computing Optimal Shape Alignment

PubMed Central

Billings, Seth D.; Boctor, Emad M.; Taylor, Russell H.

2015-01-01

We present a probabilistic registration algorithm that robustly solves the problem of rigid-body alignment between two shapes with high accuracy, by aptly modeling measurement noise in each shape, whether isotropic or anisotropic. For point-cloud shapes, the probabilistic framework additionally enables modeling locally-linear surface regions in the vicinity of each point to further improve registration accuracy. The proposed Iterative Most-Likely Point (IMLP) algorithm is formed as a variant of the popular Iterative Closest Point (ICP) algorithm, which iterates between point-correspondence and point-registration steps. IMLP’s probabilistic framework is used to incorporate a generalized noise model into both the correspondence and the registration phases of the algorithm, hence its name as a most-likely point method rather than a closest-point method. To efficiently compute the most-likely correspondences, we devise a novel search strategy based on a principal direction (PD)-tree search. We also propose a new approach to solve the generalized total-least-squares (GTLS) sub-problem of the registration phase, wherein the point correspondences are registered under a generalized noise model. Our GTLS approach has improved accuracy, efficiency, and stability compared to prior methods presented for this problem and offers a straightforward implementation using standard least squares. We evaluate the performance of IMLP relative to a large number of prior algorithms including ICP, a robust variant on ICP, Generalized ICP (GICP), and Coherent Point Drift (CPD), as well as drawing close comparison with the prior anisotropic registration methods of GTLS-ICP and A-ICP. The performance of IMLP is shown to be superior with respect to these algorithms over a wide range of noise conditions, outliers, and misalignments using both mesh and point-cloud representations of various shapes. PMID:25748700

Efficient iterative image reconstruction algorithm for dedicated breast CT

NASA Astrophysics Data System (ADS)

Antropova, Natalia; Sanchez, Adrian; Reiser, Ingrid S.; Sidky, Emil Y.; Boone, John; Pan, Xiaochuan

2016-03-01

Dedicated breast computed tomography (bCT) is currently being studied as a potential screening method for breast cancer. The X-ray exposure is set low to achieve an average glandular dose comparable to that of mammography, yielding projection data that contains high levels of noise. Iterative image reconstruction (IIR) algorithms may be well-suited for the system since they potentially reduce the effects of noise in the reconstructed images. However, IIR outcomes can be difficult to control since the algorithm parameters do not directly correspond to the image properties. Also, IIR algorithms are computationally demanding and have optimal parameter settings that depend on the size and shape of the breast and positioning of the patient. In this work, we design an efficient IIR algorithm with meaningful parameter specifications and that can be used on a large, diverse sample of bCT cases. The flexibility and efficiency of this method comes from having the final image produced by a linear combination of two separately reconstructed images - one containing gray level information and the other with enhanced high frequency components. Both of the images result from few iterations of separate IIR algorithms. The proposed algorithm depends on two parameters both of which have a well-defined impact on image quality. The algorithm is applied to numerous bCT cases from a dedicated bCT prototype system developed at University of California, Davis.

Improved event positioning in a gamma ray detector using an iterative position-weighted centre-of-gravity algorithm.

PubMed

Liu, Chen-Yi; Goertzen, Andrew L

2013-07-21

An iterative position-weighted centre-of-gravity algorithm was developed and tested for positioning events in a silicon photomultiplier (SiPM)-based scintillation detector for positron emission tomography. The algorithm used a Gaussian-based weighting function centred at the current estimate of the event location. The algorithm was applied to the signals from a 4 × 4 array of SiPM detectors that used individual channel readout and a LYSO:Ce scintillator array. Three scintillator array configurations were tested: single layer with 3.17 mm crystal pitch, matched to the SiPM size; single layer with 1.5 mm crystal pitch; and dual layer with 1.67 mm crystal pitch and a ½ crystal offset in the X and Y directions between the two layers. The flood histograms generated by this algorithm were shown to be superior to those generated by the standard centre of gravity. The width of the Gaussian weighting function of the algorithm was optimized for different scintillator array setups. The optimal width of the Gaussian curve was found to depend on the amount of light spread. The algorithm required less than 20 iterations to calculate the position of an event. The rapid convergence of this algorithm will readily allow for implementation on a front-end detector processing field programmable gate array for use in improved real-time event positioning and identification.

WE-G-207-07: Iterative CT Shading Correction Method with No Prior Information

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

Wu, P; Mao, T; Niu, T

2015-06-15

Purpose: Shading artifacts are caused by scatter contamination, beam hardening effects and other non-ideal imaging condition. Our Purpose is to propose a novel and general correction framework to eliminate low-frequency shading artifacts in CT imaging (e.g., cone-beam CT, low-kVp CT) without relying on prior information. Methods: Our method applies general knowledge of the relatively uniform CT number distribution in one tissue component. Image segmentation is applied to construct template image where each structure is filled with the same CT number of that specific tissue. By subtracting the ideal template from CT image, the residual from various error sources are generated.more » Since the forward projection is an integration process, the non-continuous low-frequency shading artifacts in the image become continuous and low-frequency signals in the line integral. Residual image is thus forward projected and its line integral is filtered using Savitzky-Golay filter to estimate the error. A compensation map is reconstructed on the error using standard FDK algorithm and added to the original image to obtain the shading corrected one. Since the segmentation is not accurate on shaded CT image, the proposed scheme is iterated until the variation of residual image is minimized. Results: The proposed method is evaluated on a Catphan600 phantom, a pelvic patient and a CT angiography scan for carotid artery assessment. Compared to the one without correction, our method reduces the overall CT number error from >200 HU to be <35 HU and increases the spatial uniformity by a factor of 1.4. Conclusion: We propose an effective iterative algorithm for shading correction in CT imaging. Being different from existing algorithms, our method is only assisted by general anatomical and physical information in CT imaging without relying on prior knowledge. Our method is thus practical and attractive as a general solution to CT shading correction. This work is supported by the National Science Foundation of China (NSFC Grant No. 81201091), National High Technology Research and Development Program of China (863 program, Grant No. 2015AA020917), and Fund Project for Excellent Abroad Scholar Personnel in Science and Technology.« less

Fast registration and reconstruction of aliased low-resolution frames by use of a modified maximum-likelihood approach.

PubMed

Alam, M S; Bognar, J G; Cain, S; Yasuda, B J

1998-03-10

During the process of microscanning a controlled vibrating mirror typically is used to produce subpixel shifts in a sequence of forward-looking infrared (FLIR) images. If the FLIR is mounted on a moving platform, such as an aircraft, uncontrolled random vibrations associated with the platform can be used to generate the shifts. Iterative techniques such as the expectation-maximization (EM) approach by means of the maximum-likelihood algorithm can be used to generate high-resolution images from multiple randomly shifted aliased frames. In the maximum-likelihood approach the data are considered to be Poisson random variables and an EM algorithm is developed that iteratively estimates an unaliased image that is compensated for known imager-system blur while it simultaneously estimates the translational shifts. Although this algorithm yields high-resolution images from a sequence of randomly shifted frames, it requires significant computation time and cannot be implemented for real-time applications that use the currently available high-performance processors. The new image shifts are iteratively calculated by evaluation of a cost function that compares the shifted and interlaced data frames with the corresponding values in the algorithm's latest estimate of the high-resolution image. We present a registration algorithm that estimates the shifts in one step. The shift parameters provided by the new algorithm are accurate enough to eliminate the need for iterative recalculation of translational shifts. Using this shift information, we apply a simplified version of the EM algorithm to estimate a high-resolution image from a given sequence of video frames. The proposed modified EM algorithm has been found to reduce significantly the computational burden when compared with the original EM algorithm, thus making it more attractive for practical implementation. Both simulation and experimental results are presented to verify the effectiveness of the proposed technique.

