Nonuniformity correction for an infrared focal plane array based on diamond search block matching.

PubMed

Sheng-Hui, Rong; Hui-Xin, Zhou; Han-Lin, Qin; Rui, Lai; Kun, Qian

2016-05-01

In scene-based nonuniformity correction algorithms, artificial ghosting and image blurring degrade the correction quality severely. In this paper, an improved algorithm based on the diamond search block matching algorithm and the adaptive learning rate is proposed. First, accurate transform pairs between two adjacent frames are estimated by the diamond search block matching algorithm. Then, based on the error between the corresponding transform pairs, the gradient descent algorithm is applied to update correction parameters. During the process of gradient descent, the local standard deviation and a threshold are utilized to control the learning rate to avoid the accumulation of matching error. Finally, the nonuniformity correction would be realized by a linear model with updated correction parameters. The performance of the proposed algorithm is thoroughly studied with four real infrared image sequences. Experimental results indicate that the proposed algorithm can reduce the nonuniformity with less ghosting artifacts in moving areas and can also overcome the problem of image blurring in static areas.

Gradient-Modulated SWIFT

PubMed Central

Zhang, Jinjin; Idiyatullin, Djaudat; Corum, Curtis A.; Kobayashi, Naoharu; Garwood, Michael

2017-01-01

Purpose Methods designed to image fast-relaxing spins, such as sweep imaging with Fourier transformation (SWIFT), often utilize high excitation bandwidth and duty cycle, and in some applications the optimal flip angle cannot be used without exceeding safe specific absorption rate (SAR) levels. The aim is to reduce SAR and increase the flexibility of SWIFT by applying time-varying gradient-modulation (GM). The modified sequence is called GM-SWIFT. Theory and Methods The method known as gradient-modulated offset independent adiabaticity was used to modulate the radiofrequency (RF) pulse and gradients. An expanded correlation algorithm was developed for GM-SWIFT to correct the phase and scale effects. Simulations and phantom and in vivo human experiments were performed to verify the correlation algorithm and to evaluate imaging performance. Results GM-SWIFT reduces SAR, RF amplitude, and acquisition time by up to 90%, 70%, and 45%, respectively, while maintaining image quality. The choice of GM parameter influences the lower limit of short T2* sensitivity, which can be exploited to suppress unwanted image haze from unresolvable ultrashort T2* signals originating from plastic materials in the coil housing and fixatives. Conclusions GM-SWIFT reduces peak and total RF power requirements and provides additional flexibility for optimizing SAR, RF amplitude, scan time, and image quality. PMID:25800547

Adaptive filtering of GOCE-derived gravity gradients of the disturbing potential in the context of the space-wise approach

NASA Astrophysics Data System (ADS)

Piretzidis, Dimitrios; Sideris, Michael G.

2017-09-01

Filtering and signal processing techniques have been widely used in the processing of satellite gravity observations to reduce measurement noise and correlation errors. The parameters and types of filters used depend on the statistical and spectral properties of the signal under investigation. Filtering is usually applied in a non-real-time environment. The present work focuses on the implementation of an adaptive filtering technique to process satellite gravity gradiometry data for gravity field modeling. Adaptive filtering algorithms are commonly used in communication systems, noise and echo cancellation, and biomedical applications. Two independent studies have been performed to introduce adaptive signal processing techniques and test the performance of the least mean-squared (LMS) adaptive algorithm for filtering satellite measurements obtained by the gravity field and steady-state ocean circulation explorer (GOCE) mission. In the first study, a Monte Carlo simulation is performed in order to gain insights about the implementation of the LMS algorithm on data with spectral behavior close to that of real GOCE data. In the second study, the LMS algorithm is implemented on real GOCE data. Experiments are also performed to determine suitable filtering parameters. Only the four accurate components of the full GOCE gravity gradient tensor of the disturbing potential are used. The characteristics of the filtered gravity gradients are examined in the time and spectral domain. The obtained filtered GOCE gravity gradients show an agreement of 63-84 mEötvös (depending on the gravity gradient component), in terms of RMS error, when compared to the gravity gradients derived from the EGM2008 geopotential model. Spectral-domain analysis of the filtered gradients shows that the adaptive filters slightly suppress frequencies in the bandwidth of approximately 10-30 mHz. The limitations of the adaptive LMS algorithm are also discussed. The tested filtering algorithm can be connected to and employed in the first computational steps of the space-wise approach, where a time-wise Wiener filter is applied at the first stage of GOCE gravity gradient filtering. The results of this work can be extended to using other adaptive filtering algorithms, such as the recursive least-squares and recursive least-squares lattice filters.

Development, validation, and comparison of ICA-based gradient artifact reduction algorithms for simultaneous EEG-spiral in/out and echo-planar fMRI recordings

PubMed Central

Ryali, S; Glover, GH; Chang, C; Menon, V

2009-01-01

EEG data acquired in an MRI scanner are heavily contaminated by gradient artifacts that can significantly compromise signal quality. We developed two new methods based on Independent Component Analysis (ICA) for reducing gradient artifacts from spiral in-out and echo-planar pulse sequences at 3T, and compared our algorithms with four other commonly used methods: average artifact subtraction (Allen et al. 2000), principal component analysis (Niazy et al. 2005), Taylor series (Wan et al. 2006) and a conventional temporal ICA algorithm. Models of gradient artifacts were derived from simulations as well as a water phantom and performance of each method was evaluated on datasets constructed using visual event-related potentials (ERPs) as well as resting EEG. Our new methods recovered ERPs and resting EEG below the beta band (< 12.5 Hz) with high signal-to-noise ratio (SNR > 4). Our algorithms outperformed all of these methods on resting EEG in the theta- and alpha-bands (SNR > 4); however, for all methods, signal recovery was modest (SNR ~ 1) in the beta-band and poor (SNR < 0.3) in the gamma-band and above. We found that the conventional ICA algorithm performed poorly with uniformly low SNR (< 0.1). Taken together, our new ICA-based methods offer a more robust technique for gradient artifact reduction when scanning at 3T using spiral in-out and echo-planar pulse sequences. We provide new insights into the strengths and weaknesses of each method using a unified subspace framework. PMID:19580873

A Parallel Nonrigid Registration Algorithm Based on B-Spline for Medical Images

PubMed Central

Wang, Yangping; Wang, Song

2016-01-01

The nonrigid registration algorithm based on B-spline Free-Form Deformation (FFD) plays a key role and is widely applied in medical image processing due to the good flexibility and robustness. However, it requires a tremendous amount of computing time to obtain more accurate registration results especially for a large amount of medical image data. To address the issue, a parallel nonrigid registration algorithm based on B-spline is proposed in this paper. First, the Logarithm Squared Difference (LSD) is considered as the similarity metric in the B-spline registration algorithm to improve registration precision. After that, we create a parallel computing strategy and lookup tables (LUTs) to reduce the complexity of the B-spline registration algorithm. As a result, the computing time of three time-consuming steps including B-splines interpolation, LSD computation, and the analytic gradient computation of LSD, is efficiently reduced, for the B-spline registration algorithm employs the Nonlinear Conjugate Gradient (NCG) optimization method. Experimental results of registration quality and execution efficiency on the large amount of medical images show that our algorithm achieves a better registration accuracy in terms of the differences between the best deformation fields and ground truth and a speedup of 17 times over the single-threaded CPU implementation due to the powerful parallel computing ability of Graphics Processing Unit (GPU). PMID:28053653

Efficient conjugate gradient algorithms for computation of the manipulator forward dynamics

NASA Technical Reports Server (NTRS)

Fijany, Amir; Scheid, Robert E.

1989-01-01

The applicability of conjugate gradient algorithms for computation of the manipulator forward dynamics is investigated. The redundancies in the previously proposed conjugate gradient algorithm are analyzed. A new version is developed which, by avoiding these redundancies, achieves a significantly greater efficiency. A preconditioned conjugate gradient algorithm is also presented. A diagonal matrix whose elements are the diagonal elements of the inertia matrix is proposed as the preconditioner. In order to increase the computational efficiency, an algorithm is developed which exploits the synergism between the computation of the diagonal elements of the inertia matrix and that required by the conjugate gradient algorithm.

Solving constrained minimum-time robot problems using the sequential gradient restoration algorithm

NASA Technical Reports Server (NTRS)

Lee, Allan Y.

1991-01-01

Three constrained minimum-time control problems of a two-link manipulator are solved using the Sequential Gradient and Restoration Algorithm (SGRA). The inequality constraints considered are reduced via Valentine-type transformations to nondifferential path equality constraints. The SGRA is then used to solve these transformed problems with equality constraints. The results obtained indicate that at least one of the two controls is at its limits at any instant in time. The remaining control then adjusts itself so that none of the system constraints is violated. Hence, the minimum-time control is either a pure bang-bang control or a combined bang-bang/singular control.

Use of the preconditioned conjugate gradient algorithm as a generic solver for mixed-model equations in animal breeding applications.

PubMed

Tsuruta, S; Misztal, I; Strandén, I

2001-05-01

Utility of the preconditioned conjugate gradient algorithm with a diagonal preconditioner for solving mixed-model equations in animal breeding applications was evaluated with 16 test problems. The problems included single- and multiple-trait analyses, with data on beef, dairy, and swine ranging from small examples to national data sets. Multiple-trait models considered low and high genetic correlations. Convergence was based on relative differences between left- and right-hand sides. The ordering of equations was fixed effects followed by random effects, with no special ordering within random effects. The preconditioned conjugate gradient program implemented with double precision converged for all models. However, when implemented in single precision, the preconditioned conjugate gradient algorithm did not converge for seven large models. The preconditioned conjugate gradient and successive overrelaxation algorithms were subsequently compared for 13 of the test problems. The preconditioned conjugate gradient algorithm was easy to implement with the iteration on data for general models. However, successive overrelaxation requires specific programming for each set of models. On average, the preconditioned conjugate gradient algorithm converged in three times fewer rounds of iteration than successive overrelaxation. With straightforward implementations, programs using the preconditioned conjugate gradient algorithm may be two or more times faster than those using successive overrelaxation. However, programs using the preconditioned conjugate gradient algorithm would use more memory than would comparable implementations using successive overrelaxation. Extensive optimization of either algorithm can influence rankings. The preconditioned conjugate gradient implemented with iteration on data, a diagonal preconditioner, and in double precision may be the algorithm of choice for solving mixed-model equations when sufficient memory is available and ease of implementation is essential.

Derivative Free Gradient Projection Algorithms for Rotation

ERIC Educational Resources Information Center

Jennrich, Robert I.

2004-01-01

A simple modification substantially simplifies the use of the gradient projection (GP) rotation algorithms of Jennrich (2001, 2002). These algorithms require subroutines to compute the value and gradient of any specific rotation criterion of interest. The gradient can be difficult to derive and program. It is shown that using numerical gradients…

Adaptive spectral filtering of PIV cross correlations

NASA Astrophysics Data System (ADS)

Giarra, Matthew; Vlachos, Pavlos; Aether Lab Team

2016-11-01

Using cross correlations (CCs) in particle image velocimetry (PIV) assumes that tracer particles in interrogation regions (IRs) move with the same velocity. But this assumption is nearly always violated because real flows exhibit velocity gradients, which degrade the signal-to-noise ratio (SNR) of the CC and are a major driver of error in PIV. Iterative methods help reduce these errors, but even they can fail when gradients are large within individual IRs. We present an algorithm to mitigate the effects of velocity gradients on PIV measurements. Our algorithm is based on a model of the CC, which predicts a relationship between the PDF of particle displacements and the variation of the correlation's SNR across the Fourier spectrum. We give an algorithm to measure this SNR from the CC, and use this insight to create a filter that suppresses the low-SNR portions of the spectrum. Our algorithm extends to the ensemble correlation, where it accelerates the convergence of the measurement and also reveals the PDF of displacements of the ensemble (and therefore of statistical metrics like diffusion coefficient). Finally, our model provides theoretical foundations for a number of "rules of thumb" in PIV, like the quarter-window rule.

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.

Algorithmic cooling in liquid-state nuclear magnetic resonance

NASA Astrophysics Data System (ADS)

Atia, Yosi; Elias, Yuval; Mor, Tal; Weinstein, Yossi

2016-01-01

Algorithmic cooling is a method that employs thermalization to increase qubit purification level; namely, it reduces the qubit system's entropy. We utilized gradient ascent pulse engineering, an optimal control algorithm, to implement algorithmic cooling in liquid-state nuclear magnetic resonance. Various cooling algorithms were applied onto the three qubits of C132-trichloroethylene, cooling the system beyond Shannon's entropy bound in several different ways. In particular, in one experiment a carbon qubit was cooled by a factor of 4.61. This work is a step towards potentially integrating tools of NMR quantum computing into in vivo magnetic-resonance spectroscopy.

Correction of eddy current distortions in high angular resolution diffusion imaging.

PubMed

Zhuang, Jiancheng; Lu, Zhong-Lin; Vidal, Christine Bouteiller; Damasio, Hanna

2013-06-01

To correct distortions caused by eddy currents induced by large diffusion gradients during high angular resolution diffusion imaging without any auxiliary reference scans. Image distortion parameters were obtained by image coregistration, performed only between diffusion-weighted images with close diffusion gradient orientations. A linear model that describes distortion parameters (translation, scale, and shear) as a function of diffusion gradient directions was numerically computed to allow individualized distortion correction for every diffusion-weighted image. The assumptions of the algorithm were successfully verified in a series of experiments on phantom and human scans. Application of the proposed algorithm in high angular resolution diffusion images markedly reduced eddy current distortions when compared to results obtained with previously published methods. The method can correct eddy current artifacts in the high angular resolution diffusion images, and it avoids the problematic procedure of cross-correlating images with significantly different contrasts resulting from very different gradient orientations or strengths. Copyright © 2012 Wiley Periodicals, Inc.

An accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems using gradient-based diffusion and tau-leaping.

PubMed

Koh, Wonryull; Blackwell, Kim T

2011-04-21

Stochastic simulation of reaction-diffusion systems enables the investigation of stochastic events arising from the small numbers and heterogeneous distribution of molecular species in biological cells. Stochastic variations in intracellular microdomains and in diffusional gradients play a significant part in the spatiotemporal activity and behavior of cells. Although an exact stochastic simulation that simulates every individual reaction and diffusion event gives a most accurate trajectory of the system's state over time, it can be too slow for many practical applications. We present an accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems designed to improve the speed of simulation by reducing the number of time-steps required to complete a simulation run. This method is unique in that it employs two strategies that have not been incorporated in existing spatial stochastic simulation algorithms. First, diffusive transfers between neighboring subvolumes are based on concentration gradients. This treatment necessitates sampling of only the net or observed diffusion events from higher to lower concentration gradients rather than sampling all diffusion events regardless of local concentration gradients. Second, we extend the non-negative Poisson tau-leaping method that was originally developed for speeding up nonspatial or homogeneous stochastic simulation algorithms. This method calculates each leap time in a unified step for both reaction and diffusion processes while satisfying the leap condition that the propensities do not change appreciably during the leap and ensuring that leaping does not cause molecular populations to become negative. Numerical results are presented that illustrate the improvement in simulation speed achieved by incorporating these two new strategies.

Convergence Rates of Finite Difference Stochastic Approximation Algorithms

DTIC Science & Technology

2016-06-01

dfferences as gradient approximations. It is shown that the convergence of these algorithms can be accelerated by controlling the implementation of the...descent algorithm, under various updating schemes using finite dfferences as gradient approximations. It is shown that the convergence of these...the Kiefer-Wolfowitz algorithm and the mirror descent algorithm, under various updating schemes using finite differences as gradient approximations. It

Comparison of genetic algorithms with conjugate gradient methods

NASA Technical Reports Server (NTRS)

Bosworth, J. L.; Foo, N. Y.; Zeigler, B. P.

1972-01-01

Genetic algorithms for mathematical function optimization are modeled on search strategies employed in natural adaptation. Comparisons of genetic algorithms with conjugate gradient methods, which were made on an IBM 1800 digital computer, show that genetic algorithms display superior performance over gradient methods for functions which are poorly behaved mathematically, for multimodal functions, and for functions obscured by additive random noise. Genetic methods offer performance comparable to gradient methods for many of the standard functions.

Large Airborne Full Tensor Gradient Data Inversion Based on a Non-Monotone Gradient Method

NASA Astrophysics Data System (ADS)

Sun, Yong; Meng, Zhaohai; Li, Fengting

2018-03-01

Following the development of gravity gradiometer instrument technology, the full tensor gravity (FTG) data can be acquired on airborne and marine platforms. Large-scale geophysical data can be obtained using these methods, making such data sets a number of the "big data" category. Therefore, a fast and effective inversion method is developed to solve the large-scale FTG data inversion problem. Many algorithms are available to accelerate the FTG data inversion, such as conjugate gradient method. However, the conventional conjugate gradient method takes a long time to complete data processing. Thus, a fast and effective iterative algorithm is necessary to improve the utilization of FTG data. Generally, inversion processing is formulated by incorporating regularizing constraints, followed by the introduction of a non-monotone gradient-descent method to accelerate the convergence rate of FTG data inversion. Compared with the conventional gradient method, the steepest descent gradient algorithm, and the conjugate gradient algorithm, there are clear advantages of the non-monotone iterative gradient-descent algorithm. Simulated and field FTG data were applied to show the application value of this new fast inversion method.

Online Coregularization for Multiview Semisupervised Learning

PubMed Central

Li, Guohui; Huang, Kuihua

2013-01-01

We propose a novel online coregularization framework for multiview semisupervised learning based on the notion of duality in constrained optimization. Using the weak duality theorem, we reduce the online coregularization to the task of increasing the dual function. We demonstrate that the existing online coregularization algorithms in previous work can be viewed as an approximation of our dual ascending process using gradient ascent. New algorithms are derived based on the idea of ascending the dual function more aggressively. For practical purpose, we also propose two sparse approximation approaches for kernel representation to reduce the computational complexity. Experiments show that our derived online coregularization algorithms achieve risk and accuracy comparable to offline algorithms while consuming less time and memory. Specially, our online coregularization algorithms are able to deal with concept drift and maintain a much smaller error rate. This paper paves a way to the design and analysis of online coregularization algorithms. PMID:24194680

Effects of a PID Control System on Electromagnetic Fields in an nEDM Experiment

NASA Astrophysics Data System (ADS)

Molina, Daniel

2017-09-01

The Kellogg Radiation Laboratory is currently testing a prototype for an experiment that hopes to identify the electric dipole moment of the neutron. As part of this testing, we have developed a PID (proportional, integral, derivative) feedback system that uses large coils to fix the value of local external magnetic fields, up to linear gradients. PID algorithms compare the current value to a set-point and use the integral and derivative of the field with respect to the set-point to maintain constant fields. We have also developed a method for zeroing linear gradients within the experimental apparatus. In order to determine the performance of the PID algorithm, measurements of both the internal and external fields were obtained with and without the algorithm running, and these results were compared for noise and time stability. We have seen that the PID algorithm can reduce the effect of disturbance to the field by a factor of 10.

Performance analysis of structured gradient algorithm. [for adaptive beamforming linear arrays

NASA Technical Reports Server (NTRS)

Godara, Lal C.

1990-01-01

The structured gradient algorithm uses a structured estimate of the array correlation matrix (ACM) to estimate the gradient required for the constrained least-mean-square (LMS) algorithm. This structure reflects the structure of the exact array correlation matrix for an equispaced linear array and is obtained by spatial averaging of the elements of the noisy correlation matrix. In its standard form the LMS algorithm does not exploit the structure of the array correlation matrix. The gradient is estimated by multiplying the array output with the receiver outputs. An analysis of the two algorithms is presented to show that the covariance of the gradient estimated by the structured method is less sensitive to the look direction signal than that estimated by the standard method. The effect of the number of elements on the signal sensitivity of the two algorithms is studied.

A Rotor Tip Vortex Tracing Algorithm for Image Post-Processing

NASA Technical Reports Server (NTRS)

Overmeyer, Austin D.

2015-01-01

A neurite tracing algorithm, originally developed for medical image processing, was used to trace the location of the rotor tip vortex in density gradient flow visualization images. The tracing algorithm was applied to several representative test images to form case studies. The accuracy of the tracing algorithm was compared to two current methods including a manual point and click method and a cross-correlation template method. It is shown that the neurite tracing algorithm can reduce the post-processing time to trace the vortex by a factor of 10 to 15 without compromising the accuracy of the tip vortex location compared to other methods presented in literature.

Ion flux through membrane channels--an enhanced algorithm for the Poisson-Nernst-Planck model.

PubMed

Dyrka, Witold; Augousti, Andy T; Kotulska, Malgorzata

2008-09-01

A novel algorithmic scheme for numerical solution of the 3D Poisson-Nernst-Planck model is proposed. The algorithmic improvements are universal and independent of the detailed physical model. They include three major steps: an adjustable gradient-based step value, an adjustable relaxation coefficient, and an optimized segmentation of the modeled space. The enhanced algorithm significantly accelerates the speed of computation and reduces the computational demands. The theoretical model was tested on a regular artificial channel and validated on a real protein channel-alpha-hemolysin, proving its efficiency. (c) 2008 Wiley Periodicals, Inc.

PDC-SGB: Prediction of effective drug combinations using a stochastic gradient boosting algorithm.

PubMed

Xu, Qian; Xiong, Yi; Dai, Hao; Kumari, Kotni Meena; Xu, Qin; Ou, Hong-Yu; Wei, Dong-Qing

2017-03-21

Combinatorial therapy is a promising strategy for combating complex diseases by improving the efficacy and reducing the side effects. To facilitate the identification of drug combinations in pharmacology, we proposed a new computational model, termed PDC-SGB, to predict effective drug combinations by integrating biological, chemical and pharmacological information based on a stochastic gradient boosting algorithm. To begin with, a set of 352 golden positive samples were collected from the public drug combination database. Then, a set of 732 dimensional feature vector involving biological, chemical and pharmaceutical information was constructed for each drug combination to describe its properties. To avoid overfitting, the maximum relevance & minimum redundancy (mRMR) method was performed to extract useful ones by removing redundant subsets. Based on the selected features, the three different type of classification algorithms were employed to build the drug combination prediction models. Our results demonstrated that the model based on the stochastic gradient boosting algorithm yield out the best performance. Furthermore, it is indicated that the feature patterns of therapy had powerful ability to discriminate effective drug combinations from non-effective ones. By analyzing various features, it is shown that the enriched features occurred frequently in golden positive samples can help predict novel drug combinations. Copyright © 2017 Elsevier Ltd. All rights reserved.

Medical image registration by combining global and local information: a chain-type diffeomorphic demons algorithm.

PubMed

Liu, Xiaozheng; Yuan, Zhenming; Zhu, Junming; Xu, Dongrong

2013-12-07

The demons algorithm is a popular algorithm for non-rigid image registration because of its computational efficiency and simple implementation. The deformation forces of the classic demons algorithm were derived from image gradients by considering the deformation to decrease the intensity dissimilarity between images. However, the methods using the difference of image intensity for medical image registration are easily affected by image artifacts, such as image noise, non-uniform imaging and partial volume effects. The gradient magnitude image is constructed from the local information of an image, so the difference in a gradient magnitude image can be regarded as more reliable and robust for these artifacts. Then, registering medical images by considering the differences in both image intensity and gradient magnitude is a straightforward selection. In this paper, based on a diffeomorphic demons algorithm, we propose a chain-type diffeomorphic demons algorithm by combining the differences in both image intensity and gradient magnitude for medical image registration. Previous work had shown that the classic demons algorithm can be considered as an approximation of a second order gradient descent on the sum of the squared intensity differences. By optimizing the new dissimilarity criteria, we also present a set of new demons forces which were derived from the gradients of the image and gradient magnitude image. We show that, in controlled experiments, this advantage is confirmed, and yields a fast convergence.

Gradient Learning Algorithms for Ontology Computing

PubMed Central

Gao, Wei; Zhu, Linli

2014-01-01

The gradient learning model has been raising great attention in view of its promising perspectives for applications in statistics, data dimensionality reducing, and other specific fields. In this paper, we raise a new gradient learning model for ontology similarity measuring and ontology mapping in multidividing setting. The sample error in this setting is given by virtue of the hypothesis space and the trick of ontology dividing operator. Finally, two experiments presented on plant and humanoid robotics field verify the efficiency of the new computation model for ontology similarity measure and ontology mapping applications in multidividing setting. PMID:25530752

Algorithms for accelerated convergence of adaptive PCA.

PubMed

Chatterjee, C; Kang, Z; Roychowdhury, V P

2000-01-01

We derive and discuss new adaptive algorithms for principal component analysis (PCA) that are shown to converge faster than the traditional PCA algorithms due to Oja, Sanger, and Xu. It is well known that traditional PCA algorithms that are derived by using gradient descent on an objective function are slow to converge. Furthermore, the convergence of these algorithms depends on appropriate choices of the gain sequences. Since online applications demand faster convergence and an automatic selection of gains, we present new adaptive algorithms to solve these problems. We first present an unconstrained objective function, which can be minimized to obtain the principal components. We derive adaptive algorithms from this objective function by using: 1) gradient descent; 2) steepest descent; 3) conjugate direction; and 4) Newton-Raphson methods. Although gradient descent produces Xu's LMSER algorithm, the steepest descent, conjugate direction, and Newton-Raphson methods produce new adaptive algorithms for PCA. We also provide a discussion on the landscape of the objective function, and present a global convergence proof of the adaptive gradient descent PCA algorithm using stochastic approximation theory. Extensive experiments with stationary and nonstationary multidimensional Gaussian sequences show faster convergence of the new algorithms over the traditional gradient descent methods.We also compare the steepest descent adaptive algorithm with state-of-the-art methods on stationary and nonstationary sequences.

Simulation of co-phase error correction of optical multi-aperture imaging system based on stochastic parallel gradient decent algorithm

NASA Astrophysics Data System (ADS)

He, Xiaojun; Ma, Haotong; Luo, Chuanxin

2016-10-01

The optical multi-aperture imaging system is an effective way to magnify the aperture and increase the resolution of telescope optical system, the difficulty of which lies in detecting and correcting of co-phase error. This paper presents a method based on stochastic parallel gradient decent algorithm (SPGD) to correct the co-phase error. Compared with the current method, SPGD method can avoid detecting the co-phase error. This paper analyzed the influence of piston error and tilt error on image quality based on double-aperture imaging system, introduced the basic principle of SPGD algorithm, and discuss the influence of SPGD algorithm's key parameters (the gain coefficient and the disturbance amplitude) on error control performance. The results show that SPGD can efficiently correct the co-phase error. The convergence speed of the SPGD algorithm is improved with the increase of gain coefficient and disturbance amplitude, but the stability of the algorithm reduced. The adaptive gain coefficient can solve this problem appropriately. This paper's results can provide the theoretical reference for the co-phase error correction of the multi-aperture imaging system.

SU-E-T-295: Simultaneous Beam Sampling and Aperture Shape Optimization for Station Parameter Optimized Radiation Therapy (SPORT)

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

Zarepisheh, M; Li, R; Xing, L

Purpose: Station Parameter Optimized Radiation Therapy (SPORT) was recently proposed to fully utilize the technical capability of emerging digital LINACs, in which the station parameters of a delivery system, (such as aperture shape and weight, couch position/angle, gantry/collimator angle) are optimized altogether. SPORT promises to deliver unprecedented radiation dose distributions efficiently, yet there does not exist any optimization algorithm to implement it. The purpose of this work is to propose an optimization algorithm to simultaneously optimize the beam sampling and aperture shapes. Methods: We build a mathematical model whose variables are beam angles (including non-coplanar and/or even nonisocentric beams) andmore » aperture shapes. To solve the resulting large scale optimization problem, we devise an exact, convergent and fast optimization algorithm by integrating three advanced optimization techniques named column generation, gradient method, and pattern search. Column generation is used to find a good set of aperture shapes as an initial solution by adding apertures sequentially. Then we apply the gradient method to iteratively improve the current solution by reshaping the aperture shapes and updating the beam angles toward the gradient. Algorithm continues by pattern search method to explore the part of the search space that cannot be reached by the gradient method. Results: The proposed technique is applied to a series of patient cases and significantly improves the plan quality. In a head-and-neck case, for example, the left parotid gland mean-dose, brainstem max-dose, spinal cord max-dose, and mandible mean-dose are reduced by 10%, 7%, 24% and 12% respectively, compared to the conventional VMAT plan while maintaining the same PTV coverage. Conclusion: Combined use of column generation, gradient search and pattern search algorithms provide an effective way to optimize simultaneously the large collection of station parameters and significantly improves quality of resultant treatment plans as compared with conventional VMAT or IMRT treatments.« less

Optimal Design of Gradient Materials and Bi-Level Optimization of Topology Using Targets (BOTT)

NASA Astrophysics Data System (ADS)

Garland, Anthony

The objective of this research is to understand the fundamental relationships necessary to develop a method to optimize both the topology and the internal gradient material distribution of a single object while meeting constraints and conflicting objectives. Functionally gradient material (FGM) objects possess continuous varying material properties throughout the object, and they allow an engineer to tailor individual regions of an object to have specific mechanical properties by locally modifying the internal material composition. A variety of techniques exists for topology optimization, and several methods exist for FGM optimization, but combining the two together is difficult. Understanding the relationship between topology and material gradient optimization enables the selection of an appropriate model and the development of algorithms, which allow engineers to design high-performance parts that better meet design objectives than optimized homogeneous material objects. For this research effort, topology optimization means finding the optimal connected structure with an optimal shape. FGM optimization means finding the optimal macroscopic material properties within an object. Tailoring the material constitutive matrix as a function of position results in gradient properties. Once, the target macroscopic properties are known, a mesostructure or a particular material nanostructure can be found which gives the target material properties at each macroscopic point. This research demonstrates that topology and gradient materials can both be optimized together for a single part. The algorithms use a discretized model of the domain and gradient based optimization algorithms. In addition, when considering two conflicting objectives the algorithms in this research generate clear 'features' within a single part. This tailoring of material properties within different areas of a single part (automated design of 'features') using computational design tools is a novel benefit of gradient material designs. A macroscopic gradient can be achieved by varying the microstructure or the mesostructures of an object. The mesostructure interpretation allows for more design freedom since the mesostructures can be tuned to have non-isotropic material properties. A new algorithm called Bi-level Optimization of Topology using Targets (BOTT) seeks to find the best distribution of mesostructure designs throughout a single object in order to minimize an objective value. On the macro level, the BOTT algorithm optimizes the macro topology and gradient material properties within the object. The BOTT algorithm optimizes the material gradient by finding the best constitutive matrix at each location with the object. In order to enhance the likelihood that a mesostructure can be generated with the same equivalent constitutive matrix, the variability of the constitutive matrix is constrained to be an orthotropic material. The stiffness in the X and Y directions (of the base coordinate system) can change in addition to rotating the orthotropic material to align with the loading at each region. Second, the BOTT algorithm designs mesostructures with macroscopic properties equal to the target properties found in step one while at the same time the algorithm seeks to minimize material usage in each mesostructure. The mesostructure algorithm maximizes the strain energy of the mesostructures unit cell when a pseudo strain is applied to the cell. A set of experiments reveals the fundamental relationship between target cell density and the strain (or pseudo strain) applied to a unit cell and the output effective properties of the mesostructure. At low density, a few mesostructure unit cell design are possible, while at higher density the mesostructure unit cell designs have many possibilities. Therefore, at low densities the effective properties of the mesostructure are a step function of the applied pseudo strain. At high densities, the effective properties of the mesostructure are continuous function of the applied pseudo strain. Finally, the macro and mesostructure designs are coordinated so that the macro and meso levels agree on the material properties at each macro region. In addition, a coordination effort seeks to coordinate the boundaries of adjacent mesostructure designs so that the macro load path is transmitted from one mesostructure design to its neighbors. The BOTT algorithm has several advantages over existing algorithms within the literature. First, the BOTT algorithm significantly reduces the computational power required to run the algorithm. Second, the BOTT algorithm indirectly enforces a minimum mesostructure density constraint which increases the manufacturability of the final design. Third, the BOTT algorithm seeks to transfer the load from one mesostructure to its neighbors by coordinating the boundaries of adjacent mesostructure designs. However, the BOTT algorithm can still be improved since it may have difficulty converging due to the step function nature of the mesostructure design problem at low density.

Peak-Seeking Optimization of Trim for Reduced Fuel Consumption: Flight-Test Results

NASA Technical Reports Server (NTRS)

Brown, Nelson Andrew; Schaefer, Jacob Robert

2013-01-01

A peak-seeking control algorithm for real-time trim optimization for reduced fuel consumption has been developed by researchers at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center to address the goals of the NASA Environmentally Responsible Aviation project to reduce fuel burn and emissions. The peak-seeking control algorithm is based on a steepest-descent algorithm using a time-varying Kalman filter to estimate the gradient of a performance function of fuel flow versus control surface positions. In real-time operation, deflections of symmetric ailerons, trailing-edge flaps, and leading-edge flaps of an F/A-18 airplane (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) are used for optimization of fuel flow. Results from six research flights are presented herein. The optimization algorithm found a trim configuration that required approximately 3 percent less fuel flow than the baseline trim at the same flight condition. The algorithm consistently rediscovered the solution from several initial conditions. These results show that the algorithm has good performance in a relevant environment.

Peak-Seeking Optimization of Trim for Reduced Fuel Consumption: Flight-test Results

NASA Technical Reports Server (NTRS)

Brown, Nelson Andrew; Schaefer, Jacob Robert

2013-01-01

A peak-seeking control algorithm for real-time trim optimization for reduced fuel consumption has been developed by researchers at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center to address the goals of the NASA Environmentally Responsible Aviation project to reduce fuel burn and emissions. The peak-seeking control algorithm is based on a steepest-descent algorithm using a time-varying Kalman filter to estimate the gradient of a performance function of fuel flow versus control surface positions. In real-time operation, deflections of symmetric ailerons, trailing-edge flaps, and leading-edge flaps of an F/A-18 airplane (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) are used for optimization of fuel flow. Results from six research flights are presented herein. The optimization algorithm found a trim configuration that required approximately 3 percent less fuel flow than the baseline trim at the same flight condition. The algorithm consistently rediscovered the solution from several initial conditions. These results show that the algorithm has good performance in a relevant environment.

Analysis of deformable image registration accuracy using computational modeling

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

Zhong Hualiang; Kim, Jinkoo; Chetty, Indrin J.

2010-03-15

Computer aided modeling of anatomic deformation, allowing various techniques and protocols in radiation therapy to be systematically verified and studied, has become increasingly attractive. In this study the potential issues in deformable image registration (DIR) were analyzed based on two numerical phantoms: One, a synthesized, low intensity gradient prostate image, and the other a lung patient's CT image data set. Each phantom was modeled with region-specific material parameters with its deformation solved using a finite element method. The resultant displacements were used to construct a benchmark to quantify the displacement errors of the Demons and B-Spline-based registrations. The results showmore » that the accuracy of these registration algorithms depends on the chosen parameters, the selection of which is closely associated with the intensity gradients of the underlying images. For the Demons algorithm, both single resolution (SR) and multiresolution (MR) registrations required approximately 300 iterations to reach an accuracy of 1.4 mm mean error in the lung patient's CT image (and 0.7 mm mean error averaged in the lung only). For the low gradient prostate phantom, these algorithms (both SR and MR) required at least 1600 iterations to reduce their mean errors to 2 mm. For the B-Spline algorithms, best performance (mean errors of 1.9 mm for SR and 1.6 mm for MR, respectively) on the low gradient prostate was achieved using five grid nodes in each direction. Adding more grid nodes resulted in larger errors. For the lung patient's CT data set, the B-Spline registrations required ten grid nodes in each direction for highest accuracy (1.4 mm for SR and 1.5 mm for MR). The numbers of iterations or grid nodes required for optimal registrations depended on the intensity gradients of the underlying images. In summary, the performance of the Demons and B-Spline registrations have been quantitatively evaluated using numerical phantoms. The results show that parameter selection for optimal accuracy is closely related to the intensity gradients of the underlying images. Also, the result that the DIR algorithms produce much lower errors in heterogeneous lung regions relative to homogeneous (low intensity gradient) regions, suggests that feature-based evaluation of deformable image registration accuracy must be viewed cautiously.« less

Study on transient beam loading compensation for China ADS proton linac injector II

NASA Astrophysics Data System (ADS)

Gao, Zheng; He, Yuan; Wang, Xian-Wu; Chang, Wei; Zhang, Rui-Feng; Zhu, Zheng-Long; Zhang, Sheng-Hu; Chen, Qi; Powers, Tom

2016-05-01

Significant transient beam loading effects were observed during beam commissioning tests of prototype II of the injector for the accelerator driven sub-critical (ADS) system, which took place at the Institute of Modern Physics, Chinese Academy of Sciences, between October and December 2014. During these tests experiments were performed with continuous wave (CW) operation of the cavities with pulsed beam current, and the system was configured to make use of a prototype digital low level radio frequency (LLRF) controller. The system was originally operated in pulsed mode with a simple proportional plus integral and deviation (PID) feedback control algorithm, which was not able to maintain the desired gradient regulation during pulsed 10 mA beam operations. A unique simple transient beam loading compensation method which made use of a combination of proportional and integral (PI) feedback and feedforward control algorithm was implemented in order to significantly reduce the beam induced transient effect in the cavity gradients. The superconducting cavity field variation was reduced to less than 1.7% after turning on this control algorithm. The design and experimental results of this system are presented in this paper. Supported by National Natural Science Foundation of China (91426303, 11525523)

Robust and Adaptive Online Time Series Prediction with Long Short-Term Memory

PubMed Central

Tao, Qing

2017-01-01

Online time series prediction is the mainstream method in a wide range of fields, ranging from speech analysis and noise cancelation to stock market analysis. However, the data often contains many outliers with the increasing length of time series in real world. These outliers can mislead the learned model if treated as normal points in the process of prediction. To address this issue, in this paper, we propose a robust and adaptive online gradient learning method, RoAdam (Robust Adam), for long short-term memory (LSTM) to predict time series with outliers. This method tunes the learning rate of the stochastic gradient algorithm adaptively in the process of prediction, which reduces the adverse effect of outliers. It tracks the relative prediction error of the loss function with a weighted average through modifying Adam, a popular stochastic gradient method algorithm for training deep neural networks. In our algorithm, the large value of the relative prediction error corresponds to a small learning rate, and vice versa. The experiments on both synthetic data and real time series show that our method achieves better performance compared to the existing methods based on LSTM. PMID:29391864

Robust and Adaptive Online Time Series Prediction with Long Short-Term Memory.

PubMed

Yang, Haimin; Pan, Zhisong; Tao, Qing

2017-01-01

Online time series prediction is the mainstream method in a wide range of fields, ranging from speech analysis and noise cancelation to stock market analysis. However, the data often contains many outliers with the increasing length of time series in real world. These outliers can mislead the learned model if treated as normal points in the process of prediction. To address this issue, in this paper, we propose a robust and adaptive online gradient learning method, RoAdam (Robust Adam), for long short-term memory (LSTM) to predict time series with outliers. This method tunes the learning rate of the stochastic gradient algorithm adaptively in the process of prediction, which reduces the adverse effect of outliers. It tracks the relative prediction error of the loss function with a weighted average through modifying Adam, a popular stochastic gradient method algorithm for training deep neural networks. In our algorithm, the large value of the relative prediction error corresponds to a small learning rate, and vice versa. The experiments on both synthetic data and real time series show that our method achieves better performance compared to the existing methods based on LSTM.

Power Control and Optimization of Photovoltaic and Wind Energy Conversion Systems

NASA Astrophysics Data System (ADS)

Ghaffari, Azad

Power map and Maximum Power Point (MPP) of Photovoltaic (PV) and Wind Energy Conversion Systems (WECS) highly depend on system dynamics and environmental parameters, e.g., solar irradiance, temperature, and wind speed. Power optimization algorithms for PV systems and WECS are collectively known as Maximum Power Point Tracking (MPPT) algorithm. Gradient-based Extremum Seeking (ES), as a non-model-based MPPT algorithm, governs the system to its peak point on the steepest descent curve regardless of changes of the system dynamics and variations of the environmental parameters. Since the power map shape defines the gradient vector, then a close estimate of the power map shape is needed to create user assignable transients in the MPPT algorithm. The Hessian gives a precise estimate of the power map in a neighborhood around the MPP. The estimate of the inverse of the Hessian in combination with the estimate of the gradient vector are the key parts to implement the Newton-based ES algorithm. Hence, we generate an estimate of the Hessian using our proposed perturbation matrix. Also, we introduce a dynamic estimator to calculate the inverse of the Hessian which is an essential part of our algorithm. We present various simulations and experiments on the micro-converter PV systems to verify the validity of our proposed algorithm. The ES scheme can also be used in combination with other control algorithms to achieve desired closed-loop performance. The WECS dynamics is slow which causes even slower response time for the MPPT based on the ES. Hence, we present a control scheme, extended from Field-Oriented Control (FOC), in combination with feedback linearization to reduce the convergence time of the closed-loop system. Furthermore, the nonlinear control prevents magnetic saturation of the stator of the Induction Generator (IG). The proposed control algorithm in combination with the ES guarantees the closed-loop system robustness with respect to high level parameter uncertainty in the IG dynamics. The simulation results verify the effectiveness of the proposed algorithm.

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.