Bounded-Angle Iterative Decoding of LDPC Codes

NASA Technical Reports Server (NTRS)

Dolinar, Samuel; Andrews, Kenneth; Pollara, Fabrizio; Divsalar, Dariush

2009-01-01

Bounded-angle iterative decoding is a modified version of conventional iterative decoding, conceived as a means of reducing undetected-error rates for short low-density parity-check (LDPC) codes. For a given code, bounded-angle iterative decoding can be implemented by means of a simple modification of the decoder algorithm, without redesigning the code. Bounded-angle iterative decoding is based on a representation of received words and code words as vectors in an n-dimensional Euclidean space (where n is an integer).

Adapting iterative algorithms for solving large sparse linear systems for efficient use on the CDC CYBER 205

NASA Technical Reports Server (NTRS)

Kincaid, D. R.; Young, D. M.

1984-01-01

Adapting and designing mathematical software to achieve optimum performance on the CYBER 205 is discussed. Comments and observations are made in light of recent work done on modifying the ITPACK software package and on writing new software for vector supercomputers. The goal was to develop very efficient vector algorithms and software for solving large sparse linear systems using iterative methods.

Optimization of image quality and acquisition time for lab-based X-ray microtomography using an iterative reconstruction algorithm

NASA Astrophysics Data System (ADS)

Lin, Qingyang; Andrew, Matthew; Thompson, William; Blunt, Martin J.; Bijeljic, Branko

2018-05-01

Non-invasive laboratory-based X-ray microtomography has been widely applied in many industrial and research disciplines. However, the main barrier to the use of laboratory systems compared to a synchrotron beamline is its much longer image acquisition time (hours per scan compared to seconds to minutes at a synchrotron), which results in limited application for dynamic in situ processes. Therefore, the majority of existing laboratory X-ray microtomography is limited to static imaging; relatively fast imaging (tens of minutes per scan) can only be achieved by sacrificing imaging quality, e.g. reducing exposure time or number of projections. To alleviate this barrier, we introduce an optimized implementation of a well-known iterative reconstruction algorithm that allows users to reconstruct tomographic images with reasonable image quality, but requires lower X-ray signal counts and fewer projections than conventional methods. Quantitative analysis and comparison between the iterative and the conventional filtered back-projection reconstruction algorithm was performed using a sandstone rock sample with and without liquid phases in the pore space. Overall, by implementing the iterative reconstruction algorithm, the required image acquisition time for samples such as this, with sparse object structure, can be reduced by a factor of up to 4 without measurable loss of sharpness or signal to noise ratio.

Autonomous Method and System for Minimizing the Magnitude of Plasma Discharge Current Oscillations in a Hall Effect Plasma Device

NASA Technical Reports Server (NTRS)

Hruby, Vladimir (Inventor); Demmons, Nathaniel (Inventor); Ehrbar, Eric (Inventor); Pote, Bruce (Inventor); Rosenblad, Nathan (Inventor)

2014-01-01

An autonomous method for minimizing the magnitude of plasma discharge current oscillations in a Hall effect plasma device includes iteratively measuring plasma discharge current oscillations of the plasma device and iteratively adjusting the magnet current delivered to the plasma device in response to measured plasma discharge current oscillations to reduce the magnitude of the plasma discharge current oscillations.

Iterative Correction of Reference Nucleotides (iCORN) using second generation sequencing technology.

PubMed

Otto, Thomas D; Sanders, Mandy; Berriman, Matthew; Newbold, Chris

2010-07-15

The accuracy of reference genomes is important for downstream analysis but a low error rate requires expensive manual interrogation of the sequence. Here, we describe a novel algorithm (Iterative Correction of Reference Nucleotides) that iteratively aligns deep coverage of short sequencing reads to correct errors in reference genome sequences and evaluate their accuracy. Using Plasmodium falciparum (81% A + T content) as an extreme example, we show that the algorithm is highly accurate and corrects over 2000 errors in the reference sequence. We give examples of its application to numerous other eukaryotic and prokaryotic genomes and suggest additional applications. The software is available at http://icorn.sourceforge.net

Improving Automated Endmember Identification for Linear Unmixing of HyspIRI Spectral Data.

NASA Astrophysics Data System (ADS)

Gader, P.

2016-12-01

The size of data sets produced by imaging spectrometers is increasing rapidly. There is already a processing bottleneck. Part of the reason for this bottleneck is the need for expert input using interactive software tools. This process can be very time consuming and laborious but is currently crucial to ensuring the quality of the analysis. Automated algorithms can mitigate this problem. Although it is unlikely that processing systems can become completely automated, there is an urgent need to increase the level of automation. Spectral unmixing is a key component to processing HyspIRI data. Algorithms such as MESMA have been demonstrated to achieve results but require carefully, expert construction of endmember libraries. Unfortunately, many endmembers found by automated algorithms for finding endmembers are deemed unsuitable by experts because they are not physically reasonable. Unfortunately, endmembers that are not physically reasonable can achieve very low errors between the linear mixing model with those endmembers and the original data. Therefore, this error is not a reasonable way to resolve the problem on "non-physical" endmembers. There are many potential approaches for resolving these issues, including using Bayesian priors, but very little attention has been given to this problem. The study reported on here considers a modification of the Sparsity Promoting Iterated Constrained Endmember (SPICE) algorithm. SPICE finds endmembers and abundances and estimates the number of endmembers. The SPICE algorithm seeks to minimize a quadratic objective function with respect to endmembers E and fractions P. The modified SPICE algorithm, which we refer to as SPICED, is obtained by adding the term D to the objective function. The term D pressures the algorithm to minimize sum of the squared differences between each endmember and a weighted sum of the data. By appropriately modifying the, the endmembers are pushed towards a subset of the data with the potential for becoming exactly equal to the data points. The algorithm has been applied to spectral data and the differences between the endmembers resulting from ecorded. The results so far are that the endmembers found SPICED are approximately 25% closer to the data with indistinguishable reconstruction error compared to those found using SPICE.

Reliable recovery of the optical properties of multi-layer turbid media by iteratively using a layered diffusion model at multiple source-detector separations

PubMed Central

Liao, Yu-Kai; Tseng, Sheng-Hao

2014-01-01

Accurately determining the optical properties of multi-layer turbid media using a layered diffusion model is often a difficult task and could be an ill-posed problem. In this study, an iterative algorithm was proposed for solving such problems. This algorithm employed a layered diffusion model to calculate the optical properties of a layered sample at several source-detector separations (SDSs). The optical properties determined at various SDSs were mutually referenced to complete one round of iteration and the optical properties were gradually revised in further iterations until a set of stable optical properties was obtained. We evaluated the performance of the proposed method using frequency domain Monte Carlo simulations and found that the method could robustly recover the layered sample properties with various layer thickness and optical property settings. It is expected that this algorithm can work with photon transport models in frequency and time domain for various applications, such as determination of subcutaneous fat or muscle optical properties and monitoring the hemodynamics of muscle. PMID:24688828

Use of Multi-class Empirical Orthogonal Function for Identification of Hydrogeological Parameters and Spatiotemporal Pattern of Multiple Recharges in Groundwater Modeling

NASA Astrophysics Data System (ADS)

Huang, C. L.; Hsu, N. S.; Yeh, W. W. G.; Hsieh, I. H.

2017-12-01

This study develops an innovative calibration method for regional groundwater modeling by using multi-class empirical orthogonal functions (EOFs). The developed method is an iterative approach. Prior to carrying out the iterative procedures, the groundwater storage hydrographs associated with the observation wells are calculated. The combined multi-class EOF amplitudes and EOF expansion coefficients of the storage hydrographs are then used to compute the initial gauss of the temporal and spatial pattern of multiple recharges. The initial guess of the hydrogeological parameters are also assigned according to in-situ pumping experiment. The recharges include net rainfall recharge and boundary recharge, and the hydrogeological parameters are riverbed leakage conductivity, horizontal hydraulic conductivity, vertical hydraulic conductivity, storage coefficient, and specific yield. The first step of the iterative algorithm is to conduct the numerical model (i.e. MODFLOW) by the initial guess / adjusted values of the recharges and parameters. Second, in order to determine the best EOF combination of the error storage hydrographs for determining the correction vectors, the objective function is devised as minimizing the root mean square error (RMSE) of the simulated storage hydrographs. The error storage hydrograph are the differences between the storage hydrographs computed from observed and simulated groundwater level fluctuations. Third, adjust the values of recharges and parameters and repeat the iterative procedures until the stopping criterion is reached. The established methodology was applied to the groundwater system of Ming-Chu Basin, Taiwan. The study period is from January 1st to December 2ed in 2012. Results showed that the optimal EOF combination for the multiple recharges and hydrogeological parameters can decrease the RMSE of the simulated storage hydrographs dramatically within three calibration iterations. It represents that the iterative approach that using EOF techniques can capture the groundwater flow tendency and detects the correction vector of the simulated error sources. Hence, the established EOF-based methodology can effectively and accurately identify the multiple recharges and hydrogeological parameters.

Modified Chebyshev Picard Iteration for Efficient Numerical Integration of Ordinary Differential Equations

NASA Astrophysics Data System (ADS)

Macomber, B.; Woollands, R. M.; Probe, A.; Younes, A.; Bai, X.; Junkins, J.

2013-09-01

Modified Chebyshev Picard Iteration (MCPI) is an iterative numerical method for approximating solutions of linear or non-linear Ordinary Differential Equations (ODEs) to obtain time histories of system state trajectories. Unlike other step-by-step differential equation solvers, the Runge-Kutta family of numerical integrators for example, MCPI approximates long arcs of the state trajectory with an iterative path approximation approach, and is ideally suited to parallel computation. Orthogonal Chebyshev Polynomials are used as basis functions during each path iteration; the integrations of the Picard iteration are then done analytically. Due to the orthogonality of the Chebyshev basis functions, the least square approximations are computed without matrix inversion; the coefficients are computed robustly from discrete inner products. As a consequence of discrete sampling and weighting adopted for the inner product definition, Runge phenomena errors are minimized near the ends of the approximation intervals. The MCPI algorithm utilizes a vector-matrix framework for computational efficiency. Additionally, all Chebyshev coefficients and integrand function evaluations are independent, meaning they can be simultaneously computed in parallel for further decreased computational cost. Over an order of magnitude speedup from traditional methods is achieved in serial processing, and an additional order of magnitude is achievable in parallel architectures. This paper presents a new MCPI library, a modular toolset designed to allow MCPI to be easily applied to a wide variety of ODE systems. Library users will not have to concern themselves with the underlying mathematics behind the MCPI method. Inputs are the boundary conditions of the dynamical system, the integrand function governing system behavior, and the desired time interval of integration, and the output is a time history of the system states over the interval of interest. Examples from the field of astrodynamics are presented to compare the output from the MCPI library to current state-of-practice numerical integration methods. It is shown that MCPI is capable of out-performing the state-of-practice in terms of computational cost and accuracy.

Rescheduling with iterative repair

NASA Technical Reports Server (NTRS)

Zweben, Monte; Davis, Eugene; Daun, Brian; Deale, Michael

1992-01-01

This paper presents a new approach to rescheduling called constraint-based iterative repair. This approach gives our system the ability to satisfy domain constraints, address optimization concerns, minimize perturbation to the original schedule, produce modified schedules, quickly, and exhibits 'anytime' behavior. The system begins with an initial, flawed schedule and then iteratively repairs constraint violations until a conflict-free schedule is produced. In an empirical demonstration, we vary the importance of minimizing perturbation and report how fast the system is able to resolve conflicts in a given time bound. We also show the anytime characteristics of the system. These experiments were performed within the domain of Space Shuttle ground processing.

Improved sensitivity of computed tomography towards iodine and gold nanoparticle contrast agents via iterative reconstruction methods

PubMed Central

Bernstein, Ally Leigh; Dhanantwari, Amar; Jurcova, Martina; Cheheltani, Rabee; Naha, Pratap Chandra; Ivanc, Thomas; Shefer, Efrat; Cormode, David Peter

2016-01-01

Computed tomography is a widely used medical imaging technique that has high spatial and temporal resolution. Its weakness is its low sensitivity towards contrast media. Iterative reconstruction techniques (ITER) have recently become available, which provide reduced image noise compared with traditional filtered back-projection methods (FBP), which may allow the sensitivity of CT to be improved, however this effect has not been studied in detail. We scanned phantoms containing either an iodine contrast agent or gold nanoparticles. We used a range of tube voltages and currents. We performed reconstruction with FBP, ITER and a novel, iterative, modal-based reconstruction (IMR) algorithm. We found that noise decreased in an algorithm dependent manner (FBP > ITER > IMR) for every scan and that no differences were observed in attenuation rates of the agents. The contrast to noise ratio (CNR) of iodine was highest at 80 kV, whilst the CNR for gold was highest at 140 kV. The CNR of IMR images was almost tenfold higher than that of FBP images. Similar trends were found in dual energy images formed using these algorithms. In conclusion, IMR-based reconstruction techniques will allow contrast agents to be detected with greater sensitivity, and may allow lower contrast agent doses to be used. PMID:27185492

Electromagnetic scattering of large structures in layered earths using integral equations

NASA Astrophysics Data System (ADS)

Xiong, Zonghou; Tripp, Alan C.

1995-07-01

An electromagnetic scattering algorithm for large conductivity structures in stratified media has been developed and is based on the method of system iteration and spatial symmetry reduction using volume electric integral equations. The method of system iteration divides a structure into many substructures and solves the resulting matrix equation using a block iterative method. The block submatrices usually need to be stored on disk in order to save computer core memory. However, this requires a large disk for large structures. If the body is discretized into equal-size cells it is possible to use the spatial symmetry relations of the Green's functions to regenerate the scattering impedance matrix in each iteration, thus avoiding expensive disk storage. Numerical tests show that the system iteration converges much faster than the conventional point-wise Gauss-Seidel iterative method. The numbers of cells do not significantly affect the rate of convergency. Thus the algorithm effectively reduces the solution of the scattering problem to an order of O(N2), instead of O(N3) as with direct solvers.