Contour Detection and Completion for Inpainting and Segmentation Based on Topological Gradient and Fast Marching Algorithms

PubMed Central

Auroux, Didier; Cohen, Laurent D.; Masmoudi, Mohamed

2011-01-01

We combine in this paper the topological gradient, which is a powerful method for edge detection in image processing, and a variant of the minimal path method in order to find connected contours. The topological gradient provides a more global analysis of the image than the standard gradient and identifies the main edges of an image. Several image processing problems (e.g., inpainting and segmentation) require continuous contours. For this purpose, we consider the fast marching algorithm in order to find minimal paths in the topological gradient image. This coupled algorithm quickly provides accurate and connected contours. We present then two numerical applications, to image inpainting and segmentation, of this hybrid algorithm. PMID:22194734

An Adaptive Orientation Estimation Method for Magnetic and Inertial Sensors in the Presence of Magnetic Disturbances

PubMed Central

Fan, Bingfei; Li, Qingguo; Wang, Chao; Liu, Tao

2017-01-01

Magnetic and inertial sensors have been widely used to estimate the orientation of human segments due to their low cost, compact size and light weight. However, the accuracy of the estimated orientation is easily affected by external factors, especially when the sensor is used in an environment with magnetic disturbances. In this paper, we propose an adaptive method to improve the accuracy of orientation estimations in the presence of magnetic disturbances. The method is based on existing gradient descent algorithms, and it is performed prior to sensor fusion algorithms. The proposed method includes stationary state detection and magnetic disturbance severity determination. The stationary state detection makes this method immune to magnetic disturbances in stationary state, while the magnetic disturbance severity determination helps to determine the credibility of magnetometer data under dynamic conditions, so as to mitigate the negative effect of the magnetic disturbances. The proposed method was validated through experiments performed on a customized three-axis instrumented gimbal with known orientations. The error of the proposed method and the original gradient descent algorithms were calculated and compared. Experimental results demonstrate that in stationary state, the proposed method is completely immune to magnetic disturbances, and in dynamic conditions, the error caused by magnetic disturbance is reduced by 51.2% compared with original MIMU gradient descent algorithm. PMID:28534858

Frequency-domain beamformers using conjugate gradient techniques for speech enhancement.

PubMed

Zhao, Shengkui; Jones, Douglas L; Khoo, Suiyang; Man, Zhihong

2014-09-01

A multiple-iteration constrained conjugate gradient (MICCG) algorithm and a single-iteration constrained conjugate gradient (SICCG) algorithm are proposed to realize the widely used frequency-domain minimum-variance-distortionless-response (MVDR) beamformers and the resulting algorithms are applied to speech enhancement. The algorithms are derived based on the Lagrange method and the conjugate gradient techniques. The implementations of the algorithms avoid any form of explicit or implicit autocorrelation matrix inversion. Theoretical analysis establishes formal convergence of the algorithms. Specifically, the MICCG algorithm is developed based on a block adaptation approach and it generates a finite sequence of estimates that converge to the MVDR solution. For limited data records, the estimates of the MICCG algorithm are better than the conventional estimators and equivalent to the auxiliary vector algorithms. The SICCG algorithm is developed based on a continuous adaptation approach with a sample-by-sample updating procedure and the estimates asymptotically converge to the MVDR solution. An illustrative example using synthetic data from a uniform linear array is studied and an evaluation on real data recorded by an acoustic vector sensor array is demonstrated. Performance of the MICCG algorithm and the SICCG algorithm are compared with the state-of-the-art approaches.

Peak-Seeking Control For Reduced Fuel Consumption: Flight-Test Results For The Full-Scale Advanced Systems Testbed FA-18 Airplane

NASA Technical Reports Server (NTRS)

Brown, Nelson

2013-01-01

A peak-seeking control algorithm for real-time trim optimization for reduced fuel consumption has been developed by researchers at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center to address the goals of the NASA Environmentally Responsible Aviation project to reduce fuel burn and emissions. The peak-seeking control algorithm is based on a steepest-descent algorithm using a time-varying Kalman filter to estimate the gradient of a performance function of fuel flow versus control surface positions. In real-time operation, deflections of symmetric ailerons, trailing-edge flaps, and leading-edge flaps of an F/A-18 airplane are used for optimization of fuel flow. Results from six research flights are presented herein. The optimization algorithm found a trim configuration that required approximately 3 percent less fuel flow than the baseline trim at the same flight condition. This presentation also focuses on the design of the flight experiment and the practical challenges of conducting the experiment.

Correction of geometric distortion in Propeller echo planar imaging using a modified reversed gradient approach.

PubMed

Chang, Hing-Chiu; Chuang, Tzu-Chao; Lin, Yi-Ru; Wang, Fu-Nien; Huang, Teng-Yi; Chung, Hsiao-Wen

2013-04-01

This study investigates the application of a modified reversed gradient algorithm to the Propeller-EPI imaging method (periodically rotated overlapping parallel lines with enhanced reconstruction based on echo-planar imaging readout) for corrections of geometric distortions due to the EPI readout. Propeller-EPI acquisition was executed with 360-degree rotational coverage of the k-space, from which the image pairs with opposite phase-encoding gradient polarities were extracted for reversed gradient geometric and intensity corrections. The spatial displacements obtained on a pixel-by-pixel basis were fitted using a two-dimensional polynomial followed by low-pass filtering to assure correction reliability in low-signal regions. Single-shot EPI images were obtained on a phantom, whereas high spatial resolution T2-weighted and diffusion tensor Propeller-EPI data were acquired in vivo from healthy subjects at 3.0 Tesla, to demonstrate the effectiveness of the proposed algorithm. Phantom images show success of the smoothed displacement map concept in providing improvements of the geometric corrections at low-signal regions. Human brain images demonstrate prominently superior reconstruction quality of Propeller-EPI images with modified reversed gradient corrections as compared with those obtained without corrections, as evidenced from verification against the distortion-free fast spin-echo images at the same level. The modified reversed gradient method is an effective approach to obtain high-resolution Propeller-EPI images with substantially reduced artifacts.

Pixel-based OPC optimization based on conjugate gradients.

PubMed

Ma, Xu; Arce, Gonzalo R

2011-01-31

Optical proximity correction (OPC) methods are resolution enhancement techniques (RET) used extensively in the semiconductor industry to improve the resolution and pattern fidelity of optical lithography. In pixel-based OPC (PBOPC), the mask is divided into small pixels, each of which is modified during the optimization process. Two critical issues in PBOPC are the required computational complexity of the optimization process, and the manufacturability of the optimized mask. Most current OPC optimization methods apply the steepest descent (SD) algorithm to improve image fidelity augmented by regularization penalties to reduce the complexity of the mask. Although simple to implement, the SD algorithm converges slowly. The existing regularization penalties, however, fall short in meeting the mask rule check (MRC) requirements often used in semiconductor manufacturing. This paper focuses on developing OPC optimization algorithms based on the conjugate gradient (CG) method which exhibits much faster convergence than the SD algorithm. The imaging formation process is represented by the Fourier series expansion model which approximates the partially coherent system as a sum of coherent systems. In order to obtain more desirable manufacturability properties of the mask pattern, a MRC penalty is proposed to enlarge the linear size of the sub-resolution assistant features (SRAFs), as well as the distances between the SRAFs and the main body of the mask. Finally, a projection method is developed to further reduce the complexity of the optimized mask pattern.

SAGE: The Self-Adaptive Grid Code. 3

NASA Technical Reports Server (NTRS)

Davies, Carol B.; Venkatapathy, Ethiraj

1999-01-01

The multi-dimensional self-adaptive grid code, SAGE, is an important tool in the field of computational fluid dynamics (CFD). It provides an efficient method to improve the accuracy of flow solutions while simultaneously reducing computer processing time. Briefly, SAGE enhances an initial computational grid by redistributing the mesh points into more appropriate locations. The movement of these points is driven by an equal-error-distribution algorithm that utilizes the relationship between high flow gradients and excessive solution errors. The method also provides a balance between clustering points in the high gradient regions and maintaining the smoothness and continuity of the adapted grid, The latest version, Version 3, includes the ability to change the boundaries of a given grid to more efficiently enclose flow structures and provides alternative redistribution algorithms.

SAGRAD: A Program for Neural Network Training with Simulated Annealing and the Conjugate Gradient Method.

PubMed

Bernal, Javier; Torres-Jimenez, Jose

2015-01-01

SAGRAD (Simulated Annealing GRADient), a Fortran 77 program for computing neural networks for classification using batch learning, is discussed. Neural network training in SAGRAD is based on a combination of simulated annealing and Møller's scaled conjugate gradient algorithm, the latter a variation of the traditional conjugate gradient method, better suited for the nonquadratic nature of neural networks. Different aspects of the implementation of the training process in SAGRAD are discussed, such as the efficient computation of gradients and multiplication of vectors by Hessian matrices that are required by Møller's algorithm; the (re)initialization of weights with simulated annealing required to (re)start Møller's algorithm the first time and each time thereafter that it shows insufficient progress in reaching a possibly local minimum; and the use of simulated annealing when Møller's algorithm, after possibly making considerable progress, becomes stuck at a local minimum or flat area of weight space. Outlines of the scaled conjugate gradient algorithm, the simulated annealing procedure and the training process used in SAGRAD are presented together with results from running SAGRAD on two examples of training data.

On Some Separated Algorithms for Separable Nonlinear Least Squares Problems.

PubMed

Gan, Min; Chen, C L Philip; Chen, Guang-Yong; Chen, Long

2017-10-03

For a class of nonlinear least squares problems, it is usually very beneficial to separate the variables into a linear and a nonlinear part and take full advantage of reliable linear least squares techniques. Consequently, the original problem is turned into a reduced problem which involves only nonlinear parameters. We consider in this paper four separated algorithms for such problems. The first one is the variable projection (VP) algorithm with full Jacobian matrix of Golub and Pereyra. The second and third ones are VP algorithms with simplified Jacobian matrices proposed by Kaufman and Ruano et al. respectively. The fourth one only uses the gradient of the reduced problem. Monte Carlo experiments are conducted to compare the performance of these four algorithms. From the results of the experiments, we find that: 1) the simplified Jacobian proposed by Ruano et al. is not a good choice for the VP algorithm; moreover, it may render the algorithm hard to converge; 2) the fourth algorithm perform moderately among these four algorithms; 3) the VP algorithm with the full Jacobian matrix perform more stable than that of the VP algorithm with Kuafman's simplified one; and 4) the combination of VP algorithm and Levenberg-Marquardt method is more effective than the combination of VP algorithm and Gauss-Newton method.

Stochastic parallel gradient descent based adaptive optics used for a high contrast imaging coronagraph

NASA Astrophysics Data System (ADS)

Dong, Bing; Ren, De-Qing; Zhang, Xi

2011-08-01

An adaptive optics (AO) system based on a stochastic parallel gradient descent (SPGD) algorithm is proposed to reduce the speckle noises in the optical system of a stellar coronagraph in order to further improve the contrast. The principle of the SPGD algorithm is described briefly and a metric suitable for point source imaging optimization is given. The feasibility and good performance of the SPGD algorithm is demonstrated by an experimental system featured with a 140-actuator deformable mirror and a Hartmann-Shark wavefront sensor. Then the SPGD based AO is applied to a liquid crystal array (LCA) based coronagraph to improve the contrast. The LCA can modulate the incoming light to generate a pupil apodization mask of any pattern. A circular stepped pattern is used in our preliminary experiment and the image contrast shows improvement from 10-3 to 10-4.5 at an angular distance of 2λ/D after being corrected by SPGD based AO.

3D-Web-GIS RFID location sensing system for construction objects.

PubMed

Ko, Chien-Ho

2013-01-01

Construction site managers could benefit from being able to visualize on-site construction objects. Radio frequency identification (RFID) technology has been shown to improve the efficiency of construction object management. The objective of this study is to develop a 3D-Web-GIS RFID location sensing system for construction objects. An RFID 3D location sensing algorithm combining Simulated Annealing (SA) and a gradient descent method is proposed to determine target object location. In the algorithm, SA is used to stabilize the search process and the gradient descent method is used to reduce errors. The locations of the analyzed objects are visualized using the 3D-Web-GIS system. A real construction site is used to validate the applicability of the proposed method, with results indicating that the proposed approach can provide faster, more accurate, and more stable 3D positioning results than other location sensing algorithms. The proposed system allows construction managers to better understand worksite status, thus enhancing managerial efficiency.

3D-Web-GIS RFID Location Sensing System for Construction Objects

PubMed Central

2013-01-01

Construction site managers could benefit from being able to visualize on-site construction objects. Radio frequency identification (RFID) technology has been shown to improve the efficiency of construction object management. The objective of this study is to develop a 3D-Web-GIS RFID location sensing system for construction objects. An RFID 3D location sensing algorithm combining Simulated Annealing (SA) and a gradient descent method is proposed to determine target object location. In the algorithm, SA is used to stabilize the search process and the gradient descent method is used to reduce errors. The locations of the analyzed objects are visualized using the 3D-Web-GIS system. A real construction site is used to validate the applicability of the proposed method, with results indicating that the proposed approach can provide faster, more accurate, and more stable 3D positioning results than other location sensing algorithms. The proposed system allows construction managers to better understand worksite status, thus enhancing managerial efficiency. PMID:23864821

Aeromagnetic gradient compensation method for helicopter based on ɛ-support vector regression algorithm

NASA Astrophysics Data System (ADS)

Wu, Peilin; Zhang, Qunying; Fei, Chunjiao; Fang, Guangyou

2017-04-01

Aeromagnetic gradients are typically measured by optically pumped magnetometers mounted on an aircraft. Any aircraft, particularly helicopters, produces significant levels of magnetic interference. Therefore, aeromagnetic compensation is essential, and least square (LS) is the conventional method used for reducing interference levels. However, the LSs approach to solving the aeromagnetic interference model has a few difficulties, one of which is in handling multicollinearity. Therefore, we propose an aeromagnetic gradient compensation method, specifically targeted for helicopter use but applicable on any airborne platform, which is based on the ɛ-support vector regression algorithm. The structural risk minimization criterion intrinsic to the method avoids multicollinearity altogether. Local aeromagnetic anomalies can be retained, and platform-generated fields are suppressed simultaneously by constructing an appropriate loss function and kernel function. The method was tested using an unmanned helicopter and obtained improvement ratios of 12.7 and 3.5 in the vertical and horizontal gradient data, respectively. Both of these values are probably better than those that would have been obtained from the conventional method applied to the same data, had it been possible to do so in a suitable comparative context. The validity of the proposed method is demonstrated by the experimental result.

Experiments with conjugate gradient algorithms for homotopy curve tracking

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

Stationary-phase optimized selectivity liquid chromatography: development of a linear gradient prediction algorithm.

PubMed

De Beer, Maarten; Lynen, Fréderic; Chen, Kai; Ferguson, Paul; Hanna-Brown, Melissa; Sandra, Pat

2010-03-01

Stationary-phase optimized selectivity liquid chromatography (SOS-LC) is a tool in reversed-phase LC (RP-LC) to optimize the selectivity for a given separation by combining stationary phases in a multisegment column. The presently (commercially) available SOS-LC optimization procedure and algorithm are only applicable to isocratic analyses. Step gradient SOS-LC has been developed, but this is still not very elegant for the analysis of complex mixtures composed of components covering a broad hydrophobicity range. A linear gradient prediction algorithm has been developed allowing one to apply SOS-LC as a generic RP-LC optimization method. The algorithm allows operation in isocratic, stepwise, and linear gradient run modes. The features of SOS-LC in the linear gradient mode are demonstrated by means of a mixture of 13 steroids, whereby baseline separation is predicted and experimentally demonstrated.

Distributed Kalman filtering compared to Fourier domain preconditioned conjugate gradient for laser guide star tomography on extremely large telescopes.

PubMed

Gilles, Luc; Massioni, Paolo; Kulcsár, Caroline; Raynaud, Henri-François; Ellerbroek, Brent

2013-05-01

This paper discusses the performance and cost of two computationally efficient Fourier-based tomographic wavefront reconstruction algorithms for wide-field laser guide star (LGS) adaptive optics (AO). The first algorithm is the iterative Fourier domain preconditioned conjugate gradient (FDPCG) algorithm developed by Yang et al. [Appl. Opt.45, 5281 (2006)], combined with pseudo-open-loop control (POLC). FDPCG's computational cost is proportional to N log(N), where N denotes the dimensionality of the tomography problem. The second algorithm is the distributed Kalman filter (DKF) developed by Massioni et al. [J. Opt. Soc. Am. A28, 2298 (2011)], which is a noniterative spatially invariant controller. When implemented in the Fourier domain, DKF's cost is also proportional to N log(N). Both algorithms are capable of estimating spatial frequency components of the residual phase beyond the wavefront sensor (WFS) cutoff frequency thanks to regularization, thereby reducing WFS spatial aliasing at the expense of more computations. We present performance and cost analyses for the LGS multiconjugate AO system under design for the Thirty Meter Telescope, as well as DKF's sensitivity to uncertainties in wind profile prior information. We found that, provided the wind profile is known to better than 10% wind speed accuracy and 20 deg wind direction accuracy, DKF, despite its spatial invariance assumptions, delivers a significantly reduced wavefront error compared to the static FDPCG minimum variance estimator combined with POLC. Due to its nonsequential nature and high degree of parallelism, DKF is particularly well suited for real-time implementation on inexpensive off-the-shelf graphics processing units.

New recursive-least-squares algorithms for nonlinear active control of sound and vibration using neural networks.

PubMed

Bouchard, M

2001-01-01

In recent years, a few articles describing the use of neural networks for nonlinear active control of sound and vibration were published. Using a control structure with two multilayer feedforward neural networks (one as a nonlinear controller and one as a nonlinear plant model), steepest descent algorithms based on two distinct gradient approaches were introduced for the training of the controller network. The two gradient approaches were sometimes called the filtered-x approach and the adjoint approach. Some recursive-least-squares algorithms were also introduced, using the adjoint approach. In this paper, an heuristic procedure is introduced for the development of recursive-least-squares algorithms based on the filtered-x and the adjoint gradient approaches. This leads to the development of new recursive-least-squares algorithms for the training of the controller neural network in the two networks structure. These new algorithms produce a better convergence performance than previously published algorithms. Differences in the performance of algorithms using the filtered-x and the adjoint gradient approaches are discussed in the paper. The computational load of the algorithms discussed in the paper is evaluated for multichannel systems of nonlinear active control. Simulation results are presented to compare the convergence performance of the algorithms, showing the convergence gain provided by the new algorithms.

SAGRAD: A Program for Neural Network Training with Simulated Annealing and the Conjugate Gradient Method

PubMed Central

Bernal, Javier; Torres-Jimenez, Jose

2015-01-01

SAGRAD (Simulated Annealing GRADient), a Fortran 77 program for computing neural networks for classification using batch learning, is discussed. Neural network training in SAGRAD is based on a combination of simulated annealing and Møller’s scaled conjugate gradient algorithm, the latter a variation of the traditional conjugate gradient method, better suited for the nonquadratic nature of neural networks. Different aspects of the implementation of the training process in SAGRAD are discussed, such as the efficient computation of gradients and multiplication of vectors by Hessian matrices that are required by Møller’s algorithm; the (re)initialization of weights with simulated annealing required to (re)start Møller’s algorithm the first time and each time thereafter that it shows insufficient progress in reaching a possibly local minimum; and the use of simulated annealing when Møller’s algorithm, after possibly making considerable progress, becomes stuck at a local minimum or flat area of weight space. Outlines of the scaled conjugate gradient algorithm, the simulated annealing procedure and the training process used in SAGRAD are presented together with results from running SAGRAD on two examples of training data. PMID:26958442

Efficient two-dimensional compressive sensing in MIMO radar

NASA Astrophysics Data System (ADS)

Shahbazi, Nafiseh; Abbasfar, Aliazam; Jabbarian-Jahromi, Mohammad

2017-12-01

Compressive sensing (CS) has been a way to lower sampling rate leading to data reduction for processing in multiple-input multiple-output (MIMO) radar systems. In this paper, we further reduce the computational complexity of a pulse-Doppler collocated MIMO radar by introducing a two-dimensional (2D) compressive sensing. To do so, we first introduce a new 2D formulation for the compressed received signals and then we propose a new measurement matrix design for our 2D compressive sensing model that is based on minimizing the coherence of sensing matrix using gradient descent algorithm. The simulation results show that our proposed 2D measurement matrix design using gradient decent algorithm (2D-MMDGD) has much lower computational complexity compared to one-dimensional (1D) methods while having better performance in comparison with conventional methods such as Gaussian random measurement matrix.

Correction of geometric distortion in Propeller echo planar imaging using a modified reversed gradient approach

PubMed Central

Chang, Hing-Chiu; Chuang, Tzu-Chao; Wang, Fu-Nien; Huang, Teng-Yi; Chung, Hsiao-Wen

2013-01-01

Objective This study investigates the application of a modified reversed gradient algorithm to the Propeller-EPI imaging method (periodically rotated overlapping parallel lines with enhanced reconstruction based on echo-planar imaging readout) for corrections of geometric distortions due to the EPI readout. Materials and methods Propeller-EPI acquisition was executed with 360-degree rotational coverage of the k-space, from which the image pairs with opposite phase-encoding gradient polarities were extracted for reversed gradient geometric and intensity corrections. The spatial displacements obtained on a pixel-by-pixel basis were fitted using a two-dimensional polynomial followed by low-pass filtering to assure correction reliability in low-signal regions. Single-shot EPI images were obtained on a phantom, whereas high spatial resolution T2-weighted and diffusion tensor Propeller-EPI data were acquired in vivo from healthy subjects at 3.0 Tesla, to demonstrate the effectiveness of the proposed algorithm. Results Phantom images show success of the smoothed displacement map concept in providing improvements of the geometric corrections at low-signal regions. Human brain images demonstrate prominently superior reconstruction quality of Propeller-EPI images with modified reversed gradient corrections as compared with those obtained without corrections, as evidenced from verification against the distortion-free fast spin-echo images at the same level. Conclusions The modified reversed gradient method is an effective approach to obtain high-resolution Propeller-EPI images with substantially reduced artifacts. PMID:23630654

Taming the Wild: A Unified Analysis of Hogwild!-Style Algorithms.