A sampling algorithm for segregation analysis

PubMed Central

Tier, Bruce; Henshall, John

2001-01-01

Methods for detecting Quantitative Trait Loci (QTL) without markers have generally used iterative peeling algorithms for determining genotype probabilities. These algorithms have considerable shortcomings in complex pedigrees. A Monte Carlo Markov chain (MCMC) method which samples the pedigree of the whole population jointly is described. Simultaneous sampling of the pedigree was achieved by sampling descent graphs using the Metropolis-Hastings algorithm. A descent graph describes the inheritance state of each allele and provides pedigrees guaranteed to be consistent with Mendelian sampling. Sampling descent graphs overcomes most, if not all, of the limitations incurred by iterative peeling algorithms. The algorithm was able to find the QTL in most of the simulated populations. However, when the QTL was not modeled or found then its effect was ascribed to the polygenic component. No QTL were detected when they were not simulated. PMID:11742631

A sparse matrix algorithm on the Boolean vector machine

NASA Technical Reports Server (NTRS)

Wagner, Robert A.; Patrick, Merrell L.

1988-01-01

VLSI technology is being used to implement a prototype Boolean Vector Machine (BVM), which is a large network of very small processors with equally small memories that operate in SIMD mode; these use bit-serial arithmetic, and communicate via cube-connected cycles network. The BVM's bit-serial arithmetic and the small memories of individual processors are noted to compromise the system's effectiveness in large numerical problem applications. Attention is presently given to the implementation of a basic matrix-vector iteration algorithm for space matrices of the BVM, in order to generate over 1 billion useful floating-point operations/sec for this iteration algorithm. The algorithm is expressed in a novel language designated 'BVM'.

Optimization of a Lunar Pallet Lander Reinforcement Structure Using a Genetic Algorithm

NASA Technical Reports Server (NTRS)

Burt, Adam O.; Hull, Patrick V.

2014-01-01

This paper presents a design automation process using optimization via a genetic algorithm to design the conceptual structure of a Lunar Pallet Lander. The goal is to determine a design that will have the primary natural frequencies at or above a target value as well as minimize the total mass. Several iterations of the process are presented. First, a concept optimization is performed to determine what class of structure would produce suitable candidate designs. From this a stiffened sheet metal approach was selected leading to optimization of beam placement through generating a two-dimensional mesh and varying the physical location of reinforcing beams. Finally, the design space is reformulated as a binary problem using 1-dimensional beam elements to truncate the design space to allow faster convergence and additional mechanical failure criteria to be included in the optimization responses. Results are presented for each design space configuration. The final flight design was derived from these results.

Segmentation methodology for automated classification and differentiation of soft tissues in multiband images of high-resolution ultrasonic transmission tomography.

PubMed

Jeong, Jeong-Won; Shin, Dae C; Do, Synho; Marmarelis, Vasilis Z

2006-08-01

This paper presents a novel segmentation methodology for automated classification and differentiation of soft tissues using multiband data obtained with the newly developed system of high-resolution ultrasonic transmission tomography (HUTT) for imaging biological organs. This methodology extends and combines two existing approaches: the L-level set active contour (AC) segmentation approach and the agglomerative hierarchical kappa-means approach for unsupervised clustering (UC). To prevent the trapping of the current iterative minimization AC algorithm in a local minimum, we introduce a multiresolution approach that applies the level set functions at successively increasing resolutions of the image data. The resulting AC clusters are subsequently rearranged by the UC algorithm that seeks the optimal set of clusters yielding the minimum within-cluster distances in the feature space. The presented results from Monte Carlo simulations and experimental animal-tissue data demonstrate that the proposed methodology outperforms other existing methods without depending on heuristic parameters and provides a reliable means for soft tissue differentiation in HUTT images.

Spectral CT Reconstruction with Image Sparsity and Spectral Mean

PubMed Central

Zhang, Yi; Xi, Yan; Yang, Qingsong; Cong, Wenxiang; Zhou, Jiliu

2017-01-01

Photon-counting detectors can acquire x-ray intensity data in different energy bins. The signal to noise ratio of resultant raw data in each energy bin is generally low due to the narrow bin width and quantum noise. To address this problem, here we propose an image reconstruction approach for spectral CT to simultaneously reconstructs x-ray attenuation coefficients in all the energy bins. Because the measured spectral data are highly correlated among the x-ray energy bins, the intra-image sparsity and inter-image similarity are important prior acknowledge for image reconstruction. Inspired by this observation, the total variation (TV) and spectral mean (SM) measures are combined to improve the quality of reconstructed images. For this purpose, a linear mapping function is used to minimalize image differences between energy bins. The split Bregman technique is applied to perform image reconstruction. Our numerical and experimental results show that the proposed algorithms outperform competing iterative algorithms in this context. PMID:29034267

Optimizing Monitoring Designs under Alternative Objectives

DOE PAGES

Gastelum, Jason A.; USA, Richland Washington; Porter, Ellen A.; ...

2014-12-31

This paper describes an approach to identify monitoring designs that optimize detection of CO2 leakage from a carbon capture and sequestration (CCS) reservoir and compares the results generated under two alternative objective functions. The first objective function minimizes the expected time to first detection of CO2 leakage, the second more conservative objective function minimizes the maximum time to leakage detection across the set of realizations. The approach applies a simulated annealing algorithm that searches the solution space by iteratively mutating the incumbent monitoring design. The approach takes into account uncertainty by evaluating the performance of potential monitoring designs across amore » set of simulated leakage realizations. The approach relies on a flexible two-tiered signature to infer that CO2 leakage has occurred. This research is part of the National Risk Assessment Partnership, a U.S. Department of Energy (DOE) project tasked with conducting risk and uncertainty analysis in the areas of reservoir performance, natural leakage pathways, wellbore integrity, groundwater protection, monitoring, and systems level modeling.« less

New regularization scheme for blind color image deconvolution

NASA Astrophysics Data System (ADS)

Chen, Li; He, Yu; Yap, Kim-Hui

2011-01-01

This paper proposes a new regularization scheme to address blind color image deconvolution. Color images generally have a significant correlation among the red, green, and blue channels. Conventional blind monochromatic deconvolution algorithms handle each color image channels independently, thereby ignoring the interchannel correlation present in the color images. In view of this, a unified regularization scheme for image is developed to recover edges of color images and reduce color artifacts. In addition, by using the color image properties, a spectral-based regularization operator is adopted to impose constraints on the blurs. Further, this paper proposes a reinforcement regularization framework that integrates a soft parametric learning term in addressing blind color image deconvolution. A blur modeling scheme is developed to evaluate the relevance of manifold parametric blur structures, and the information is integrated into the deconvolution scheme. An optimization procedure called alternating minimization is then employed to iteratively minimize the image- and blur-domain cost functions. Experimental results show that the method is able to achieve satisfactory restored color images under different blurring conditions.

An Assessment of Iterative Reconstruction Methods for Sparse Ultrasound Imaging

PubMed Central

Valente, Solivan A.; Zibetti, Marcelo V. W.; Pipa, Daniel R.; Maia, Joaquim M.; Schneider, Fabio K.

2017-01-01

Ultrasonic image reconstruction using inverse problems has recently appeared as an alternative to enhance ultrasound imaging over beamforming methods. This approach depends on the accuracy of the acquisition model used to represent transducers, reflectivity, and medium physics. Iterative methods, well known in general sparse signal reconstruction, are also suited for imaging. In this paper, a discrete acquisition model is assessed by solving a linear system of equations by an ℓ1-regularized least-squares minimization, where the solution sparsity may be adjusted as desired. The paper surveys 11 variants of four well-known algorithms for sparse reconstruction, and assesses their optimization parameters with the goal of finding the best approach for iterative ultrasound imaging. The strategy for the model evaluation consists of using two distinct datasets. We first generate data from a synthetic phantom that mimics real targets inside a professional ultrasound phantom device. This dataset is contaminated with Gaussian noise with an estimated SNR, and all methods are assessed by their resulting images and performances. The model and methods are then assessed with real data collected by a research ultrasound platform when scanning the same phantom device, and results are compared with beamforming. A distinct real dataset is finally used to further validate the proposed modeling. Although high computational effort is required by iterative methods, results show that the discrete model may lead to images closer to ground-truth than traditional beamforming. However, computing capabilities of current platforms need to evolve before frame rates currently delivered by ultrasound equipments are achievable. PMID:28282862

New Parallel Algorithms for Structural Analysis and Design of Aerospace Structures

NASA Technical Reports Server (NTRS)

Nguyen, Duc T.

1998-01-01

Subspace and Lanczos iterations have been developed, well documented, and widely accepted as efficient methods for obtaining p-lowest eigen-pair solutions of large-scale, practical engineering problems. The focus of this paper is to incorporate recent developments in vectorized sparse technologies in conjunction with Subspace and Lanczos iterative algorithms for computational enhancements. Numerical performance, in terms of accuracy and efficiency of the proposed sparse strategies for Subspace and Lanczos algorithm, is demonstrated by solving for the lowest frequencies and mode shapes of structural problems on the IBM-R6000/590 and SunSparc 20 workstations.

Road detection in SAR images using a tensor voting algorithm

NASA Astrophysics Data System (ADS)

Shen, Dajiang; Hu, Chun; Yang, Bing; Tian, Jinwen; Liu, Jian

2007-11-01

In this paper, the problem of the detection of road networks in Synthetic Aperture Radar (SAR) images is addressed. Most of the previous methods extract the road by detecting lines and network reconstruction. Traditional algorithms such as MRFs, GA, Level Set, used in the progress of reconstruction are iterative. The tensor voting methodology we proposed is non-iterative, and non-sensitive to initialization. Furthermore, the only free parameter is the size of the neighborhood, related to the scale. The algorithm we present is verified to be effective when it's applied to the road extraction using the real Radarsat Image.

An algebraic iterative reconstruction technique for differential X-ray phase-contrast computed tomography.

PubMed

Fu, Jian; Schleede, Simone; Tan, Renbo; Chen, Liyuan; Bech, Martin; Achterhold, Klaus; Gifford, Martin; Loewen, Rod; Ruth, Ronald; Pfeiffer, Franz

2013-09-01

Iterative reconstruction has a wide spectrum of proven advantages in the field of conventional X-ray absorption-based computed tomography (CT). In this paper, we report on an algebraic iterative reconstruction technique for grating-based differential phase-contrast CT (DPC-CT). Due to the differential nature of DPC-CT projections, a differential operator and a smoothing operator are added to the iterative reconstruction, compared to the one commonly used for absorption-based CT data. This work comprises a numerical study of the algorithm and its experimental verification using a dataset measured at a two-grating interferometer setup. Since the algorithm is easy to implement and allows for the extension to various regularization possibilities, we expect a significant impact of the method for improving future medical and industrial DPC-CT applications. Copyright © 2012. Published by Elsevier GmbH.

A simple suboptimal least-squares algorithm for attitude determination with multiple sensors

NASA Technical Reports Server (NTRS)

Brozenec, Thomas F.; Bender, Douglas J.

1994-01-01

Three-axis attitude determination is equivalent to finding a coordinate transformation matrix which transforms a set of reference vectors fixed in inertial space to a set of measurement vectors fixed in the spacecraft. The attitude determination problem can be expressed as a constrained optimization problem. The constraint is that a coordinate transformation matrix must be proper, real, and orthogonal. A transformation matrix can be thought of as optimal in the least-squares sense if it maps the measurement vectors to the reference vectors with minimal 2-norm errors and meets the above constraint. This constrained optimization problem is known as Wahba's problem. Several algorithms which solve Wahba's problem exactly have been developed and used. These algorithms, while steadily improving, are all rather complicated. Furthermore, they involve such numerically unstable or sensitive operations as matrix determinant, matrix adjoint, and Newton-Raphson iterations. This paper describes an algorithm which minimizes Wahba's loss function, but without the constraint. When the constraint is ignored, the problem can be solved by a straightforward, numerically stable least-squares algorithm such as QR decomposition. Even though the algorithm does not explicitly take the constraint into account, it still yields a nearly orthogonal matrix for most practical cases; orthogonality only becomes corrupted when the sensor measurements are very noisy, on the same order of magnitude as the attitude rotations. The algorithm can be simplified if the attitude rotations are small enough so that the approximation sin(theta) approximately equals theta holds. We then compare the computational requirements for several well-known algorithms. For the general large-angle case, the QR least-squares algorithm is competitive with all other know algorithms and faster than most. If attitude rotations are small, the least-squares algorithm can be modified to run faster, and this modified algorithm is faster than all but a similarly specialized version of the QUEST algorithm. We also introduce a novel measurement averaging technique which reduces the n-measurement case to the two measurement case for our particular application, a star tracker and earth sensor mounted on an earth-pointed geosynchronous communications satellite. Using this technique, many n-measurement problems reduce to less than or equal to 3 measurements; this reduces the amount of required calculation without significant degradation in accuracy. Finally, we present the results of some tests which compare the least-squares algorithm with the QUEST and FOAM algorithms in the two-measurement case. For our example case, all three algorithms performed with similar accuracy.

Adaptive control of turbulence intensity is accelerated by frugal flow sampling.

PubMed

Quinn, Daniel B; van Halder, Yous; Lentink, David

2017-11-01

The aerodynamic performance of vehicles and animals, as well as the productivity of turbines and energy harvesters, depends on the turbulence intensity of the incoming flow. Previous studies have pointed at the potential benefits of active closed-loop turbulence control. However, it is unclear what the minimal sensory and algorithmic requirements are for realizing this control. Here we show that very low-bandwidth anemometers record sufficient information for an adaptive control algorithm to converge quickly. Our online Newton-Raphson algorithm tunes the turbulence in a recirculating wind tunnel by taking readings from an anemometer in the test section. After starting at 9% turbulence intensity, the algorithm converges on values ranging from 10% to 45% in less than 12 iterations within 1% accuracy. By down-sampling our measurements, we show that very-low-bandwidth anemometers record sufficient information for convergence. Furthermore, down-sampling accelerates convergence by smoothing gradients in turbulence intensity. Our results explain why low-bandwidth anemometers in engineering and mechanoreceptors in biology may be sufficient for adaptive control of turbulence intensity. Finally, our analysis suggests that, if certain turbulent eddy sizes are more important to control than others, frugal adaptive control schemes can be particularly computationally effective for improving performance. © 2017 The Author(s).