PubMed

De Sa, Christopher; Zhang, Ce; Olukotun, Kunle; Ré, Christopher

2015-12-01

Stochastic gradient descent (SGD) is a ubiquitous algorithm for a variety of machine learning problems. Researchers and industry have developed several techniques to optimize SGD's runtime performance, including asynchronous execution and reduced precision. Our main result is a martingale-based analysis that enables us to capture the rich noise models that may arise from such techniques. Specifically, we use our new analysis in three ways: (1) we derive convergence rates for the convex case (Hogwild!) with relaxed assumptions on the sparsity of the problem; (2) we analyze asynchronous SGD algorithms for non-convex matrix problems including matrix completion; and (3) we design and analyze an asynchronous SGD algorithm, called Buckwild!, that uses lower-precision arithmetic. We show experimentally that our algorithms run efficiently for a variety of problems on modern hardware.

Matrix preconditioning: a robust operation for optical linear algebra processors.

PubMed

Ghosh, A; Paparao, P

1987-07-15

Analog electrooptical processors are best suited for applications demanding high computational throughput with tolerance for inaccuracies. Matrix preconditioning is one such application. Matrix preconditioning is a preprocessing step for reducing the condition number of a matrix and is used extensively with gradient algorithms for increasing the rate of convergence and improving the accuracy of the solution. In this paper, we describe a simple parallel algorithm for matrix preconditioning, which can be implemented efficiently on a pipelined optical linear algebra processor. From the results of our numerical experiments we show that the efficacy of the preconditioning algorithm is affected very little by the errors of the optical system.

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models.

PubMed

Yuan, Gonglin; Duan, Xiabin; Liu, Wenjie; Wang, Xiaoliang; Cui, Zengru; Sheng, Zhou

2015-01-01

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1) βk ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations.

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models

PubMed Central

Yuan, Gonglin; Duan, Xiabin; Liu, Wenjie; Wang, Xiaoliang; Cui, Zengru; Sheng, Zhou

2015-01-01

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1)β k ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations. PMID:26502409

Approximate solution of the p-median minimization problem

NASA Astrophysics Data System (ADS)

Il'ev, V. P.; Il'eva, S. D.; Navrotskaya, A. A.

2016-09-01

A version of the facility location problem (the well-known p-median minimization problem) and its generalization—the problem of minimizing a supermodular set function—is studied. These problems are NP-hard, and they are approximately solved by a gradient algorithm that is a discrete analog of the steepest descent algorithm. A priori bounds on the worst-case behavior of the gradient algorithm for the problems under consideration are obtained. As a consequence, a bound on the performance guarantee of the gradient algorithm for the p-median minimization problem in terms of the production and transportation cost matrix is obtained.

Enhanced spatial resolution in fluorescence molecular tomography using restarted L1-regularized nonlinear conjugate gradient algorithm.

PubMed

Shi, Junwei; Liu, Fei; Zhang, Guanglei; Luo, Jianwen; Bai, Jing

2014-04-01

Owing to the high degree of scattering of light through tissues, the ill-posedness of fluorescence molecular tomography (FMT) inverse problem causes relatively low spatial resolution in the reconstruction results. Unlike L2 regularization, L1 regularization can preserve the details and reduce the noise effectively. Reconstruction is obtained through a restarted L1 regularization-based nonlinear conjugate gradient (re-L1-NCG) algorithm, which has been proven to be able to increase the computational speed with low memory consumption. The algorithm consists of inner and outer iterations. In the inner iteration, L1-NCG is used to obtain the L1-regularized results. In the outer iteration, the restarted strategy is used to increase the convergence speed of L1-NCG. To demonstrate the performance of re-L1-NCG in terms of spatial resolution, simulation and physical phantom studies with fluorescent targets located with different edge-to-edge distances were carried out. The reconstruction results show that the re-L1-NCG algorithm has the ability to resolve targets with an edge-to-edge distance of 0.1 cm at a depth of 1.5 cm, which is a significant improvement for FMT.

A real-time MTFC algorithm of space remote-sensing camera based on FPGA

NASA Astrophysics Data System (ADS)

Zhao, Liting; Huang, Gang; Lin, Zhe

2018-01-01

A real-time MTFC algorithm of space remote-sensing camera based on FPGA was designed. The algorithm can provide real-time image processing to enhance image clarity when the remote-sensing camera running on-orbit. The image restoration algorithm adopted modular design. The MTF measurement calculation module on-orbit had the function of calculating the edge extension function, line extension function, ESF difference operation, normalization MTF and MTFC parameters. The MTFC image filtering and noise suppression had the function of filtering algorithm and effectively suppressing the noise. The algorithm used System Generator to design the image processing algorithms to simplify the design structure of system and the process redesign. The image gray gradient dot sharpness edge contrast and median-high frequency were enhanced. The image SNR after recovery reduced less than 1 dB compared to the original image. The image restoration system can be widely used in various fields.

Realization of preconditioned Lanczos and conjugate gradient algorithms on optical linear algebra processors.

PubMed

Ghosh, A

1988-08-01

Lanczos and conjugate gradient algorithms are important in computational linear algebra. In this paper, a parallel pipelined realization of these algorithms on a ring of optical linear algebra processors is described. The flow of data is designed to minimize the idle times of the optical multiprocessor and the redundancy of computations. The effects of optical round-off errors on the solutions obtained by the optical Lanczos and conjugate gradient algorithms are analyzed, and it is shown that optical preconditioning can improve the accuracy of these algorithms substantially. Algorithms for optical preconditioning and results of numerical experiments on solving linear systems of equations arising from partial differential equations are discussed. Since the Lanczos algorithm is used mostly with sparse matrices, a folded storage scheme to represent sparse matrices on spatial light modulators is also described.

Gradient maintenance: A new algorithm for fast online replanning

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

Ahunbay, Ergun E., E-mail: eahunbay@mcw.edu; Li, X. Allen

2015-06-15

Purpose: Clinical use of online adaptive replanning has been hampered by the unpractically long time required to delineate volumes based on the image of the day. The authors propose a new replanning algorithm, named gradient maintenance (GM), which does not require the delineation of organs at risk (OARs), and can enhance automation, drastically reducing planning time and improving consistency and throughput of online replanning. Methods: The proposed GM algorithm is based on the hypothesis that if the dose gradient toward each OAR in daily anatomy can be maintained the same as that in the original plan, the intended plan qualitymore » of the original plan would be preserved in the adaptive plan. The algorithm requires a series of partial concentric rings (PCRs) to be automatically generated around the target toward each OAR on the planning and the daily images. The PCRs are used in the daily optimization objective function. The PCR dose constraints are generated with dose–volume data extracted from the original plan. To demonstrate this idea, GM plans generated using daily images acquired using an in-room CT were compared to regular optimization and image guided radiation therapy repositioning plans for representative prostate and pancreatic cancer cases. Results: The adaptive replanning using the GM algorithm, requiring only the target contour from the CT of the day, can be completed within 5 min without using high-power hardware. The obtained adaptive plans were almost as good as the regular optimization plans and were better than the repositioning plans for the cases studied. Conclusions: The newly proposed GM replanning algorithm, requiring only target delineation, not full delineation of OARs, substantially increased planning speed for online adaptive replanning. The preliminary results indicate that the GM algorithm may be a solution to improve the ability for automation and may be especially suitable for sites with small-to-medium size targets surrounded by several critical structures.« less

Aircraft Detection in High-Resolution SAR Images Based on a Gradient Textural Saliency Map.

PubMed

Tan, Yihua; Li, Qingyun; Li, Yansheng; Tian, Jinwen

2015-09-11

This paper proposes a new automatic and adaptive aircraft target detection algorithm in high-resolution synthetic aperture radar (SAR) images of airport. The proposed method is based on gradient textural saliency map under the contextual cues of apron area. Firstly, the candidate regions with the possible existence of airport are detected from the apron area. Secondly, directional local gradient distribution detector is used to obtain a gradient textural saliency map in the favor of the candidate regions. In addition, the final targets will be detected by segmenting the saliency map using CFAR-type algorithm. The real high-resolution airborne SAR image data is used to verify the proposed algorithm. The results demonstrate that this algorithm can detect aircraft targets quickly and accurately, and decrease the false alarm rate.

A homotopy algorithm for digital optimal projection control GASD-HADOC

NASA Technical Reports Server (NTRS)

Collins, Emmanuel G., Jr.; Richter, Stephen; Davis, Lawrence D.

1993-01-01

The linear-quadratic-gaussian (LQG) compensator was developed to facilitate the design of control laws for multi-input, multi-output (MIMO) systems. The compensator is computed by solving two algebraic equations for which standard closed-loop solutions exist. Unfortunately, the minimal dimension of an LQG compensator is almost always equal to the dimension of the plant and can thus often violate practical implementation constraints on controller order. This deficiency is especially highlighted when considering control-design for high-order systems such as flexible space structures. This deficiency motivated the development of techniques that enable the design of optimal controllers whose dimension is less than that of the design plant. A homotopy approach based on the optimal projection equations that characterize the necessary conditions for optimal reduced-order control. Homotopy algorithms have global convergence properties and hence do not require that the initializing reduced-order controller be close to the optimal reduced-order controller to guarantee convergence. However, the homotopy algorithm previously developed for solving the optimal projection equations has sublinear convergence properties and the convergence slows at higher authority levels and may fail. A new homotopy algorithm for synthesizing optimal reduced-order controllers for discrete-time systems is described. Unlike the previous homotopy approach, the new algorithm is a gradient-based, parameter optimization formulation and was implemented in MATLAB. The results reported may offer the foundation for a reliable approach to optimal, reduced-order controller design.

Conjugate Gradient Algorithms For Manipulator Simulation

NASA Technical Reports Server (NTRS)

Fijany, Amir; Scheid, Robert E.

1991-01-01

Report discusses applicability of conjugate-gradient algorithms to computation of forward dynamics of robotic manipulators. Rapid computation of forward dynamics essential to teleoperation and other advanced robotic applications. Part of continuing effort to find algorithms meeting requirements for increased computational efficiency and speed. Method used for iterative solution of systems of linear equations.

Tomographic reconstruction of tracer gas concentration profiles in a room with the use of a single OP-FTIR and two iterative algorithms: ART and PWLS.

PubMed

Park, D Y; Fessler, J A; Yost, M G; Levine, S P

2000-03-01

Computed tomographic (CT) reconstructions of air contaminant concentration fields were conducted in a room-sized chamber employing a single open-path Fourier transform infrared (OP-FTIR) instrument and a combination of 52 flat mirrors and 4 retroreflectors. A total of 56 beam path data were repeatedly collected for around 1 hr while maintaining a stable concentration gradient. The plane of the room was divided into 195 pixels (13 x 15) for reconstruction. The algebraic reconstruction technique (ART) failed to reconstruct the original concentration gradient patterns for most cases. These poor results were caused by the "highly underdetermined condition" in which the number of unknown values (156 pixels) exceeds that of known data (56 path integral concentrations) in the experimental setting. A new CT algorithm, called the penalized weighted least-squares (PWLS), was applied to remedy this condition. The peak locations were correctly positioned in the PWLS-CT reconstructions. A notable feature of the PWLS-CT reconstructions was a significant reduction of highly irregular noise peaks found in the ART-CT reconstructions. However, the peak heights were slightly reduced in the PWLS-CT reconstructions due to the nature of the PWLS algorithm. PWLS could converge on the original concentration gradient even when a fairly high error was embedded into some experimentally measured path integral concentrations. It was also found in the simulation tests that the PWLS algorithm was very robust with respect to random errors in the path integral concentrations. This beam geometry and the use of a single OP-FTIR scanning system, in combination with the PWLS algorithm, is a system applicable to both environmental and industrial settings.

Tomographic Reconstruction of Tracer Gas Concentration Profiles in a Room with the Use of a Single OP-FTIR and Two Iterative Algorithms: ART and PWLS.

PubMed

Park, Doo Y; Fessier, Jeffrey A; Yost, Michael G; Levine, Steven P

2000-03-01

Computed tomographic (CT) reconstructions of air contaminant concentration fields were conducted in a room-sized chamber employing a single open-path Fourier transform infrared (OP-FTIR) instrument and a combination of 52 flat mirrors and 4 retroreflectors. A total of 56 beam path data were repeatedly collected for around 1 hr while maintaining a stable concentration gradient. The plane of the room was divided into 195 pixels (13 × 15) for reconstruction. The algebraic reconstruction technique (ART) failed to reconstruct the original concentration gradient patterns for most cases. These poor results were caused by the "highly underdetermined condition" in which the number of unknown values (156 pixels) exceeds that of known data (56 path integral concentrations) in the experimental setting. A new CT algorithm, called the penalized weighted least-squares (PWLS), was applied to remedy this condition. The peak locations were correctly positioned in the PWLS-CT reconstructions. A notable feature of the PWLS-CT reconstructions was a significant reduction of highly irregular noise peaks found in the ART-CT reconstructions. However, the peak heights were slightly reduced in the PWLS-CT reconstructions due to the nature of the PWLS algorithm. PWLS could converge on the original concentration gradient even when a fairly high error was embedded into some experimentally measured path integral concentrations. It was also found in the simulation tests that the PWLS algorithm was very robust with respect to random errors in the path integral concentrations. This beam geometry and the use of a single OP-FTIR scanning system, in combination with the PWLS algorithm, is a system applicable to both environmental and industrial settings.

Optimization in Quaternion Dynamic Systems: Gradient, Hessian, and Learning Algorithms.

PubMed

Xu, Dongpo; Xia, Yili; Mandic, Danilo P

2016-02-01

The optimization of real scalar functions of quaternion variables, such as the mean square error or array output power, underpins many practical applications. Solutions typically require the calculation of the gradient and Hessian. However, real functions of quaternion variables are essentially nonanalytic, which are prohibitive to the development of quaternion-valued learning systems. To address this issue, we propose new definitions of quaternion gradient and Hessian, based on the novel generalized Hamilton-real (GHR) calculus, thus making a possible efficient derivation of general optimization algorithms directly in the quaternion field, rather than using the isomorphism with the real domain, as is current practice. In addition, unlike the existing quaternion gradients, the GHR calculus allows for the product and chain rule, and for a one-to-one correspondence of the novel quaternion gradient and Hessian with their real counterparts. Properties of the quaternion gradient and Hessian relevant to numerical applications are also introduced, opening a new avenue of research in quaternion optimization and greatly simplified the derivations of learning algorithms. The proposed GHR calculus is shown to yield the same generic algorithm forms as the corresponding real- and complex-valued algorithms. Advantages of the proposed framework are illuminated over illustrative simulations in quaternion signal processing and neural networks.

Speed and convergence properties of gradient algorithms for optimization of IMRT.

PubMed

Zhang, Xiaodong; Liu, Helen; Wang, Xiaochun; Dong, Lei; Wu, Qiuwen; Mohan, Radhe

2004-05-01

Gradient algorithms are the most commonly employed search methods in the routine optimization of IMRT plans. It is well known that local minima can exist for dose-volume-based and biology-based objective functions. The purpose of this paper is to compare the relative speed of different gradient algorithms, to investigate the strategies for accelerating the optimization process, to assess the validity of these strategies, and to study the convergence properties of these algorithms for dose-volume and biological objective functions. With these aims in mind, we implemented Newton's, conjugate gradient (CG), and the steepest decent (SD) algorithms for dose-volume- and EUD-based objective functions. Our implementation of Newton's algorithm approximates the second derivative matrix (Hessian) by its diagonal. The standard SD algorithm and the CG algorithm with "line minimization" were also implemented. In addition, we investigated the use of a variation of the CG algorithm, called the "scaled conjugate gradient" (SCG) algorithm. To accelerate the optimization process, we investigated the validity of the use of a "hybrid optimization" strategy, in which approximations to calculated dose distributions are used during most of the iterations. Published studies have indicated that getting trapped in local minima is not a significant problem. To investigate this issue further, we first obtained, by trial and error, and starting with uniform intensity distributions, the parameters of the dose-volume- or EUD-based objective functions which produced IMRT plans that satisfied the clinical requirements. Using the resulting optimized intensity distributions as the initial guess, we investigated the possibility of getting trapped in a local minimum. For most of the results presented, we used a lung cancer case. To illustrate the generality of our methods, the results for a prostate case are also presented. For both dose-volume and EUD based objective functions, Newton's method far outperforms other algorithms in terms of speed. The SCG algorithm, which avoids expensive "line minimization," can speed up the standard CG algorithm by at least a factor of 2. For the same initial conditions, all algorithms converge essentially to the same plan. However, we demonstrate that for any of the algorithms studied, starting with previously optimized intensity distributions as the initial guess but for different objective function parameters, the solution frequently gets trapped in local minima. We found that the initial intensity distribution obtained from IMRT optimization utilizing objective function parameters, which favor a specific anatomic structure, would lead to a local minimum corresponding to that structure. Our results indicate that from among the gradient algorithms tested, Newton's method appears to be the fastest by far. Different gradient algorithms have the same convergence properties for dose-volume- and EUD-based objective functions. The hybrid dose calculation strategy is valid and can significantly accelerate the optimization process. The degree of acceleration achieved depends on the type of optimization problem being addressed (e.g., IMRT optimization, intensity modulated beam configuration optimization, or objective function parameter optimization). Under special conditions, gradient algorithms will get trapped in local minima, and reoptimization, starting with the results of previous optimization, will lead to solutions that are generally not significantly different from the local minimum.

Solution of nonlinear multivariable constrained systems using a gradient projection digital algorithm that is insensitive to the initial state

NASA Technical Reports Server (NTRS)

Hargrove, A.

1982-01-01

Optimal digital control of nonlinear multivariable constrained systems was studied. The optimal controller in the form of an algorithm was improved and refined by reducing running time and storage requirements. A particularly difficult system of nine nonlinear state variable equations was chosen as a test problem for analyzing and improving the controller. Lengthy analysis, modeling, computing and optimization were accomplished. A remote interactive teletype terminal was installed. Analysis requiring computer usage of short duration was accomplished using Tuskegee's VAX 11/750 system.

Noise-shaping gradient descent-based online adaptation algorithms for digital calibration of analog circuits.

PubMed

Chakrabartty, Shantanu; Shaga, Ravi K; Aono, Kenji

2013-04-01

Analog circuits that are calibrated using digital-to-analog converters (DACs) use a digital signal processor-based algorithm for real-time adaptation and programming of system parameters. In this paper, we first show that this conventional framework for adaptation yields suboptimal calibration properties because of artifacts introduced by quantization noise. We then propose a novel online stochastic optimization algorithm called noise-shaping or ΣΔ gradient descent, which can shape the quantization noise out of the frequency regions spanning the parameter adaptation trajectories. As a result, the proposed algorithms demonstrate superior parameter search properties compared to floating-point gradient methods and better convergence properties than conventional quantized gradient-methods. In the second part of this paper, we apply the ΣΔ gradient descent algorithm to two examples of real-time digital calibration: 1) balancing and tracking of bias currents, and 2) frequency calibration of a band-pass Gm-C biquad filter biased in weak inversion. For each of these examples, the circuits have been prototyped in a 0.5-μm complementary metal-oxide-semiconductor process, and we demonstrate that the proposed algorithm is able to find the optimal solution even in the presence of spurious local minima, which are introduced by the nonlinear and non-monotonic response of calibration DACs.

A fast, preconditioned conjugate gradient Toeplitz solver

NASA Technical Reports Server (NTRS)

Pan, Victor; Schrieber, Robert

1989-01-01

A simple factorization is given of an arbitrary hermitian, positive definite matrix in which the factors are well-conditioned, hermitian, and positive definite. In fact, given knowledge of the extreme eigenvalues of the original matrix A, an optimal improvement can be achieved, making the condition numbers of each of the two factors equal to the square root of the condition number of A. This technique is to applied to the solution of hermitian, positive definite Toeplitz systems. Large linear systems with hermitian, positive definite Toeplitz matrices arise in some signal processing applications. A stable fast algorithm is given for solving these systems that is based on the preconditioned conjugate gradient method. The algorithm exploits Toeplitz structure to reduce the cost of an iteration to O(n log n) by applying the fast Fourier Transform to compute matrix-vector products. Matrix factorization is used as a preconditioner.