Iterative image reconstruction for multienergy computed tomography via structure tensor total variation regularization

NASA Astrophysics Data System (ADS)

Zeng, Dong; Bian, Zhaoying; Gong, Changfei; Huang, Jing; He, Ji; Zhang, Hua; Lu, Lijun; Feng, Qianjin; Liang, Zhengrong; Ma, Jianhua

2016-03-01

Multienergy computed tomography (MECT) has the potential to simultaneously offer multiple sets of energy- selective data belonging to specific energy windows. However, because sufficient photon counts are not available in the specific energy windows compared with that in the whole energy window, the MECT images reconstructed by the analytical approach often suffer from poor signal-to-noise (SNR) and strong streak artifacts. To eliminate this drawback, in this work we present a penalized weighted least-squares (PWLS) scheme by incorporating the new concept of structure tensor total variation (STV) regularization to improve the MECT images quality from low-milliampere-seconds (low-mAs) data acquisitions. Henceforth the present scheme is referred to as `PWLS- STV' for simplicity. Specifically, the STV regularization is derived by penalizing the eigenvalues of the structure tensor of every point in the MECT images. Thus it can provide more robust measures of image variation, which can eliminate the patchy artifacts often observed in total variation regularization. Subsequently, an alternating optimization algorithm was adopted to minimize the objective function. Experiments with a digital XCAT phantom clearly demonstrate that the present PWLS-STV algorithm can achieve more gains than the existing TV-based algorithms and the conventional filtered backpeojection (FBP) algorithm in terms of noise-induced artifacts suppression, resolution preservation, and material decomposition assessment.

Constrained Total Generalized p-Variation Minimization for Few-View X-Ray Computed Tomography Image Reconstruction.

PubMed

Zhang, Hanming; Wang, Linyuan; Yan, Bin; Li, Lei; Cai, Ailong; Hu, Guoen

2016-01-01

Total generalized variation (TGV)-based computed tomography (CT) image reconstruction, which utilizes high-order image derivatives, is superior to total variation-based methods in terms of the preservation of edge information and the suppression of unfavorable staircase effects. However, conventional TGV regularization employs l1-based form, which is not the most direct method for maximizing sparsity prior. In this study, we propose a total generalized p-variation (TGpV) regularization model to improve the sparsity exploitation of TGV and offer efficient solutions to few-view CT image reconstruction problems. To solve the nonconvex optimization problem of the TGpV minimization model, we then present an efficient iterative algorithm based on the alternating minimization of augmented Lagrangian function. All of the resulting subproblems decoupled by variable splitting admit explicit solutions by applying alternating minimization method and generalized p-shrinkage mapping. In addition, approximate solutions that can be easily performed and quickly calculated through fast Fourier transform are derived using the proximal point method to reduce the cost of inner subproblems. The accuracy and efficiency of the simulated and real data are qualitatively and quantitatively evaluated to validate the efficiency and feasibility of the proposed method. Overall, the proposed method exhibits reasonable performance and outperforms the original TGV-based method when applied to few-view problems.

A Centered Projective Algorithm for Linear Programming

DTIC Science & Technology

1988-02-01

zx/l to (PA Karmarkar’s algorithm iterates this procedure. An alternative method, the so-called affine variant (first proposed by Dikin [6] in 1967...trajectories, II. Legendre transform coordinates . central trajectories," manuscripts, to appear in Transactions of the American [6] I.I. Dikin ...34Iterative solution of problems of linear and quadratic programming," Soviet Mathematics Dokladv 8 (1967), 674-675. [7] I.I. Dikin , "On the speed of an

Discrete fourier transform (DFT) analysis for applications using iterative transform methods

NASA Technical Reports Server (NTRS)

Dean, Bruce H. (Inventor)

2012-01-01

According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

Iterative simulated quenching for designing irregular-spot-array generators.

PubMed

Gillet, J N; Sheng, Y

2000-07-10

We propose a novel, to our knowledge, algorithm of iterative simulated quenching with temperature rescaling for designing diffractive optical elements, based on an analogy between simulated annealing and statistical thermodynamics. The temperature is iteratively rescaled at the end of each quenching process according to ensemble statistics to bring the system back from a frozen imperfect state with a local minimum of energy to a dynamic state in a Boltzmann heat bath in thermal equilibrium at the rescaled temperature. The new algorithm achieves much lower cost function and reconstruction error and higher diffraction efficiency than conventional simulated annealing with a fast exponential cooling schedule and is easy to program. The algorithm is used to design binary-phase generators of large irregular spot arrays. The diffractive phase elements have trapezoidal apertures of varying heights, which fit ideal arbitrary-shaped apertures better than do trapezoidal apertures of fixed heights.

A frequency dependent preconditioned wavelet method for atmospheric tomography

NASA Astrophysics Data System (ADS)

Yudytskiy, Mykhaylo; Helin, Tapio; Ramlau, Ronny

2013-12-01

Atmospheric tomography, i.e. the reconstruction of the turbulence in the atmosphere, is a main task for the adaptive optics systems of the next generation telescopes. For extremely large telescopes, such as the European Extremely Large Telescope, this problem becomes overly complex and an efficient algorithm is needed to reduce numerical costs. Recently, a conjugate gradient method based on wavelet parametrization of turbulence layers was introduced [5]. An iterative algorithm can only be numerically efficient when the number of iterations required for a sufficient reconstruction is low. A way to achieve this is to design an efficient preconditioner. In this paper we propose a new frequency-dependent preconditioner for the wavelet method. In the context of a multi conjugate adaptive optics (MCAO) system simulated on the official end-to-end simulation tool OCTOPUS of the European Southern Observatory we demonstrate robustness and speed of the preconditioned algorithm. We show that three iterations are sufficient for a good reconstruction.

A novel dynamical community detection algorithm based on weighting scheme

NASA Astrophysics Data System (ADS)

Li, Ju; Yu, Kai; Hu, Ke

2015-12-01

Network dynamics plays an important role in analyzing the correlation between the function properties and the topological structure. In this paper, we propose a novel dynamical iteration (DI) algorithm, which incorporates the iterative process of membership vector with weighting scheme, i.e. weighting W and tightness T. These new elements can be used to adjust the link strength and the node compactness for improving the speed and accuracy of community structure detection. To estimate the optimal stop time of iteration, we utilize a new stability measure which is defined as the Markov random walk auto-covariance. We do not need to specify the number of communities in advance. It naturally supports the overlapping communities by associating each node with a membership vector describing the node's involvement in each community. Theoretical analysis and experiments show that the algorithm can uncover communities effectively and efficiently.

Efficient solutions to the Euler equations for supersonic flow with embedded subsonic regions

NASA Technical Reports Server (NTRS)

Walters, Robert W.; Dwoyer, Douglas L.