Adaptive control and noise suppression by a variable-gain gradient algorithm

NASA Technical Reports Server (NTRS)

Merhav, S. J.; Mehta, R. S.

1987-01-01

An adaptive control system based on normalized LMS filters is investigated. The finite impulse response of the nonparametric controller is adaptively estimated using a given reference model. Specifically, the following issues are addressed: The stability of the closed loop system is analyzed and heuristically established. Next, the adaptation process is studied for piecewise constant plant parameters. It is shown that by introducing a variable-gain in the gradient algorithm, a substantial reduction in the LMS adaptation rate can be achieved. Finally, process noise at the plant output generally causes a biased estimate of the controller. By introducing a noise suppression scheme, this bias can be substantially reduced and the response of the adapted system becomes very close to that of the reference model. Extensive computer simulations validate these and demonstrate assertions that the system can rapidly adapt to random jumps in plant parameters.

Gradient descent learning algorithm overview: a general dynamical systems perspective.

PubMed

Baldi, P

1995-01-01

Gives a unified treatment of gradient descent learning algorithms for neural networks using a general framework of dynamical systems. This general approach organizes and simplifies all the known algorithms and results which have been originally derived for different problems (fixed point/trajectory learning), for different models (discrete/continuous), for different architectures (forward/recurrent), and using different techniques (backpropagation, variational calculus, adjoint methods, etc.). The general approach can also be applied to derive new algorithms. The author then briefly examines some of the complexity issues and limitations intrinsic to gradient descent learning. Throughout the paper, the author focuses on the problem of trajectory learning.

Gradient gravitational search: An efficient metaheuristic algorithm for global optimization.

PubMed

Dash, Tirtharaj; Sahu, Prabhat K

2015-05-30

The adaptation of novel techniques developed in the field of computational chemistry to solve the concerned problems for large and flexible molecules is taking the center stage with regard to efficient algorithm, computational cost and accuracy. In this article, the gradient-based gravitational search (GGS) algorithm, using analytical gradients for a fast minimization to the next local minimum has been reported. Its efficiency as metaheuristic approach has also been compared with Gradient Tabu Search and others like: Gravitational Search, Cuckoo Search, and Back Tracking Search algorithms for global optimization. Moreover, the GGS approach has also been applied to computational chemistry problems for finding the minimal value potential energy of two-dimensional and three-dimensional off-lattice protein models. The simulation results reveal the relative stability and physical accuracy of protein models with efficient computational cost. © 2015 Wiley Periodicals, Inc.

Aircraft Detection in High-Resolution SAR Images Based on a Gradient Textural Saliency Map

PubMed Central

Tan, Yihua; Li, Qingyun; Li, Yansheng; Tian, Jinwen

2015-01-01

This paper proposes a new automatic and adaptive aircraft target detection algorithm in high-resolution synthetic aperture radar (SAR) images of airport. The proposed method is based on gradient textural saliency map under the contextual cues of apron area. Firstly, the candidate regions with the possible existence of airport are detected from the apron area. Secondly, directional local gradient distribution detector is used to obtain a gradient textural saliency map in the favor of the candidate regions. In addition, the final targets will be detected by segmenting the saliency map using CFAR-type algorithm. The real high-resolution airborne SAR image data is used to verify the proposed algorithm. The results demonstrate that this algorithm can detect aircraft targets quickly and accurately, and decrease the false alarm rate. PMID:26378543

A split finite element algorithm for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.

1979-01-01

An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.

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

Solar collector parameter identification from unsteady data by a discrete-gradient optimization algorithm

NASA Technical Reports Server (NTRS)

Hotchkiss, G. B.; Burmeister, L. C.; Bishop, K. A.

1980-01-01

A discrete-gradient optimization algorithm is used to identify the parameters in a one-node and a two-node capacitance model of a flat-plate collector. Collector parameters are first obtained by a linear-least-squares fit to steady state data. These parameters, together with the collector heat capacitances, are then determined from unsteady data by use of the discrete-gradient optimization algorithm with less than 10 percent deviation from the steady state determination. All data were obtained in the indoor solar simulator at the NASA Lewis Research Center.

Conjugate-Gradient Algorithms For Dynamics Of Manipulators

NASA Technical Reports Server (NTRS)

Fijany, Amir; Scheid, Robert E.

1993-01-01

Algorithms for serial and parallel computation of forward dynamics of multiple-link robotic manipulators by conjugate-gradient method developed. Parallel algorithms have potential for speedup of computations on multiple linked, specialized processors implemented in very-large-scale integrated circuits. Such processors used to stimulate dynamics, possibly faster than in real time, for purposes of planning and control.

A sparsity-based iterative algorithm for reconstruction of micro-CT images from highly undersampled projection datasets obtained with a synchrotron X-ray source

NASA Astrophysics Data System (ADS)

Melli, S. Ali; Wahid, Khan A.; Babyn, Paul; Cooper, David M. L.; Gopi, Varun P.

2016-12-01

Synchrotron X-ray Micro Computed Tomography (Micro-CT) is an imaging technique which is increasingly used for non-invasive in vivo preclinical imaging. However, it often requires a large number of projections from many different angles to reconstruct high-quality images leading to significantly high radiation doses and long scan times. To utilize this imaging technique further for in vivo imaging, we need to design reconstruction algorithms that reduce the radiation dose and scan time without reduction of reconstructed image quality. This research is focused on using a combination of gradient-based Douglas-Rachford splitting and discrete wavelet packet shrinkage image denoising methods to design an algorithm for reconstruction of large-scale reduced-view synchrotron Micro-CT images with acceptable quality metrics. These quality metrics are computed by comparing the reconstructed images with a high-dose reference image reconstructed from 1800 equally spaced projections spanning 180°. Visual and quantitative-based performance assessment of a synthetic head phantom and a femoral cortical bone sample imaged in the biomedical imaging and therapy bending magnet beamline at the Canadian Light Source demonstrates that the proposed algorithm is superior to the existing reconstruction algorithms. Using the proposed reconstruction algorithm to reduce the number of projections in synchrotron Micro-CT is an effective way to reduce the overall radiation dose and scan time which improves in vivo imaging protocols.

Minimizing inner product data dependencies in conjugate gradient iteration

NASA Technical Reports Server (NTRS)

Vanrosendale, J.

1983-01-01

The amount of concurrency available in conjugate gradient iteration is limited by the summations required in the inner product computations. The inner product of two vectors of length N requires time c log(N), if N or more processors are available. This paper describes an algebraic restructuring of the conjugate gradient algorithm which minimizes data dependencies due to inner product calculations. After an initial start up, the new algorithm can perform a conjugate gradient iteration in time c*log(log(N)).

Gradient Evolution-based Support Vector Machine Algorithm for Classification

NASA Astrophysics Data System (ADS)

Zulvia, Ferani E.; Kuo, R. J.

2018-03-01

This paper proposes a classification algorithm based on a support vector machine (SVM) and gradient evolution (GE) algorithms. SVM algorithm has been widely used in classification. However, its result is significantly influenced by the parameters. Therefore, this paper aims to propose an improvement of SVM algorithm which can find the best SVMs’ parameters automatically. The proposed algorithm employs a GE algorithm to automatically determine the SVMs’ parameters. The GE algorithm takes a role as a global optimizer in finding the best parameter which will be used by SVM algorithm. The proposed GE-SVM algorithm is verified using some benchmark datasets and compared with other metaheuristic-based SVM algorithms. The experimental results show that the proposed GE-SVM algorithm obtains better results than other algorithms tested in this paper.

A conjugate gradients/trust regions algorithms for training multilayer perceptrons for nonlinear mapping

NASA Technical Reports Server (NTRS)

Madyastha, Raghavendra K.; Aazhang, Behnaam; Henson, Troy F.; Huxhold, Wendy L.

1992-01-01

This paper addresses the issue of applying a globally convergent optimization algorithm to the training of multilayer perceptrons, a class of Artificial Neural Networks. The multilayer perceptrons are trained towards the solution of two highly nonlinear problems: (1) signal detection in a multi-user communication network, and (2) solving the inverse kinematics for a robotic manipulator. The research is motivated by the fact that a multilayer perceptron is theoretically capable of approximating any nonlinear function to within a specified accuracy. The algorithm that has been employed in this study combines the merits of two well known optimization algorithms, the Conjugate Gradients and the Trust Regions Algorithms. The performance is compared to a widely used algorithm, the Backpropagation Algorithm, that is basically a gradient-based algorithm, and hence, slow in converging. The performances of the two algorithms are compared with the convergence rate. Furthermore, in the case of the signal detection problem, performances are also benchmarked by the decision boundaries drawn as well as the probability of error obtained in either case.

On the usefulness of gradient information in multi-objective deformable image registration using a B-spline-based dual-dynamic transformation model: comparison of three optimization algorithms

NASA Astrophysics Data System (ADS)

Pirpinia, Kleopatra; Bosman, Peter A. N.; Sonke, Jan-Jakob; van Herk, Marcel; Alderliesten, Tanja

2015-03-01

The use of gradient information is well-known to be highly useful in single-objective optimization-based image registration methods. However, its usefulness has not yet been investigated for deformable image registration from a multi-objective optimization perspective. To this end, within a previously introduced multi-objective optimization framework, we use a smooth B-spline-based dual-dynamic transformation model that allows us to derive gradient information analytically, while still being able to account for large deformations. Within the multi-objective framework, we previously employed a powerful evolutionary algorithm (EA) that computes and advances multiple outcomes at once, resulting in a set of solutions (a so-called Pareto front) that represents efficient trade-offs between the objectives. With the addition of the B-spline-based transformation model, we studied the usefulness of gradient information in multiobjective deformable image registration using three different optimization algorithms: the (gradient-less) EA, a gradientonly algorithm, and a hybridization of these two. We evaluated the algorithms to register highly deformed images: 2D MRI slices of the breast in prone and supine positions. Results demonstrate that gradient-based multi-objective optimization significantly speeds up optimization in the initial stages of optimization. However, allowing sufficient computational resources, better results could still be obtained with the EA. Ultimately, the hybrid EA found the best overall approximation of the optimal Pareto front, further indicating that adding gradient-based optimization for multiobjective optimization-based deformable image registration can indeed be beneficial

RES: Regularized Stochastic BFGS Algorithm

NASA Astrophysics Data System (ADS)

Mokhtari, Aryan; Ribeiro, Alejandro

2014-12-01

RES, a regularized stochastic version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method is proposed to solve convex optimization problems with stochastic objectives. The use of stochastic gradient descent algorithms is widespread, but the number of iterations required to approximate optimal arguments can be prohibitive in high dimensional problems. Application of second order methods, on the other hand, is impracticable because computation of objective function Hessian inverses incurs excessive computational cost. BFGS modifies gradient descent by introducing a Hessian approximation matrix computed from finite gradient differences. RES utilizes stochastic gradients in lieu of deterministic gradients for both, the determination of descent directions and the approximation of the objective function's curvature. Since stochastic gradients can be computed at manageable computational cost RES is realizable and retains the convergence rate advantages of its deterministic counterparts. Convergence results show that lower and upper bounds on the Hessian egeinvalues of the sample functions are sufficient to guarantee convergence to optimal arguments. Numerical experiments showcase reductions in convergence time relative to stochastic gradient descent algorithms and non-regularized stochastic versions of BFGS. An application of RES to the implementation of support vector machines is developed.

An algorithm to estimate unsteady and quasi-steady pressure fields from velocity field measurements.

PubMed

Dabiri, John O; Bose, Sanjeeb; Gemmell, Brad J; Colin, Sean P; Costello, John H

2014-02-01

We describe and characterize a method for estimating the pressure field corresponding to velocity field measurements such as those obtained by using particle image velocimetry. The pressure gradient is estimated from a time series of velocity fields for unsteady calculations or from a single velocity field for quasi-steady calculations. The corresponding pressure field is determined based on median polling of several integration paths through the pressure gradient field in order to reduce the effect of measurement errors that accumulate along individual integration paths. Integration paths are restricted to the nodes of the measured velocity field, thereby eliminating the need for measurement interpolation during this step and significantly reducing the computational cost of the algorithm relative to previous approaches. The method is validated by using numerically simulated flow past a stationary, two-dimensional bluff body and a computational model of a three-dimensional, self-propelled anguilliform swimmer to study the effects of spatial and temporal resolution, domain size, signal-to-noise ratio and out-of-plane effects. Particle image velocimetry measurements of a freely swimming jellyfish medusa and a freely swimming lamprey are analyzed using the method to demonstrate the efficacy of the approach when applied to empirical data.

Full Gradient Solution to Adaptive Hybrid Control

NASA Technical Reports Server (NTRS)

Bean, Jacob; Schiller, Noah H.; Fuller, Chris

2017-01-01

This paper focuses on the adaptation mechanisms in adaptive hybrid controllers. Most adaptive hybrid controllers update two filters individually according to the filtered reference least mean squares (FxLMS) algorithm. Because this algorithm was derived for feedforward control, it does not take into account the presence of a feedback loop in the gradient calculation. This paper provides a derivation of the proper weight vector gradient for hybrid (or feedback) controllers that takes into account the presence of feedback. In this formulation, a single weight vector is updated rather than two individually. An internal model structure is assumed for the feedback part of the controller. The full gradient is equivalent to that used in the standard FxLMS algorithm with the addition of a recursive term that is a function of the modeling error. Some simulations are provided to highlight the advantages of using the full gradient in the weight vector update rather than the approximation.

Full Gradient Solution to Adaptive Hybrid Control

NASA Technical Reports Server (NTRS)

Bean, Jacob; Schiller, Noah H.; Fuller, Chris

2016-01-01

This paper focuses on the adaptation mechanisms in adaptive hybrid controllers. Most adaptive hybrid controllers update two filters individually according to the filtered-reference least mean squares (FxLMS) algorithm. Because this algorithm was derived for feedforward control, it does not take into account the presence of a feedback loop in the gradient calculation. This paper provides a derivation of the proper weight vector gradient for hybrid (or feedback) controllers that takes into account the presence of feedback. In this formulation, a single weight vector is updated rather than two individually. An internal model structure is assumed for the feedback part of the controller. The full gradient is equivalent to that used in the standard FxLMS algorithm with the addition of a recursive term that is a function of the modeling error. Some simulations are provided to highlight the advantages of using the full gradient in the weight vector update rather than the approximation.

Multiple objects tracking with HOGs matching in circular windows

NASA Astrophysics Data System (ADS)

Miramontes-Jaramillo, Daniel; Kober, Vitaly; Díaz-Ramírez, Víctor H.

2014-09-01

In recent years tracking applications with development of new technologies like smart TVs, Kinect, Google Glass and Oculus Rift become very important. When tracking uses a matching algorithm, a good prediction algorithm is required to reduce the search area for each object to be tracked as well as processing time. In this work, we analyze the performance of different tracking algorithms based on prediction and matching for a real-time tracking multiple objects. The used matching algorithm utilizes histograms of oriented gradients. It carries out matching in circular windows, and possesses rotation invariance and tolerance to viewpoint and scale changes. The proposed algorithm is implemented in a personal computer with GPU, and its performance is analyzed in terms of processing time in real scenarios. Such implementation takes advantage of current technologies and helps to process video sequences in real-time for tracking several objects at the same time.

Nested Conjugate Gradient Algorithm with Nested Preconditioning for Non-linear Image Restoration.

PubMed

Skariah, Deepak G; Arigovindan, Muthuvel

2017-06-19

We develop a novel optimization algorithm, which we call Nested Non-Linear Conjugate Gradient algorithm (NNCG), for image restoration based on quadratic data fitting and smooth non-quadratic regularization. The algorithm is constructed as a nesting of two conjugate gradient (CG) iterations. The outer iteration is constructed as a preconditioned non-linear CG algorithm; the preconditioning is performed by the inner CG iteration that is linear. The inner CG iteration, which performs preconditioning for outer CG iteration, itself is accelerated by an another FFT based non-iterative preconditioner. We prove that the method converges to a stationary point for both convex and non-convex regularization functionals. We demonstrate experimentally that proposed method outperforms the well-known majorization-minimization method used for convex regularization, and a non-convex inertial-proximal method for non-convex regularization functional.

A gradient based algorithm to solve inverse plane bimodular problems of identification

NASA Astrophysics Data System (ADS)

Ran, Chunjiang; Yang, Haitian; Zhang, Guoqing

2018-02-01

This paper presents a gradient based algorithm to solve inverse plane bimodular problems of identifying constitutive parameters, including tensile/compressive moduli and tensile/compressive Poisson's ratios. For the forward bimodular problem, a FE tangent stiffness matrix is derived facilitating the implementation of gradient based algorithms, for the inverse bimodular problem of identification, a two-level sensitivity analysis based strategy is proposed. Numerical verification in term of accuracy and efficiency is provided, and the impacts of initial guess, number of measurement points, regional inhomogeneity, and noisy data on the identification are taken into accounts.

A novel retinal vessel extraction algorithm based on matched filtering and gradient vector flow

NASA Astrophysics Data System (ADS)

Yu, Lei; Xia, Mingliang; Xuan, Li

2013-10-01

The microvasculature network of retina plays an important role in the study and diagnosis of retinal diseases (age-related macular degeneration and diabetic retinopathy for example). Although it is possible to noninvasively acquire high-resolution retinal images with modern retinal imaging technologies, non-uniform illumination, the low contrast of thin vessels and the background noises all make it difficult for diagnosis. In this paper, we introduce a novel retinal vessel extraction algorithm based on gradient vector flow and matched filtering to segment retinal vessels with different likelihood. Firstly, we use isotropic Gaussian kernel and adaptive histogram equalization to smooth and enhance the retinal images respectively. Secondly, a multi-scale matched filtering method is adopted to extract the retinal vessels. Then, the gradient vector flow algorithm is introduced to locate the edge of the retinal vessels. Finally, we combine the results of matched filtering method and gradient vector flow algorithm to extract the vessels at different likelihood levels. The experiments demonstrate that our algorithm is efficient and the intensities of vessel images exactly represent the likelihood of the vessels.

An historical survey of computational methods in optimal control.

NASA Technical Reports Server (NTRS)

Polak, E.

1973-01-01

Review of some of the salient theoretical developments in the specific area of optimal control algorithms. The first algorithms for optimal control were aimed at unconstrained problems and were derived by using first- and second-variation methods of the calculus of variations. These methods have subsequently been recognized as gradient, Newton-Raphson, or Gauss-Newton methods in function space. A much more recent addition to the arsenal of unconstrained optimal control algorithms are several variations of conjugate-gradient methods. At first, constrained optimal control problems could only be solved by exterior penalty function methods. Later algorithms specifically designed for constrained problems have appeared. Among these are methods for solving the unconstrained linear quadratic regulator problem, as well as certain constrained minimum-time and minimum-energy problems. Differential-dynamic programming was developed from dynamic programming considerations. The conditional-gradient method, the gradient-projection method, and a couple of feasible directions methods were obtained as extensions or adaptations of related algorithms for finite-dimensional problems. Finally, the so-called epsilon-methods combine the Ritz method with penalty function techniques.

An improved conjugate gradient scheme to the solution of least squares SVM.

PubMed

Chu, Wei; Ong, Chong Jin; Keerthi, S Sathiya

2005-03-01

The least square support vector machines (LS-SVM) formulation corresponds to the solution of a linear system of equations. Several approaches to its numerical solutions have been proposed in the literature. In this letter, we propose an improved method to the numerical solution of LS-SVM and show that the problem can be solved using one reduced system of linear equations. Compared with the existing algorithm for LS-SVM, the approach used in this letter is about twice as efficient. Numerical results using the proposed method are provided for comparisons with other existing algorithms.

A projected preconditioned conjugate gradient algorithm for computing many extreme eigenpairs of a Hermitian matrix [A projected preconditioned conjugate gradient algorithm for computing a large eigenspace of a Hermitian matrix

DOE PAGES

Vecharynski, Eugene; Yang, Chao; Pask, John E.