1987-01-01

A line Gauss-Seidel (LGS) relaxation algorithm in conjunction with a one-parameter family of upwind discretizations of the Euler equations in two dimensions is described. Convergence of the basic algorithm to the steady state is quadratic for fully supersonic flows and is linear for other flows. This is in contrast to the block alternating direction implicit methods (either central or upwind differenced) and the upwind biased relaxation schemes, all of which converge linearly, independent of the flow regime. Moreover, the algorithm presented herein is easily coupled with methods to detect regions of subsonic flow embedded in supersonic flow. This allows marching by lines in the supersonic regions, converging each line quadratically, and iterating in the subsonic regions, and yields a very efficient iteration strategy. Numerical results are presented for two-dimensional supersonic and transonic flows containing oblique and normal shock waves which confirm the efficiency of the iteration strategy.

Accelerated Path-following Iterative Shrinkage Thresholding Algorithm with Application to Semiparametric Graph Estimation

PubMed Central

Zhao, Tuo; Liu, Han

2016-01-01

We propose an accelerated path-following iterative shrinkage thresholding algorithm (APISTA) for solving high dimensional sparse nonconvex learning problems. The main difference between APISTA and the path-following iterative shrinkage thresholding algorithm (PISTA) is that APISTA exploits an additional coordinate descent subroutine to boost the computational performance. Such a modification, though simple, has profound impact: APISTA not only enjoys the same theoretical guarantee as that of PISTA, i.e., APISTA attains a linear rate of convergence to a unique sparse local optimum with good statistical properties, but also significantly outperforms PISTA in empirical benchmarks. As an application, we apply APISTA to solve a family of nonconvex optimization problems motivated by estimating sparse semiparametric graphical models. APISTA allows us to obtain new statistical recovery results which do not exist in the existing literature. Thorough numerical results are provided to back up our theory. PMID:28133430

Vehicle detection from very-high-resolution (VHR) aerial imagery using attribute belief propagation (ABP)

NASA Astrophysics Data System (ADS)

Wang, Yanli; Li, Ying; Zhang, Li; Huang, Yuchun

2016-10-01

With the popularity of very-high-resolution (VHR) aerial imagery, the shape, color, and context attribute of vehicles are better characterized. Due to the various road surroundings and imaging conditions, vehicle attributes could be adversely affected so that vehicle is mistakenly detected or missed. This paper is motivated to robustly extract the rich attribute feature for detecting the vehicles of VHR imagery under different scenarios. Based on the hierarchical component tree of vehicle context, attribute belief propagation (ABP) is proposed to detect salient vehicles from the statistical perspective. With the Max-tree data structure, the multi-level component tree around the road network is efficiently created. The spatial relationship between vehicle and its belonging context is established with the belief definition of vehicle attribute. To effectively correct single-level belief error, the inter-level belief linkages enforce consistency of belief assignment between corresponding components at different levels. ABP starts from an initial set of vehicle belief calculated by vehicle attribute, and then iterates through each component by applying inter-level belief passing until convergence. The optimal value of vehicle belief of each component is obtained via minimizing its belief function iteratively. The proposed algorithm is tested on a diverse set of VHR imagery acquired in the city and inter-city areas of the West and South China. Experimental results show that the proposed algorithm can detect vehicle efficiently and suppress the erroneous effectively. The proposed ABP framework is promising to robustly classify the vehicles from VHR Aerial imagery.

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

DOE PAGES

Desai, Ajit; Khalil, Mohammad; Pettit, Chris; ...

2017-09-21

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolutionmore » in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.« less

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

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

Desai, Ajit; Khalil, Mohammad; Pettit, Chris

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolutionmore » in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.« less

Iterative Track Fitting Using Cluster Classification in Multi Wire Proportional Chamber

NASA Astrophysics Data System (ADS)

Primor, David; Mikenberg, Giora; Etzion, Erez; Messer, Hagit

2007-10-01

This paper addresses the problem of track fitting of a charged particle in a multi wire proportional chamber (MWPC) using cathode readout strips. When a charged particle crosses a MWPC, a positive charge is induced on a cluster of adjacent strips. In the presence of high radiation background, the cluster charge measurements may be contaminated due to background particles, leading to less accurate hit position estimation. The least squares method for track fitting assumes the same position error distribution for all hits and thus loses its optimal properties on contaminated data. For this reason, a new robust algorithm is proposed. The algorithm first uses the known spatial charge distribution caused by a single charged particle over the strips, and classifies the clusters into ldquocleanrdquo and ldquodirtyrdquo clusters. Then, using the classification results, it performs an iterative weighted least squares fitting procedure, updating its optimal weights each iteration. The performance of the suggested algorithm is compared to other track fitting techniques using a simulation of tracks with radiation background. It is shown that the algorithm improves the track fitting performance significantly. A practical implementation of the algorithm is presented for muon track fitting in the cathode strip chamber (CSC) of the ATLAS experiment.

MPI-FAUN: An MPI-Based Framework for Alternating-Updating Nonnegative Matrix Factorization

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

Kannan, Ramakrishnan; Ballard, Grey; Park, Haesun

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors W and H, for the given input matrix A, such that A≈WH. NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient parallel algorithms to solve the problem for big data sets. The main contribution of this work is a new, high-performance parallel computational framework for a broad class of NMF algorithms thatmore » iteratively solves alternating non-negative least squares (NLS) subproblems for W and H. It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). The framework is flexible and able to leverage a variety of NMF and NLS algorithms, including Multiplicative Update, Hierarchical Alternating Least Squares, and Block Principal Pivoting. Our implementation allows us to benchmark and compare different algorithms on massive dense and sparse data matrices of size that spans from few hundreds of millions to billions. We demonstrate the scalability of our algorithm and compare it with baseline implementations, showing significant performance improvements. The code and the datasets used for conducting the experiments are available online.« less

Combining Acceleration Techniques for Low-Dose X-Ray Cone Beam Computed Tomography Image Reconstruction.

PubMed

Huang, Hsuan-Ming; Hsiao, Ing-Tsung

2017-01-01

Over the past decade, image quality in low-dose computed tomography has been greatly improved by various compressive sensing- (CS-) based reconstruction methods. However, these methods have some disadvantages including high computational cost and slow convergence rate. Many different speed-up techniques for CS-based reconstruction algorithms have been developed. The purpose of this paper is to propose a fast reconstruction framework that combines a CS-based reconstruction algorithm with several speed-up techniques. First, total difference minimization (TDM) was implemented using the soft-threshold filtering (STF). Second, we combined TDM-STF with the ordered subsets transmission (OSTR) algorithm for accelerating the convergence. To further speed up the convergence of the proposed method, we applied the power factor and the fast iterative shrinkage thresholding algorithm to OSTR and TDM-STF, respectively. Results obtained from simulation and phantom studies showed that many speed-up techniques could be combined to greatly improve the convergence speed of a CS-based reconstruction algorithm. More importantly, the increased computation time (≤10%) was minor as compared to the acceleration provided by the proposed method. In this paper, we have presented a CS-based reconstruction framework that combines several acceleration techniques. Both simulation and phantom studies provide evidence that the proposed method has the potential to satisfy the requirement of fast image reconstruction in practical CT.