2015-02-25

Here, we present an iterative algorithm for computing an invariant subspace associated with the algebraically smallest eigenvalues of a large sparse or structured Hermitian matrix A. We are interested in the case in which the dimension of the invariant subspace is large (e.g., over several hundreds or thousands) even though it may still be small relative to the dimension of A. These problems arise from, for example, density functional theory (DFT) based electronic structure calculations for complex materials. The key feature of our algorithm is that it performs fewer Rayleigh–Ritz calculations compared to existing algorithms such as the locally optimalmore » block preconditioned conjugate gradient or the Davidson algorithm. It is a block algorithm, and hence can take advantage of efficient BLAS3 operations and be implemented with multiple levels of concurrency. We discuss a number of practical issues that must be addressed in order to implement the algorithm efficiently on a high performance computer.« less

An Efficient Supervised Training Algorithm for Multilayer Spiking Neural Networks

PubMed Central

Xie, Xiurui; Qu, Hong; Liu, Guisong; Zhang, Malu; Kurths, Jürgen

2016-01-01

The spiking neural networks (SNNs) are the third generation of neural networks and perform remarkably well in cognitive tasks such as pattern recognition. The spike emitting and information processing mechanisms found in biological cognitive systems motivate the application of the hierarchical structure and temporal encoding mechanism in spiking neural networks, which have exhibited strong computational capability. However, the hierarchical structure and temporal encoding approach require neurons to process information serially in space and time respectively, which reduce the training efficiency significantly. For training the hierarchical SNNs, most existing methods are based on the traditional back-propagation algorithm, inheriting its drawbacks of the gradient diffusion and the sensitivity on parameters. To keep the powerful computation capability of the hierarchical structure and temporal encoding mechanism, but to overcome the low efficiency of the existing algorithms, a new training algorithm, the Normalized Spiking Error Back Propagation (NSEBP) is proposed in this paper. In the feedforward calculation, the output spike times are calculated by solving the quadratic function in the spike response model instead of detecting postsynaptic voltage states at all time points in traditional algorithms. Besides, in the feedback weight modification, the computational error is propagated to previous layers by the presynaptic spike jitter instead of the gradient decent rule, which realizes the layer-wised training. Furthermore, our algorithm investigates the mathematical relation between the weight variation and voltage error change, which makes the normalization in the weight modification applicable. Adopting these strategies, our algorithm outperforms the traditional SNN multi-layer algorithms in terms of learning efficiency and parameter sensitivity, that are also demonstrated by the comprehensive experimental results in this paper. PMID:27044001

Improved artificial bee colony algorithm for wavefront sensor-less system in free space optical communication

NASA Astrophysics Data System (ADS)

Niu, Chaojun; Han, Xiang'e.

2015-10-01

Adaptive optics (AO) technology is an effective way to alleviate the effect of turbulence on free space optical communication (FSO). A new adaptive compensation method can be used without a wave-front sensor. Artificial bee colony algorithm (ABC) is a population-based heuristic evolutionary algorithm inspired by the intelligent foraging behaviour of the honeybee swarm with the advantage of simple, good convergence rate, robust and less parameter setting. In this paper, we simulate the application of the improved ABC to correct the distorted wavefront and proved its effectiveness. Then we simulate the application of ABC algorithm, differential evolution (DE) algorithm and stochastic parallel gradient descent (SPGD) algorithm to the FSO system and analyze the wavefront correction capabilities by comparison of the coupling efficiency, the error rate and the intensity fluctuation in different turbulence before and after the correction. The results show that the ABC algorithm has much faster correction speed than DE algorithm and better correct ability for strong turbulence than SPGD algorithm. Intensity fluctuation can be effectively reduced in strong turbulence, but not so effective in week turbulence.

ILUBCG2-11: Solution of 11-banded nonsymmetric linear equation systems by a preconditioned biconjugate gradient routine

NASA Astrophysics Data System (ADS)

Chen, Y.-M.; Koniges, A. E.; Anderson, D. V.

1989-10-01

The biconjugate gradient method (BCG) provides an attractive alternative to the usual conjugate gradient algorithms for the solution of sparse systems of linear equations with nonsymmetric and indefinite matrix operators. A preconditioned algorithm is given, whose form resembles the incomplete L-U conjugate gradient scheme (ILUCG2) previously presented. Although the BCG scheme requires the storage of two additional vectors, it converges in a significantly lesser number of iterations (often half), while the number of calculations per iteration remains essentially the same.

Stochastic Models of Polymer Systems

DTIC Science & Technology

2016-01-01

SECURITY CLASSIFICATION OF: The stochastic gradient decent algorithm is the now the "algorithm of choice" for very large machine learning problems...information about the behavior of the algorithm. At the same time, we were also able to formulate various acceleration techniques in precise math terms... gradient decent, REPORT DOCUMENTATION PAGE 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 10. SPONSOR/MONITOR’S ACRONYM(S) ARO 8. PERFORMING

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).

Efficiency of unconstrained minimization techniques in nonlinear analysis

NASA Technical Reports Server (NTRS)

Kamat, M. P.; Knight, N. F., Jr.

1978-01-01

Unconstrained minimization algorithms have been critically evaluated for their effectiveness in solving structural problems involving geometric and material nonlinearities. The algorithms have been categorized as being zeroth, first, or second order depending upon the highest derivative of the function required by the algorithm. The sensitivity of these algorithms to the accuracy of derivatives clearly suggests using analytically derived gradients instead of finite difference approximations. The use of analytic gradients results in better control of the number of minimizations required for convergence to the exact solution.

Gaussian diffusion sinogram inpainting for X-ray CT metal artifact reduction.

PubMed

Peng, Chengtao; Qiu, Bensheng; Li, Ming; Guan, Yihui; Zhang, Cheng; Wu, Zhongyi; Zheng, Jian

2017-01-05

Metal objects implanted in the bodies of patients usually generate severe streaking artifacts in reconstructed images of X-ray computed tomography, which degrade the image quality and affect the diagnosis of disease. Therefore, it is essential to reduce these artifacts to meet the clinical demands. In this work, we propose a Gaussian diffusion sinogram inpainting metal artifact reduction algorithm based on prior images to reduce these artifacts for fan-beam computed tomography reconstruction. In this algorithm, prior information that originated from a tissue-classified prior image is used for the inpainting of metal-corrupted projections, and it is incorporated into a Gaussian diffusion function. The prior knowledge is particularly designed to locate the diffusion position and improve the sparsity of the subtraction sinogram, which is obtained by subtracting the prior sinogram of the metal regions from the original sinogram. The sinogram inpainting algorithm is implemented through an approach of diffusing prior energy and is then solved by gradient descent. The performance of the proposed metal artifact reduction algorithm is compared with two conventional metal artifact reduction algorithms, namely the interpolation metal artifact reduction algorithm and normalized metal artifact reduction algorithm. The experimental datasets used included both simulated and clinical datasets. By evaluating the results subjectively, the proposed metal artifact reduction algorithm causes fewer secondary artifacts than the two conventional metal artifact reduction algorithms, which lead to severe secondary artifacts resulting from impertinent interpolation and normalization. Additionally, the objective evaluation shows the proposed approach has the smallest normalized mean absolute deviation and the highest signal-to-noise ratio, indicating that the proposed method has produced the image with the best quality. No matter for the simulated datasets or the clinical datasets, the proposed algorithm has reduced the metal artifacts apparently.

Registration of PET and CT images based on multiresolution gradient of mutual information demons algorithm for positioning esophageal cancer patients.

PubMed

Jin, Shuo; Li, Dengwang; Wang, Hongjun; Yin, Yong

2013-01-07

Accurate registration of 18F-FDG PET (positron emission tomography) and CT (computed tomography) images has important clinical significance in radiation oncology. PET and CT images are acquired from (18)F-FDG PET/CT scanner, but the two acquisition processes are separate and take a long time. As a result, there are position errors in global and deformable errors in local caused by respiratory movement or organ peristalsis. The purpose of this work was to implement and validate a deformable CT to PET image registration method in esophageal cancer to eventually facilitate accurate positioning the tumor target on CT, and improve the accuracy of radiation therapy. Global registration was firstly utilized to preprocess position errors between PET and CT images, achieving the purpose of aligning these two images on the whole. Demons algorithm, based on optical flow field, has the features of fast process speed and high accuracy, and the gradient of mutual information-based demons (GMI demons) algorithm adds an additional external force based on the gradient of mutual information (GMI) between two images, which is suitable for multimodality images registration. In this paper, GMI demons algorithm was used to achieve local deformable registration of PET and CT images, which can effectively reduce errors between internal organs. In addition, to speed up the registration process, maintain its robustness, and avoid the local extremum, multiresolution image pyramid structure was used before deformable registration. By quantitatively and qualitatively analyzing cases with esophageal cancer, the registration scheme proposed in this paper can improve registration accuracy and speed, which is helpful for precisely positioning tumor target and developing the radiation treatment planning in clinical radiation therapy application.

Registration of PET and CT images based on multiresolution gradient of mutual information demons algorithm for positioning esophageal cancer patients

PubMed Central

Jin, Shuo; Li, Dengwang; Yin, Yong

2013-01-01

Accurate registration of  18F−FDG PET (positron emission tomography) and CT (computed tomography) images has important clinical significance in radiation oncology. PET and CT images are acquired from  18F−FDG PET/CT scanner, but the two acquisition processes are separate and take a long time. As a result, there are position errors in global and deformable errors in local caused by respiratory movement or organ peristalsis. The purpose of this work was to implement and validate a deformable CT to PET image registration method in esophageal cancer to eventually facilitate accurate positioning the tumor target on CT, and improve the accuracy of radiation therapy. Global registration was firstly utilized to preprocess position errors between PET and CT images, achieving the purpose of aligning these two images on the whole. Demons algorithm, based on optical flow field, has the features of fast process speed and high accuracy, and the gradient of mutual information‐based demons (GMI demons) algorithm adds an additional external force based on the gradient of mutual information (GMI) between two images, which is suitable for multimodality images registration. In this paper, GMI demons algorithm was used to achieve local deformable registration of PET and CT images, which can effectively reduce errors between internal organs. In addition, to speed up the registration process, maintain its robustness, and avoid the local extremum, multiresolution image pyramid structure was used before deformable registration. By quantitatively and qualitatively analyzing cases with esophageal cancer, the registration scheme proposed in this paper can improve registration accuracy and speed, which is helpful for precisely positioning tumor target and developing the radiation treatment planning in clinical radiation therapy application. PACS numbers: 87.57.nj, 87.57.Q‐, 87.57.uk PMID:23318381

A hand tracking algorithm with particle filter and improved GVF snake model

NASA Astrophysics Data System (ADS)

Sun, Yi-qi; Wu, Ai-guo; Dong, Na; Shao, Yi-zhe

2017-07-01

To solve the problem that the accurate information of hand cannot be obtained by particle filter, a hand tracking algorithm based on particle filter combined with skin-color adaptive gradient vector flow (GVF) snake model is proposed. Adaptive GVF and skin color adaptive external guidance force are introduced to the traditional GVF snake model, guiding the curve to quickly converge to the deep concave region of hand contour and obtaining the complex hand contour accurately. This algorithm realizes a real-time correction of the particle filter parameters, avoiding the particle drift phenomenon. Experimental results show that the proposed algorithm can reduce the root mean square error of the hand tracking by 53%, and improve the accuracy of hand tracking in the case of complex and moving background, even with a large range of occlusion.

Regional regularization method for ECT based on spectral transformation of Laplacian

NASA Astrophysics Data System (ADS)

Guo, Z. H.; Kan, Z.; Lv, D. C.; Shao, F. Q.

2016-10-01

Image reconstruction in electrical capacitance tomography is an ill-posed inverse problem, and regularization techniques are usually used to solve the problem for suppressing noise. An anisotropic regional regularization algorithm for electrical capacitance tomography is constructed using a novel approach called spectral transformation. Its function is derived and applied to the weighted gradient magnitude of the sensitivity of Laplacian as a regularization term. With the optimum regional regularizer, the a priori knowledge on the local nonlinearity degree of the forward map is incorporated into the proposed online reconstruction algorithm. Simulation experimentations were performed to verify the capability of the new regularization algorithm to reconstruct a superior quality image over two conventional Tikhonov regularization approaches. The advantage of the new algorithm for improving performance and reducing shape distortion is demonstrated with the experimental data.

A biconjugate gradient type algorithm on massively parallel architectures

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Hochbruck, Marlis

1991-01-01

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. Recently, Freund and Nachtigal have proposed a novel BCG type approach, the quasi-minimal residual method (QMR), which overcomes the problems of BCG. Here, an implementation is presented of QMR based on an s-step version of the nonsymmetric look-ahead Lanczos algorithm. The main feature of the s-step Lanczos algorithm is that, in general, all inner products, except for one, can be computed in parallel at the end of each block; this is unlike the other standard Lanczos process where inner products are generated sequentially. The resulting implementation of QMR is particularly attractive on massively parallel SIMD architectures, such as the Connection Machine.

Data-driven gradient algorithm for high-precision quantum control

NASA Astrophysics Data System (ADS)

Wu, Re-Bing; Chu, Bing; Owens, David H.; Rabitz, Herschel

2018-04-01

In the quest to achieve scalable quantum information processing technologies, gradient-based optimal control algorithms (e.g., grape) are broadly used for implementing high-precision quantum gates, but their performance is often hindered by deterministic or random errors in the system model and the control electronics. In this paper, we show that grape can be taught to be more effective by jointly learning from the design model and the experimental data obtained from process tomography. The resulting data-driven gradient optimization algorithm (d-grape) can in principle correct all deterministic gate errors, with a mild efficiency loss. The d-grape algorithm may become more powerful with broadband controls that involve a large number of control parameters, while other algorithms usually slow down due to the increased size of the search space. These advantages are demonstrated by simulating the implementation of a two-qubit controlled-not gate.

Three-dimensional contour edge detection algorithm

NASA Astrophysics Data System (ADS)

Wang, Yizhou; Ong, Sim Heng; Kassim, Ashraf A.; Foong, Kelvin W. C.

2000-06-01

This paper presents a novel algorithm for automatically extracting 3D contour edges, which are points of maximum surface curvature in a surface range image. The 3D image data are represented as a surface polygon mesh. The algorithm transforms the range data, obtained by scanning a dental plaster cast, into a 2D gray scale image by linearly converting the z-value of each vertex to a gray value. The Canny operator is applied to the median-filtered image to obtain the edge pixels and their orientations. A vertex in the 3D object corresponding to the detected edge pixel and its neighbors in the direction of the edge gradient are further analyzed with respect to their n-curvatures to extract the real 3D contour edges. This algorithm provides a fast method of reducing and sorting the unwieldy data inherent in the surface mesh representation. It employs powerful 2D algorithms to extract features from the transformed 3D models and refers to the 3D model for further analysis of selected data. This approach substantially reduces the computational burden without losing accuracy. It is also easily extended to detect 3D landmarks and other geometrical features, thus making it applicable to a wide range of applications.

Algorithm for Training a Recurrent Multilayer Perceptron

NASA Technical Reports Server (NTRS)

Parlos, Alexander G.; Rais, Omar T.; Menon, Sunil K.; Atiya, Amir F.

2004-01-01

An improved algorithm has been devised for training a recurrent multilayer perceptron (RMLP) for optimal performance in predicting the behavior of a complex, dynamic, and noisy system multiple time steps into the future. [An RMLP is a computational neural network with self-feedback and cross-talk (both delayed by one time step) among neurons in hidden layers]. Like other neural-network-training algorithms, this algorithm adjusts network biases and synaptic-connection weights according to a gradient-descent rule. The distinguishing feature of this algorithm is a combination of global feedback (the use of predictions as well as the current output value in computing the gradient at each time step) and recursiveness. The recursive aspect of the algorithm lies in the inclusion of the gradient of predictions at each time step with respect to the predictions at the preceding time step; this recursion enables the RMLP to learn the dynamics. It has been conjectured that carrying the recursion to even earlier time steps would enable the RMLP to represent a noisier, more complex system.

Quantification of susceptibility change at high-concentrated SPIO-labeled target by characteristic phase gradient recognition.

PubMed

Zhu, Haitao; Nie, Binbin; Liu, Hua; Guo, Hua; Demachi, Kazuyuki; Sekino, Masaki; Shan, Baoci

2016-05-01

Phase map cross-correlation detection and quantification may produce highlighted signal at superparamagnetic iron oxide nanoparticles, and distinguish them from other hypointensities. The method may quantify susceptibility change by performing least squares analysis between a theoretically generated magnetic field template and an experimentally scanned phase image. Because characteristic phase recognition requires the removal of phase wrap and phase background, additional steps of phase unwrapping and filtering may increase the chance of computing error and enlarge the inconsistence among algorithms. To solve problem, phase gradient cross-correlation and quantification method is developed by recognizing characteristic phase gradient pattern instead of phase image because phase gradient operation inherently includes unwrapping and filtering functions. However, few studies have mentioned the detectable limit of currently used phase gradient calculation algorithms. The limit may lead to an underestimation of large magnetic susceptibility change caused by high-concentrated iron accumulation. In this study, mathematical derivation points out the value of maximum detectable phase gradient calculated by differential chain algorithm in both spatial and Fourier domain. To break through the limit, a modified quantification method is proposed by using unwrapped forward differentiation for phase gradient generation. The method enlarges the detectable range of phase gradient measurement and avoids the underestimation of magnetic susceptibility. Simulation and phantom experiments were used to quantitatively compare different methods. In vivo application performs MRI scanning on nude mice implanted by iron-labeled human cancer cells. Results validate the limit of detectable phase gradient and the consequent susceptibility underestimation. Results also demonstrate the advantage of unwrapped forward differentiation compared with differential chain algorithms for susceptibility quantification at high-concentrated iron accumulation. Copyright © 2015 Elsevier Inc. All rights reserved.

Multi-GPU Accelerated Admittance Method for High-Resolution Human Exposure Evaluation.

PubMed

Xiong, Zubiao; Feng, Shi; Kautz, Richard; Chandra, Sandeep; Altunyurt, Nevin; Chen, Ji

2015-12-01

A multi-graphics processing unit (GPU) accelerated admittance method solver is presented for solving the induced electric field in high-resolution anatomical models of human body when exposed to external low-frequency magnetic fields. In the solver, the anatomical model is discretized as a three-dimensional network of admittances. The conjugate orthogonal conjugate gradient (COCG) iterative algorithm is employed to take advantage of the symmetric property of the complex-valued linear system of equations. Compared against the widely used biconjugate gradient stabilized method, the COCG algorithm can reduce the solving time by 3.5 times and reduce the storage requirement by about 40%. The iterative algorithm is then accelerated further by using multiple NVIDIA GPUs. The computations and data transfers between GPUs are overlapped in time by using asynchronous concurrent execution design. The communication overhead is well hidden so that the acceleration is nearly linear with the number of GPU cards. Numerical examples show that our GPU implementation running on four NVIDIA Tesla K20c cards can reach 90 times faster than the CPU implementation running on eight CPU cores (two Intel Xeon E5-2603 processors). The implemented solver is able to solve large dimensional problems efficiently. A whole adult body discretized in 1-mm resolution can be solved in just several minutes. The high efficiency achieved makes it practical to investigate human exposure involving a large number of cases with a high resolution that meets the requirements of international dosimetry guidelines.

Multiple-Point Temperature Gradient Algorithm for Ring Laser Gyroscope Bias Compensation

PubMed Central

Li, Geng; Zhang, Pengfei; Wei, Guo; Xie, Yuanping; Yu, Xudong; Long, Xingwu

2015-01-01

To further improve ring laser gyroscope (RLG) bias stability, a multiple-point temperature gradient algorithm is proposed for RLG bias compensation in this paper. Based on the multiple-point temperature measurement system, a complete thermo-image of the RLG block is developed. Combined with the multiple-point temperature gradients between different points of the RLG block, the particle swarm optimization algorithm is used to tune the support vector machine (SVM) parameters, and an optimized design for selecting the thermometer locations is also discussed. The experimental results validate the superiority of the introduced method and enhance the precision and generalizability in the RLG bias compensation model. PMID:26633401

LASER APPLICATIONS AND OTHER TOPICS IN QUANTUM ELECTRONICS: Application of the stochastic parallel gradient descent algorithm for numerical simulation and analysis of the coherent summation of radiation from fibre amplifiers

NASA Astrophysics Data System (ADS)

Zhou, Pu; Wang, Xiaolin; Li, Xiao; Chen, Zilum; Xu, Xiaojun; Liu, Zejin

2009-10-01

Coherent summation of fibre laser beams, which can be scaled to a relatively large number of elements, is simulated by using the stochastic parallel gradient descent (SPGD) algorithm. The applicability of this algorithm for coherent summation is analysed and its optimisaton parameters and bandwidth limitations are studied.

Policy Gradient Adaptive Dynamic Programming for Data-Based Optimal Control.

PubMed

Luo, Biao; Liu, Derong; Wu, Huai-Ning; Wang, Ding; Lewis, Frank L

2017-10-01

The model-free optimal control problem of general discrete-time nonlinear systems is considered in this paper, and a data-based policy gradient adaptive dynamic programming (PGADP) algorithm is developed to design an adaptive optimal controller method. By using offline and online data rather than the mathematical system model, the PGADP algorithm improves control policy with a gradient descent scheme. The convergence of the PGADP algorithm is proved by demonstrating that the constructed Q -function sequence converges to the optimal Q -function. Based on the PGADP algorithm, the adaptive control method is developed with an actor-critic structure and the method of weighted residuals. Its convergence properties are analyzed, where the approximate Q -function converges to its optimum. Computer simulation results demonstrate the effectiveness of the PGADP-based adaptive control method.

Switching neuronal state: optimal stimuli revealed using a stochastically-seeded gradient algorithm.

PubMed

Chang, Joshua; Paydarfar, David

2014-12-01

Inducing a switch in neuronal state using energy optimal stimuli is relevant to a variety of problems in neuroscience. Analytical techniques from optimal control theory can identify such stimuli; however, solutions to the optimization problem using indirect variational approaches can be elusive in models that describe neuronal behavior. Here we develop and apply a direct gradient-based optimization algorithm to find stimulus waveforms that elicit a change in neuronal state while minimizing energy usage. We analyze standard models of neuronal behavior, the Hodgkin-Huxley and FitzHugh-Nagumo models, to show that the gradient-based algorithm: (1) enables automated exploration of a wide solution space, using stochastically generated initial waveforms that converge to multiple locally optimal solutions; and (2) finds optimal stimulus waveforms that achieve a physiological outcome condition, without a priori knowledge of the optimal terminal condition of all state variables. Analysis of biological systems using stochastically-seeded gradient methods can reveal salient dynamical mechanisms underlying the optimal control of system behavior. The gradient algorithm may also have practical applications in future work, for example, finding energy optimal waveforms for therapeutic neural stimulation that minimizes power usage and diminishes off-target effects and damage to neighboring tissue.

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].

Observations on computational methodologies for use in large-scale, gradient-based, multidisciplinary design incorporating advanced CFD codes

NASA Technical Reports Server (NTRS)

Newman, P. A.; Hou, G. J.-W.; Jones, H. E.; Taylor, A. C., III; Korivi, V. M.

1992-01-01

How a combination of various computational methodologies could reduce the enormous computational costs envisioned in using advanced CFD codes in gradient based optimized multidisciplinary design (MdD) procedures is briefly outlined. Implications of these MdD requirements upon advanced CFD codes are somewhat different than those imposed by a single discipline design. A means for satisfying these MdD requirements for gradient information is presented which appear to permit: (1) some leeway in the CFD solution algorithms which can be used; (2) an extension to 3-D problems; and (3) straightforward use of other computational methodologies. Many of these observations have previously been discussed as possibilities for doing parts of the problem more efficiently; the contribution here is observing how they fit together in a mutually beneficial way.

Multigrid one shot methods for optimal control problems: Infinite dimensional control

NASA Technical Reports Server (NTRS)

Arian, Eyal; Taasan, Shlomo

1994-01-01

The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times.

Optical fringe-reflection deflectometry with sparse representation

NASA Astrophysics Data System (ADS)

Xiao, Yong-Liang; Li, Sikun; Zhang, Qican; Zhong, Jianxin; Su, Xianyu; You, Zhisheng

2018-05-01

Optical fringe-reflection deflectometry is a surprisingly attractive scratch detection technique for specular surfaces owing to its unparalleled local sensibility. Full-field surface topography is obtained from a measured normal field using gradient integration. However, there may not be an ideal measured gradient field for deflectometry reconstruction in practice. Both the non-integrability condition and various kinds of image noise distributions, which are present in the indirect measured gradient field, may lead to ambiguity about the scratches on specular surfaces. In order to reduce misjudgment of scratches, sparse representation is introduced into the Southwell curl equation for deflectometry. The curl can be represented as a linear combination of the given redundant dictionary for curl and the sparsest solution for gradient refinement. The non-integrability condition and noise permutation can be overcome with sparse representation for gradient refinement. Numerical simulations demonstrate that the accuracy rate of judgment of scratches can be enhanced with sparse representation compared to the standard least-squares integration. Preliminary experiments are performed with the application of practical measured deflectometric data to verify the validity of the algorithm.

A fast random walk algorithm for computing the pulsed-gradient spin-echo signal in multiscale porous media.

PubMed

Grebenkov, Denis S

2011-02-01

A new method for computing the signal attenuation due to restricted diffusion in a linear magnetic field gradient is proposed. A fast random walk (FRW) algorithm for simulating random trajectories of diffusing spin-bearing particles is combined with gradient encoding. As random moves of a FRW are continuously adapted to local geometrical length scales, the method is efficient for simulating pulsed-gradient spin-echo experiments in hierarchical or multiscale porous media such as concrete, sandstones, sedimentary rocks and, potentially, brain or lungs. Copyright © 2010 Elsevier Inc. All rights reserved.

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

Gradient Optimization for Analytic conTrols - GOAT

NASA Astrophysics Data System (ADS)

Assémat, Elie; Machnes, Shai; Tannor, David; Wilhelm-Mauch, Frank

Quantum optimal control becomes a necessary step in a number of studies in the quantum realm. Recent experimental advances showed that superconducting qubits can be controlled with an impressive accuracy. However, most of the standard optimal control algorithms are not designed to manage such high accuracy. To tackle this issue, a novel quantum optimal control algorithm have been introduced: the Gradient Optimization for Analytic conTrols (GOAT). It avoids the piecewise constant approximation of the control pulse used by standard algorithms. This allows an efficient implementation of very high accuracy optimization. It also includes a novel method to compute the gradient that provides many advantages, e.g. the absence of backpropagation or the natural route to optimize the robustness of the control pulses. This talk will present the GOAT algorithm and a few applications to transmons systems.

Fast gravity, gravity partials, normalized gravity, gravity gradient torque and magnetic field: Derivation, code and data

NASA Technical Reports Server (NTRS)

Gottlieb, Robert G.

1993-01-01

Derivation of first and second partials of the gravitational potential is given in both normalized and unnormalized form. Two different recursion formulas are considered. Derivation of a general gravity gradient torque algorithm which uses the second partial of the gravitational potential is given. Derivation of the geomagnetic field vector is given in a form that closely mimics the gravitational algorithm. Ada code for all algorithms that precomputes all possible data is given. Test cases comparing the new algorithms with previous data are given, as well as speed comparisons showing the relative efficiencies of the new algorithms.

Stereo Image Dense Matching by Integrating Sift and Sgm Algorithm

NASA Astrophysics Data System (ADS)

Zhou, Y.; Song, Y.; Lu, J.

2018-05-01

Semi-global matching(SGM) performs the dynamic programming by treating the different path directions equally. It does not consider the impact of different path directions on cost aggregation, and with the expansion of the disparity search range, the accuracy and efficiency of the algorithm drastically decrease. This paper presents a dense matching algorithm by integrating SIFT and SGM. It takes the successful matching pairs matched by SIFT as control points to direct the path in dynamic programming with truncating error propagation. Besides, matching accuracy can be improved by using the gradient direction of the detected feature points to modify the weights of the paths in different directions. The experimental results based on Middlebury stereo data sets and CE-3 lunar data sets demonstrate that the proposed algorithm can effectively cut off the error propagation, reduce disparity search range and improve matching accuracy.

Numerical optimization in Hilbert space using inexact function and gradient evaluations

NASA Technical Reports Server (NTRS)

Carter, Richard G.

1989-01-01

Trust region algorithms provide a robust iterative technique for solving non-convex unstrained optimization problems, but in many instances it is prohibitively expensive to compute high accuracy function and gradient values for the method. Of particular interest are inverse and parameter estimation problems, since function and gradient evaluations involve numerically solving large systems of differential equations. A global convergence theory is presented for trust region algorithms in which neither function nor gradient values are known exactly. The theory is formulated in a Hilbert space setting so that it can be applied to variational problems as well as the finite dimensional problems normally seen in trust region literature. The conditions concerning allowable error are remarkably relaxed: relative errors in the gradient error condition is automatically satisfied if the error is orthogonal to the gradient approximation. A technique for estimating gradient error and improving the approximation is also presented.

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

A Parallel Particle Swarm Optimization Algorithm Accelerated by Asynchronous Evaluations

NASA Technical Reports Server (NTRS)

Venter, Gerhard; Sobieszczanski-Sobieski, Jaroslaw

2005-01-01

A parallel Particle Swarm Optimization (PSO) algorithm is presented. Particle swarm optimization is a fairly recent addition to the family of non-gradient based, probabilistic search algorithms that is based on a simplified social model and is closely tied to swarming theory. Although PSO algorithms present several attractive properties to the designer, they are plagued by high computational cost as measured by elapsed time. One approach to reduce the elapsed time is to make use of coarse-grained parallelization to evaluate the design points. Previous parallel PSO algorithms were mostly implemented in a synchronous manner, where all design points within a design iteration are evaluated before the next iteration is started. This approach leads to poor parallel speedup in cases where a heterogeneous parallel environment is used and/or where the analysis time depends on the design point being analyzed. This paper introduces an asynchronous parallel PSO algorithm that greatly improves the parallel e ciency. The asynchronous algorithm is benchmarked on a cluster assembled of Apple Macintosh G5 desktop computers, using the multi-disciplinary optimization of a typical transport aircraft wing as an example.

A novel Gravity-FREAK feature extraction and Gravity-KLT tracking registration algorithm based on iPhone MEMS mobile sensor in mobile environment

PubMed Central

Lin, Fan; Xiao, Bin

2017-01-01

Based on the traditional Fast Retina Keypoint (FREAK) feature description algorithm, this paper proposed a Gravity-FREAK feature description algorithm based on Micro-electromechanical Systems (MEMS) sensor to overcome the limited computing performance and memory resources of mobile devices and further improve the reality interaction experience of clients through digital information added to the real world by augmented reality technology. The algorithm takes the gravity projection vector corresponding to the feature point as its feature orientation, which saved the time of calculating the neighborhood gray gradient of each feature point, reduced the cost of calculation and improved the accuracy of feature extraction. In the case of registration method of matching and tracking natural features, the adaptive and generic corner detection based on the Gravity-FREAK matching purification algorithm was used to eliminate abnormal matches, and Gravity Kaneda-Lucas Tracking (KLT) algorithm based on MEMS sensor can be used for the tracking registration of the targets and robustness improvement of tracking registration algorithm under mobile environment. PMID:29088228

A novel Gravity-FREAK feature extraction and Gravity-KLT tracking registration algorithm based on iPhone MEMS mobile sensor in mobile environment.

PubMed

Hong, Zhiling; Lin, Fan; Xiao, Bin

2017-01-01

Based on the traditional Fast Retina Keypoint (FREAK) feature description algorithm, this paper proposed a Gravity-FREAK feature description algorithm based on Micro-electromechanical Systems (MEMS) sensor to overcome the limited computing performance and memory resources of mobile devices and further improve the reality interaction experience of clients through digital information added to the real world by augmented reality technology. The algorithm takes the gravity projection vector corresponding to the feature point as its feature orientation, which saved the time of calculating the neighborhood gray gradient of each feature point, reduced the cost of calculation and improved the accuracy of feature extraction. In the case of registration method of matching and tracking natural features, the adaptive and generic corner detection based on the Gravity-FREAK matching purification algorithm was used to eliminate abnormal matches, and Gravity Kaneda-Lucas Tracking (KLT) algorithm based on MEMS sensor can be used for the tracking registration of the targets and robustness improvement of tracking registration algorithm under mobile environment.

A combined finite element-boundary element formulation for solution of two-dimensional problems via CGFFT

NASA Technical Reports Server (NTRS)

Collins, Jeffery D.; Jin, Jian-Ming; Volakis, John L.

1990-01-01

A method for the computation of electromagnetic scattering from arbitrary two-dimensional bodies is presented. The method combines the finite element and boundary element methods leading to a system for solution via the conjugate gradient Fast Fourier Transform (FFT) algorithm. Two forms of boundaries aimed at reducing the storage requirement of the boundary integral are investigated. It is shown that the boundary integral becomes convolutional when a circular enclosure is chosen, resulting in reduced storage requirement when the system is solved via the conjugate gradient FFT method. The same holds for the ogival enclosure, except that some of the boundary integrals are not convolutional and must be carefully treated to maintain O(N) memory requirement. Results for several circular and ogival structures are presented and shown to be in excellent agreement with those obtained by traditional methods.

Particle swarm optimization-based automatic parameter selection for deep neural networks and its applications in large-scale and high-dimensional data

PubMed Central

2017-01-01

In this paper, we propose a new automatic hyperparameter selection approach for determining the optimal network configuration (network structure and hyperparameters) for deep neural networks using particle swarm optimization (PSO) in combination with a steepest gradient descent algorithm. In the proposed approach, network configurations were coded as a set of real-number m-dimensional vectors as the individuals of the PSO algorithm in the search procedure. During the search procedure, the PSO algorithm is employed to search for optimal network configurations via the particles moving in a finite search space, and the steepest gradient descent algorithm is used to train the DNN classifier with a few training epochs (to find a local optimal solution) during the population evaluation of PSO. After the optimization scheme, the steepest gradient descent algorithm is performed with more epochs and the final solutions (pbest and gbest) of the PSO algorithm to train a final ensemble model and individual DNN classifiers, respectively. The local search ability of the steepest gradient descent algorithm and the global search capabilities of the PSO algorithm are exploited to determine an optimal solution that is close to the global optimum. We constructed several experiments on hand-written characters and biological activity prediction datasets to show that the DNN classifiers trained by the network configurations expressed by the final solutions of the PSO algorithm, employed to construct an ensemble model and individual classifier, outperform the random approach in terms of the generalization performance. Therefore, the proposed approach can be regarded an alternative tool for automatic network structure and parameter selection for deep neural networks. PMID:29236718

Gradient-based Optimization for Poroelastic and Viscoelastic MR Elastography

PubMed Central

Tan, Likun; McGarry, Matthew D.J.; Van Houten, Elijah E.W.; Ji, Ming; Solamen, Ligin; Weaver, John B.

2017-01-01

We describe an efficient gradient computation for solving inverse problems arising in magnetic resonance elastography (MRE). The algorithm can be considered as a generalized ‘adjoint method’ based on a Lagrangian formulation. One requirement for the classic adjoint method is assurance of the self-adjoint property of the stiffness matrix in the elasticity problem. In this paper, we show this property is no longer a necessary condition in our algorithm, but the computational performance can be as efficient as the classic method, which involves only two forward solutions and is independent of the number of parameters to be estimated. The algorithm is developed and implemented in material property reconstructions using poroelastic and viscoelastic modeling. Various gradient- and Hessian-based optimization techniques have been tested on simulation, phantom and in vivo brain data. The numerical results show the feasibility and the efficiency of the proposed scheme for gradient calculation. PMID:27608454

The notion of a plastic material spin in atomistic simulations

NASA Astrophysics Data System (ADS)

Dickel, D.; Tenev, T. G.; Gullett, P.; Horstemeyer, M. F.

2016-12-01

A kinematic algorithm is proposed to extend existing constructions of strain tensors from atomistic data to decouple elastic and plastic contributions to the strain. Elastic and plastic deformation and ultimately the plastic spin, useful quantities in continuum mechanics and finite element simulations, are computed from the full, discrete deformation gradient and an algorithm for the local elastic deformation gradient. This elastic deformation gradient algorithm identifies a crystal type using bond angle analysis (Ackland and Jones 2006 Phys. Rev. B 73 054104) and further exploits the relationship between bond angles to determine the local deformation from an ideal crystal lattice. Full definitions of plastic deformation follow directly using a multiplicative decomposition of the deformation gradient. The results of molecular dynamics simulations of copper in simple shear and torsion are presented to demonstrate the ability of these new discrete measures to describe plastic material spin in atomistic simulation and to compare them with continuum theory.

MO-G-17A-07: Improved Image Quality in Brain F-18 FDG PET Using Penalized-Likelihood Image Reconstruction Via a Generalized Preconditioned Alternating Projection Algorithm: The First Patient Results

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

Schmidtlein, CR; Beattie, B; Humm, J

2014-06-15

Purpose: To investigate the performance of a new penalized-likelihood PET image reconstruction algorithm using the 1{sub 1}-norm total-variation (TV) sum of the 1st through 4th-order gradients as the penalty. Simulated and brain patient data sets were analyzed. Methods: This work represents an extension of the preconditioned alternating projection algorithm (PAPA) for emission-computed tomography. In this new generalized algorithm (GPAPA), the penalty term is expanded to allow multiple components, in this case the sum of the 1st to 4th order gradients, to reduce artificial piece-wise constant regions (“staircase” artifacts typical for TV) seen in PAPA images penalized with only the 1stmore » order gradient. Simulated data were used to test for “staircase” artifacts and to optimize the penalty hyper-parameter in the root-mean-squared error (RMSE) sense. Patient FDG brain scans were acquired on a GE D690 PET/CT (370 MBq at 1-hour post-injection for 10 minutes) in time-of-flight mode and in all cases were reconstructed using resolution recovery projectors. GPAPA images were compared PAPA and RMSE-optimally filtered OSEM (fully converged) in simulations and to clinical OSEM reconstructions (3 iterations, 32 subsets) with 2.6 mm XYGaussian and standard 3-point axial smoothing post-filters. Results: The results from the simulated data show a significant reduction in the 'staircase' artifact for GPAPA compared to PAPA and lower RMSE (up to 35%) compared to optimally filtered OSEM. A simple power-law relationship between the RMSE-optimal hyper-parameters and the noise equivalent counts (NEC) per voxel is revealed. Qualitatively, the patient images appear much sharper and with less noise than standard clinical images. The convergence rate is similar to OSEM. Conclusions: GPAPA reconstructions using the 1{sub 1}-norm total-variation sum of the 1st through 4th-order gradients as the penalty show great promise for the improvement of image quality over that currently achieved with clinical OSEM reconstructions.« less

Numerical experience with a class of algorithms for nonlinear optimization using inexact function and gradient information

NASA Technical Reports Server (NTRS)

Carter, Richard G.

1989-01-01

For optimization problems associated with engineering design, parameter estimation, image reconstruction, and other optimization/simulation applications, low accuracy function and gradient values are frequently much less expensive to obtain than high accuracy values. Here, researchers investigate the computational performance of trust region methods for nonlinear optimization when high accuracy evaluations are unavailable or prohibitively expensive, and confirm earlier theoretical predictions when the algorithm is convergent even with relative gradient errors of 0.5 or more. The proper choice of the amount of accuracy to use in function and gradient evaluations can result in orders-of-magnitude savings in computational cost.

Radiofrequency pulse design using nonlinear gradient magnetic fields.

PubMed

Kopanoglu, Emre; Constable, R Todd

2015-09-01

An iterative k-space trajectory and radiofrequency (RF) pulse design method is proposed for excitation using nonlinear gradient magnetic fields. The spatial encoding functions (SEFs) generated by nonlinear gradient fields are linearly dependent in Cartesian coordinates. Left uncorrected, this may lead to flip angle variations in excitation profiles. In the proposed method, SEFs (k-space samples) are selected using a matching pursuit algorithm, and the RF pulse is designed using a conjugate gradient algorithm. Three variants of the proposed approach are given: the full algorithm, a computationally cheaper version, and a third version for designing spoke-based trajectories. The method is demonstrated for various target excitation profiles using simulations and phantom experiments. The method is compared with other iterative (matching pursuit and conjugate gradient) and noniterative (coordinate-transformation and Jacobian-based) pulse design methods as well as uniform density spiral and EPI trajectories. The results show that the proposed method can increase excitation fidelity. An iterative method for designing k-space trajectories and RF pulses using nonlinear gradient fields is proposed. The method can either be used for selecting the SEFs individually to guide trajectory design, or can be adapted to design and optimize specific trajectories of interest. © 2014 Wiley Periodicals, Inc.

Forward collision warning based on kernelized correlation filters

NASA Astrophysics Data System (ADS)

Pu, Jinchuan; Liu, Jun; Zhao, Yong

2017-07-01

A vehicle detection and tracking system is one of the indispensable methods to reduce the occurrence of traffic accidents. The nearest vehicle is the most likely to cause harm to us. So, this paper will do more research on about the nearest vehicle in the region of interest (ROI). For this system, high accuracy, real-time and intelligence are the basic requirement. In this paper, we set up a system that combines the advanced KCF tracking algorithm with the HaarAdaBoost detection algorithm. The KCF algorithm reduces computation time and increase the speed through the cyclic shift and diagonalization. This algorithm satisfies the real-time requirement. At the same time, Haar features also have the same advantage of simple operation and high speed for detection. The combination of this two algorithm contribute to an obvious improvement of the system running rate comparing with previous works. The detection result of the HaarAdaBoost classifier provides the initial value for the KCF algorithm. This fact optimizes KCF algorithm flaws that manual car marking in the initial phase, which is more scientific and more intelligent. Haar detection and KCF tracking with Histogram of Oriented Gradient (HOG) ensures the accuracy of the system. We evaluate the performance of framework on dataset that were self-collected. The experimental results demonstrate that the proposed method is robust and real-time. The algorithm can effectively adapt to illumination variation, even in the night it can meet the detection and tracking requirements, which is an improvement compared with the previous work.

On a concurrent element-by-element preconditioned conjugate gradient algorithm for multiple load cases

NASA Technical Reports Server (NTRS)

Watson, Brian; Kamat, M. P.

1990-01-01

Element-by-element preconditioned conjugate gradient (EBE-PCG) algorithms have been advocated for use in parallel/vector processing environments as being superior to the conventional LDL(exp T) decomposition algorithm for single load cases. Although there may be some advantages in using such algorithms for a single load case, when it comes to situations involving multiple load cases, the LDL(exp T) decomposition algorithm would appear to be decidedly more cost-effective. The authors have outlined an EBE-PCG algorithm suitable for multiple load cases and compared its effectiveness to the highly efficient LDL(exp T) decomposition scheme. The proposed algorithm offers almost no advantages over the LDL(exp T) algorithm for the linear problems investigated on the Alliant FX/8. However, there may be some merit in the algorithm in solving nonlinear problems with load incrementation, but that remains to be investigated.