A novel pipeline based FPGA implementation of a genetic algorithm

NASA Astrophysics Data System (ADS)

Thirer, Nonel

2014-05-01

To solve problems when an analytical solution is not available, more and more bio-inspired computation techniques have been applied in the last years. Thus, an efficient algorithm is the Genetic Algorithm (GA), which imitates the biological evolution process, finding the solution by the mechanism of "natural selection", where the strong has higher chances to survive. A genetic algorithm is an iterative procedure which operates on a population of individuals called "chromosomes" or "possible solutions" (usually represented by a binary code). GA performs several processes with the population individuals to produce a new population, like in the biological evolution. To provide a high speed solution, pipelined based FPGA hardware implementations are used, with a nstages pipeline for a n-phases genetic algorithm. The FPGA pipeline implementations are constraints by the different execution time of each stage and by the FPGA chip resources. To minimize these difficulties, we propose a bio-inspired technique to modify the crossover step by using non identical twins. Thus two of the chosen chromosomes (parents) will build up two new chromosomes (children) not only one as in classical GA. We analyze the contribution of this method to reduce the execution time in the asynchronous and synchronous pipelines and also the possibility to a cheaper FPGA implementation, by using smaller populations. The full hardware architecture for a FPGA implementation to our target ALTERA development card is presented and analyzed.

A depth-first search algorithm to compute elementary flux modes by linear programming

PubMed Central

2014-01-01

Background The decomposition of complex metabolic networks into elementary flux modes (EFMs) provides a useful framework for exploring reaction interactions systematically. Generating a complete set of EFMs for large-scale models, however, is near impossible. Even for moderately-sized models (<400 reactions), existing approaches based on the Double Description method must iterate through a large number of combinatorial candidates, thus imposing an immense processor and memory demand. Results Based on an alternative elementarity test, we developed a depth-first search algorithm using linear programming (LP) to enumerate EFMs in an exhaustive fashion. Constraints can be introduced to directly generate a subset of EFMs satisfying the set of constraints. The depth-first search algorithm has a constant memory overhead. Using flux constraints, a large LP problem can be massively divided and parallelized into independent sub-jobs for deployment into computing clusters. Since the sub-jobs do not overlap, the approach scales to utilize all available computing nodes with minimal coordination overhead or memory limitations. Conclusions The speed of the algorithm was comparable to efmtool, a mainstream Double Description method, when enumerating all EFMs; the attrition power gained from performing flux feasibility tests offsets the increased computational demand of running an LP solver. Unlike the Double Description method, the algorithm enables accelerated enumeration of all EFMs satisfying a set of constraints. PMID:25074068

MPI-FAUN: An MPI-Based Framework for Alternating-Updating Nonnegative Matrix Factorization

DOE PAGES

Kannan, Ramakrishnan; Ballard, Grey; Park, Haesun

2017-10-30

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors W and H, for the given input matrix A, such that A≈WH. NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient parallel algorithms to solve the problem for big data sets. The main contribution of this work is a new, high-performance parallel computational framework for a broad class of NMF algorithms thatmore » iteratively solves alternating non-negative least squares (NLS) subproblems for W and H. It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). The framework is flexible and able to leverage a variety of NMF and NLS algorithms, including Multiplicative Update, Hierarchical Alternating Least Squares, and Block Principal Pivoting. Our implementation allows us to benchmark and compare different algorithms on massive dense and sparse data matrices of size that spans from few hundreds of millions to billions. We demonstrate the scalability of our algorithm and compare it with baseline implementations, showing significant performance improvements. The code and the datasets used for conducting the experiments are available online.« less

Distributed Control by Lagrangian Steepest Descent

NASA Technical Reports Server (NTRS)

Wolpert, David H.; Bieniawski, Stefan

2004-01-01

Often adaptive, distributed control can be viewed as an iterated game between independent players. The coupling between the players mixed strategies, arising as the system evolves from one instant to the next, is determined by the system designer. Information theory tells us that the most likely joint strategy of the players, given a value of the expectation of the overall control objective function, is the minimizer of a function o the joint strategy. So the goal of the system designer is to speed evolution of the joint strategy to that Lagrangian mhimbhgpoint,lowerthe expectated value of the control objective function, and repeat Here we elaborate the theory of algorithms that do this using local descent procedures, and that thereby achieve efficient, adaptive, distributed control.

Numerical methods for the design of gradient-index optical coatings.

PubMed

Anzengruber, Stephan W; Klann, Esther; Ramlau, Ronny; Tonova, Diana

2012-12-01

We formulate the problem of designing gradient-index optical coatings as the task of solving a system of operator equations. We use iterative numerical procedures known from the theory of inverse problems to solve it with respect to the coating refractive index profile and thickness. The mathematical derivations necessary for the application of the procedures are presented, and different numerical methods (Landweber, Newton, and Gauss-Newton methods, Tikhonov minimization with surrogate functionals) are implemented. Procedures for the transformation of the gradient coating designs into quasi-gradient ones (i.e., multilayer stacks of homogeneous layers with different refractive indices) are also developed. The design algorithms work with physically available coating materials that could be produced with the modern coating technologies.

A variable-gain output feedback control design approach

NASA Technical Reports Server (NTRS)

Haylo, Nesim

1989-01-01

A multi-model design technique to find a variable-gain control law defined over the whole operating range is proposed. The design is formulated as an optimal control problem which minimizes a cost function weighing the performance at many operating points. The solution is obtained by embedding into the Multi-Configuration Control (MCC) problem, a multi-model robust control design technique. In contrast to conventional gain scheduling which uses a curve fit of single model designs, the optimal variable-gain control law stabilizes the plant at every operating point included in the design. An iterative algorithm to compute the optimal control gains is presented. The methodology has been successfully applied to reconfigurable aircraft flight control and to nonlinear flight control systems.

Objective evaluation of linear and nonlinear tomosynthetic reconstruction algorithms

NASA Astrophysics Data System (ADS)

Webber, Richard L.; Hemler, Paul F.; Lavery, John E.

2000-04-01

This investigation objectively tests five different tomosynthetic reconstruction methods involving three different digital sensors, each used in a different radiologic application: chest, breast, and pelvis, respectively. The common task was to simulate a specific representative projection for each application by summation of appropriately shifted tomosynthetically generated slices produced by using the five algorithms. These algorithms were, respectively, (1) conventional back projection, (2) iteratively deconvoluted back projection, (3) a nonlinear algorithm similar to back projection, except that the minimum value from all of the component projections for each pixel is computed instead of the average value, (4) a similar algorithm wherein the maximum value was computed instead of the minimum value, and (5) the same type of algorithm except that the median value was computed. Using these five algorithms, we obtained data from each sensor-tissue combination, yielding three factorially distributed series of contiguous tomosynthetic slices. The respective slice stacks then were aligned orthogonally and averaged to yield an approximation of a single orthogonal projection radiograph of the complete (unsliced) tissue thickness. Resulting images were histogram equalized, and actual projection control images were subtracted from their tomosynthetically synthesized counterparts. Standard deviations of the resulting histograms were recorded as inverse figures of merit (FOMs). Visual rankings of image differences by five human observers of a subset (breast data only) also were performed to determine whether their subjective observations correlated with homologous FOMs. Nonparametric statistical analysis of these data demonstrated significant differences (P > 0.05) between reconstruction algorithms. The nonlinear minimization reconstruction method nearly always outperformed the other methods tested. Observer rankings were similar to those measured objectively.

An Improved Newton's Method.

ERIC Educational Resources Information Center

Mathews, John H.

1989-01-01

Describes Newton's method to locate roots of an equation using the Newton-Raphson iteration formula. Develops an adaptive method overcoming limitations of the iteration method. Provides the algorithm and computer program of the adaptive Newton-Raphson method. (YP)