Constrained H1-regularization schemes for diffeomorphic image registration

PubMed Central

Mang, Andreas; Biros, George

2017-01-01

We propose regularization schemes for deformable registration and efficient algorithms for their numerical approximation. We treat image registration as a variational optimal control problem. The deformation map is parametrized by its velocity. Tikhonov regularization ensures well-posedness. Our scheme augments standard smoothness regularization operators based on H1- and H2-seminorms with a constraint on the divergence of the velocity field, which resembles variational formulations for Stokes incompressible flows. In our formulation, we invert for a stationary velocity field and a mass source map. This allows us to explicitly control the compressibility of the deformation map and by that the determinant of the deformation gradient. We also introduce a new regularization scheme that allows us to control shear. We use a globalized, preconditioned, matrix-free, reduced space (Gauss–)Newton–Krylov scheme for numerical optimization. We exploit variable elimination techniques to reduce the number of unknowns of our system; we only iterate on the reduced space of the velocity field. Our current implementation is limited to the two-dimensional case. The numerical experiments demonstrate that we can control the determinant of the deformation gradient without compromising registration quality. This additional control allows us to avoid oversmoothing of the deformation map. We also demonstrate that we can promote or penalize shear whilst controlling the determinant of the deformation gradient. PMID:29075361

Precise locating approach of the beacon based on gray gradient segmentation interpolation in satellite optical communications.

PubMed

Wang, Qiang; Liu, Yuefei; Chen, Yiqiang; Ma, Jing; Tan, Liying; Yu, Siyuan

2017-03-01

Accurate location computation for a beacon is an important factor of the reliability of satellite optical communications. However, location precision is generally limited by the resolution of CCD. How to improve the location precision of a beacon is an important and urgent issue. In this paper, we present two precise centroid computation methods for locating a beacon in satellite optical communications. First, in terms of its characteristics, the beacon is divided into several parts according to the gray gradients. Afterward, different numbers of interpolation points and different interpolation methods are applied in the interpolation area; we calculate the centroid position after interpolation and choose the best strategy according to the algorithm. The method is called a "gradient segmentation interpolation approach," or simply, a GSI (gradient segmentation interpolation) algorithm. To take full advantage of the pixels of the beacon's central portion, we also present an improved segmentation square weighting (SSW) algorithm, whose effectiveness is verified by the simulation experiment. Finally, an experiment is established to verify GSI and SSW algorithms. The results indicate that GSI and SSW algorithms can improve locating accuracy over that calculated by a traditional gray centroid method. These approaches help to greatly improve the location precision for a beacon in satellite optical communications.

Gradient descent algorithm applied to wavefront retrieval from through-focus images by an extreme ultraviolet microscope with partially coherent source

DOE PAGES

Yamazoe, Kenji; Mochi, Iacopo; Goldberg, Kenneth A.

2014-12-01

The wavefront retrieval by gradient descent algorithm that is typically applied to coherent or incoherent imaging is extended to retrieve a wavefront from a series of through-focus images by partially coherent illumination. For accurate retrieval, we modeled partial coherence as well as object transmittance into the gradient descent algorithm. However, this modeling increases the computation time due to the complexity of partially coherent imaging simulation that is repeatedly used in the optimization loop. To accelerate the computation, we incorporate not only the Fourier transform but also an eigenfunction decomposition of the image. As a demonstration, the extended algorithm is appliedmore » to retrieve a field-dependent wavefront of a microscope operated at extreme ultraviolet wavelength (13.4 nm). The retrieved wavefront qualitatively matches the expected characteristics of the lens design.« less

Gradient descent algorithm applied to wavefront retrieval from through-focus images by an extreme ultraviolet microscope with partially coherent source

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

Yamazoe, Kenji; Mochi, Iacopo; Goldberg, Kenneth A.

The wavefront retrieval by gradient descent algorithm that is typically applied to coherent or incoherent imaging is extended to retrieve a wavefront from a series of through-focus images by partially coherent illumination. For accurate retrieval, we modeled partial coherence as well as object transmittance into the gradient descent algorithm. However, this modeling increases the computation time due to the complexity of partially coherent imaging simulation that is repeatedly used in the optimization loop. To accelerate the computation, we incorporate not only the Fourier transform but also an eigenfunction decomposition of the image. As a demonstration, the extended algorithm is appliedmore » to retrieve a field-dependent wavefront of a microscope operated at extreme ultraviolet wavelength (13.4 nm). The retrieved wavefront qualitatively matches the expected characteristics of the lens design.« less

Preliminary Structural Design Using Topology Optimization with a Comparison of Results from Gradient and Genetic Algorithm Methods

NASA Technical Reports Server (NTRS)

Burt, Adam O.; Tinker, Michael L.

2014-01-01

In this paper, genetic algorithm based and gradient-based topology optimization is presented in application to a real hardware design problem. Preliminary design of a planetary lander mockup structure is accomplished using these methods that prove to provide major weight savings by addressing the structural efficiency during the design cycle. This paper presents two alternative formulations of the topology optimization problem. The first is the widely-used gradient-based implementation using commercially available algorithms. The second is formulated using genetic algorithms and internally developed capabilities. These two approaches are applied to a practical design problem for hardware that has been built, tested and proven to be functional. Both formulations converged on similar solutions and therefore were proven to be equally valid implementations of the process. This paper discusses both of these formulations at a high level.

A smoothing algorithm using cubic spline functions

NASA Technical Reports Server (NTRS)

Smith, R. E., Jr.; Price, J. M.; Howser, L. M.

1974-01-01

Two algorithms are presented for smoothing arbitrary sets of data. They are the explicit variable algorithm and the parametric variable algorithm. The former would be used where large gradients are not encountered because of the smaller amount of calculation required. The latter would be used if the data being smoothed were double valued or experienced large gradients. Both algorithms use a least-squares technique to obtain a cubic spline fit to the data. The advantage of the spline fit is that the first and second derivatives are continuous. This method is best used in an interactive graphics environment so that the junction values for the spline curve can be manipulated to improve the fit.

Superfast maximum-likelihood reconstruction for quantum tomography

NASA Astrophysics Data System (ADS)

Shang, Jiangwei; Zhang, Zhengyun; Ng, Hui Khoon

2017-06-01

Conventional methods for computing maximum-likelihood estimators (MLE) often converge slowly in practical situations, leading to a search for simplifying methods that rely on additional assumptions for their validity. In this work, we provide a fast and reliable algorithm for maximum-likelihood reconstruction that avoids this slow convergence. Our method utilizes the state-of-the-art convex optimization scheme, an accelerated projected-gradient method, that allows one to accommodate the quantum nature of the problem in a different way than in the standard methods. We demonstrate the power of our approach by comparing its performance with other algorithms for n -qubit state tomography. In particular, an eight-qubit situation that purportedly took weeks of computation time in 2005 can now be completed in under a minute for a single set of data, with far higher accuracy than previously possible. This refutes the common claim that MLE reconstruction is slow and reduces the need for alternative methods that often come with difficult-to-verify assumptions. In fact, recent methods assuming Gaussian statistics or relying on compressed sensing ideas are demonstrably inapplicable for the situation under consideration here. Our algorithm can be applied to general optimization problems over the quantum state space; the philosophy of projected gradients can further be utilized for optimization contexts with general constraints.

Toward an Integrated Framwork for Data-Efficient Parametric Adaptive Detection

DTIC Science & Technology

2012-02-27

any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a ...SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18. NUMBER OF PAGES 19a. NAME OF RESPONSIBLE PERSON a . REPORT...2012-0534 Distribution A - Approved for Public Release The conjugate-gradient (CG) algorithm is investigated for reduced-rank STAP detection. A family

Improvement and implementation for Canny edge detection algorithm

NASA Astrophysics Data System (ADS)

Yang, Tao; Qiu, Yue-hong

2015-07-01

Edge detection is necessary for image segmentation and pattern recognition. In this paper, an improved Canny edge detection approach is proposed due to the defect of traditional algorithm. A modified bilateral filter with a compensation function based on pixel intensity similarity judgment was used to smooth image instead of Gaussian filter, which could preserve edge feature and remove noise effectively. In order to solve the problems of sensitivity to the noise in gradient calculating, the algorithm used 4 directions gradient templates. Finally, Otsu algorithm adaptively obtain the dual-threshold. All of the algorithm simulated with OpenCV 2.4.0 library in the environments of vs2010, and through the experimental analysis, the improved algorithm has been proved to detect edge details more effectively and with more adaptability.

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.

Learning Incoherent Sparse and Low-Rank Patterns from Multiple Tasks

PubMed Central

Chen, Jianhui; Liu, Ji; Ye, Jieping

2013-01-01

We consider the problem of learning incoherent sparse and low-rank patterns from multiple tasks. Our approach is based on a linear multi-task learning formulation, in which the sparse and low-rank patterns are induced by a cardinality regularization term and a low-rank constraint, respectively. This formulation is non-convex; we convert it into its convex surrogate, which can be routinely solved via semidefinite programming for small-size problems. We propose to employ the general projected gradient scheme to efficiently solve such a convex surrogate; however, in the optimization formulation, the objective function is non-differentiable and the feasible domain is non-trivial. We present the procedures for computing the projected gradient and ensuring the global convergence of the projected gradient scheme. The computation of projected gradient involves a constrained optimization problem; we show that the optimal solution to such a problem can be obtained via solving an unconstrained optimization subproblem and an Euclidean projection subproblem. We also present two projected gradient algorithms and analyze their rates of convergence in details. In addition, we illustrate the use of the presented projected gradient algorithms for the proposed multi-task learning formulation using the least squares loss. Experimental results on a collection of real-world data sets demonstrate the effectiveness of the proposed multi-task learning formulation and the efficiency of the proposed projected gradient algorithms. PMID:24077658

Learning Incoherent Sparse and Low-Rank Patterns from Multiple Tasks.

PubMed

Chen, Jianhui; Liu, Ji; Ye, Jieping

2012-02-01

We consider the problem of learning incoherent sparse and low-rank patterns from multiple tasks. Our approach is based on a linear multi-task learning formulation, in which the sparse and low-rank patterns are induced by a cardinality regularization term and a low-rank constraint, respectively. This formulation is non-convex; we convert it into its convex surrogate, which can be routinely solved via semidefinite programming for small-size problems. We propose to employ the general projected gradient scheme to efficiently solve such a convex surrogate; however, in the optimization formulation, the objective function is non-differentiable and the feasible domain is non-trivial. We present the procedures for computing the projected gradient and ensuring the global convergence of the projected gradient scheme. The computation of projected gradient involves a constrained optimization problem; we show that the optimal solution to such a problem can be obtained via solving an unconstrained optimization subproblem and an Euclidean projection subproblem. We also present two projected gradient algorithms and analyze their rates of convergence in details. In addition, we illustrate the use of the presented projected gradient algorithms for the proposed multi-task learning formulation using the least squares loss. Experimental results on a collection of real-world data sets demonstrate the effectiveness of the proposed multi-task learning formulation and the efficiency of the proposed projected gradient algorithms.

Two-step reconstruction method using global optimization and conjugate gradient for ultrasound-guided diffuse optical tomography.

PubMed

Tavakoli, Behnoosh; Zhu, Quing

2013-01-01

Ultrasound-guided diffuse optical tomography (DOT) is a promising method for characterizing malignant and benign lesions in the female breast. We introduce a new two-step algorithm for DOT inversion in which the optical parameters are estimated with the global optimization method, genetic algorithm. The estimation result is applied as an initial guess to the conjugate gradient (CG) optimization method to obtain the absorption and scattering distributions simultaneously. Simulations and phantom experiments have shown that the maximum absorption and reduced scattering coefficients are reconstructed with less than 10% and 25% errors, respectively. This is in contrast with the CG method alone, which generates about 20% error for the absorption coefficient and does not accurately recover the scattering distribution. A new measure of scattering contrast has been introduced to characterize benign and malignant breast lesions. The results of 16 clinical cases reconstructed with the two-step method demonstrates that, on average, the absorption coefficient and scattering contrast of malignant lesions are about 1.8 and 3.32 times higher than the benign cases, respectively.

A hybrid neural network model for noisy data regression.

PubMed

Lee, Eric W M; Lim, Chee Peng; Yuen, Richard K K; Lo, S M

2004-04-01

A hybrid neural network model, based on the fusion of fuzzy adaptive resonance theory (FA ART) and the general regression neural network (GRNN), is proposed in this paper. Both FA and the GRNN are incremental learning systems and are very fast in network training. The proposed hybrid model, denoted as GRNNFA, is able to retain these advantages and, at the same time, to reduce the computational requirements in calculating and storing information of the kernels. A clustering version of the GRNN is designed with data compression by FA for noise removal. An adaptive gradient-based kernel width optimization algorithm has also been devised. Convergence of the gradient descent algorithm can be accelerated by the geometric incremental growth of the updating factor. A series of experiments with four benchmark datasets have been conducted to assess and compare effectiveness of GRNNFA with other approaches. The GRNNFA model is also employed in a novel application task for predicting the evacuation time of patrons at typical karaoke centers in Hong Kong in the event of fire. The results positively demonstrate the applicability of GRNNFA in noisy data regression problems.

RF Pulse Design using Nonlinear Gradient Magnetic Fields

PubMed Central

Kopanoglu, Emre; Constable, R. Todd

2014-01-01

Purpose An iterative k-space trajectory and radio-frequency (RF) pulse design method is proposed for Excitation using Nonlinear Gradient Magnetic fields (ENiGMa). Theory and Methods The spatial encoding functions (SEFs) generated by nonlinear gradient fields (NLGFs) are linearly dependent in Cartesian-coordinates. Left uncorrected, this may lead to flip-angle variations in excitation profiles. In the proposed method, SEFs (k-space samples) are selected using a Matching-Pursuit algorithm, and the RF pulse is designed using a Conjugate-Gradient algorithm. Three variants of the proposed approach are given: the full-algorithm, a computationally-cheaper version, and a third version for designing spoke-based trajectories. The method is demonstrated for various target excitation profiles using simulations and phantom experiments. Results The method is compared to other iterative (Matching-Pursuit and Conjugate Gradient) and non-iterative (coordinate-transformation and Jacobian-based) pulse design methods as well as uniform density spiral and EPI trajectories. The results show that the proposed method can increase excitation fidelity significantly. Conclusion An iterative method for designing k-space trajectories and RF pulses using nonlinear gradient fields is proposed. The method can either be used for selecting the SEFs individually to guide trajectory design, or can be adapted to design and optimize specific trajectories of interest. PMID:25203286

Designing Waveform Sets with Good Correlation and Stopband Properties for MIMO Radar via the Gradient-Based Method

PubMed Central

Tang, Liang; Zhu, Yongfeng; Fu, Qiang

2017-01-01

Waveform sets with good correlation and/or stopband properties have received extensive attention and been widely used in multiple-input multiple-output (MIMO) radar. In this paper, we aim at designing unimodular waveform sets with good correlation and stopband properties. To formulate the problem, we construct two criteria to measure the correlation and stopband properties and then establish an unconstrained problem in the frequency domain. After deducing the phase gradient and the step size, an efficient gradient-based algorithm with monotonicity is proposed to minimize the objective function directly. For the design problem without considering the correlation weights, we develop a simplified algorithm, which only requires a few fast Fourier transform (FFT) operations and is more efficient. Because both of the algorithms can be implemented via the FFT operations and the Hadamard product, they are computationally efficient and can be used to design waveform sets with a large waveform number and waveform length. Numerical experiments show that the proposed algorithms can provide better performance than the state-of-the-art algorithms in terms of the computational complexity. PMID:28468308

Designing Waveform Sets with Good Correlation and Stopband Properties for MIMO Radar via the Gradient-Based Method.

PubMed

Tang, Liang; Zhu, Yongfeng; Fu, Qiang

2017-05-01

Waveform sets with good correlation and/or stopband properties have received extensive attention and been widely used in multiple-input multiple-output (MIMO) radar. In this paper, we aim at designing unimodular waveform sets with good correlation and stopband properties. To formulate the problem, we construct two criteria to measure the correlation and stopband properties and then establish an unconstrained problem in the frequency domain. After deducing the phase gradient and the step size, an efficient gradient-based algorithm with monotonicity is proposed to minimize the objective function directly. For the design problem without considering the correlation weights, we develop a simplified algorithm, which only requires a few fast Fourier transform (FFT) operations and is more efficient. Because both of the algorithms can be implemented via the FFT operations and the Hadamard product, they are computationally efficient and can be used to design waveform sets with a large waveform number and waveform length. Numerical experiments show that the proposed algorithms can provide better performance than the state-of-the-art algorithms in terms of the computational complexity.

2D joint inversion of CSAMT and magnetic data based on cross-gradient theory

NASA Astrophysics Data System (ADS)

Wang, Kun-Peng; Tan, Han-Dong; Wang, Tao

2017-06-01

A two-dimensional forward and backward algorithm for the controlled-source audio-frequency magnetotelluric (CSAMT) method is developed to invert data in the entire region (near, transition, and far) and deal with the effects of artificial sources. First, a regularization factor is introduced in the 2D magnetic inversion, and the magnetic susceptibility is updated in logarithmic form so that the inversion magnetic susceptibility is always positive. Second, the joint inversion of the CSAMT and magnetic methods is completed with the introduction of the cross gradient. By searching for the weight of the cross-gradient term in the objective function, the mutual influence between two different physical properties at different locations are avoided. Model tests show that the joint inversion based on cross-gradient theory offers better results than the single-method inversion. The 2D forward and inverse algorithm for CSAMT with source can effectively deal with artificial sources and ensures the reliability of the final joint inversion algorithm.

Infrared and visible image fusion based on total variation and augmented Lagrangian.

PubMed

Guo, Hanqi; Ma, Yong; Mei, Xiaoguang; Ma, Jiayi

2017-11-01

This paper proposes a new algorithm for infrared and visible image fusion based on gradient transfer that achieves fusion by preserving the intensity of the infrared image and then transferring gradients in the corresponding visible one to the result. The gradient transfer suffers from the problems of low dynamic range and detail loss because it ignores the intensity from the visible image. The new algorithm solves these problems by providing additive intensity from the visible image to balance the intensity between the infrared image and the visible one. It formulates the fusion task as an l 1 -l 1 -TV minimization problem and then employs variable splitting and augmented Lagrangian to convert the unconstrained problem to a constrained one that can be solved in the framework of alternating the multiplier direction method. Experiments demonstrate that the new algorithm achieves better fusion results with a high computation efficiency in both qualitative and quantitative tests than gradient transfer and most state-of-the-art methods.

Longitudinal gradient coils with enhanced radial uniformity in restricted diameter: Single-current and multiple-current approaches.

PubMed

Romero, Javier A; Domínguez, Gabriela A; Anoardo, Esteban

2017-03-01

An important requirement for a gradient coil is that the uniformity of the generated magnetic field gradient should be maximal within the active volume of the coil. For a cylindrical geometry, the radial uniformity of the gradient turns critic, particularly in cases where the gradient-unit has to be designed to fit into the inner bore of a compact magnet of reduced dimensions, like those typically used in fast-field-cycling NMR. In this paper we present two practical solutions aimed to fulfill this requirement. We propose a matrix-inversion optimization algorithm based on the Biot-Savart law, that using a proper cost function, allows maximizing the uniformity of the gradient and power efficiency. The used methodology and the simulation code were validated in a single-current design, by comparing the computer simulated field map with the experimental data measured in a real prototype. After comparing the obtained results with the target field approach, a multiple-element coil driven by independent current sources is discussed, and a real prototype evaluated. Opposed equispaced independent windings are connected in pairs conforming an arrangement of independent anti-Helmholtz units. This last coil seizes 80% of its radial dimension with a gradient uniformity better than 5%. The design also provides an adaptable region of uniformity along with adjustable coil efficiency. Copyright © 2017 Elsevier Inc. All rights reserved.

Research on particle swarm optimization algorithm based on optimal movement probability

NASA Astrophysics Data System (ADS)

Ma, Jianhong; Zhang, Han; He, Baofeng

2017-01-01

The particle swarm optimization algorithm to improve the control precision, and has great application value training neural network and fuzzy system control fields etc.The traditional particle swarm algorithm is used for the training of feed forward neural networks,the search efficiency is low, and easy to fall into local convergence.An improved particle swarm optimization algorithm is proposed based on error back propagation gradient descent. Particle swarm optimization for Solving Least Squares Problems to meme group, the particles in the fitness ranking, optimization problem of the overall consideration, the error back propagation gradient descent training BP neural network, particle to update the velocity and position according to their individual optimal and global optimization, make the particles more to the social optimal learning and less to its optimal learning, it can avoid the particles fall into local optimum, by using gradient information can accelerate the PSO local search ability, improve the multi beam particle swarm depth zero less trajectory information search efficiency, the realization of improved particle swarm optimization algorithm. Simulation results show that the algorithm in the initial stage of rapid convergence to the global optimal solution can be near to the global optimal solution and keep close to the trend, the algorithm has faster convergence speed and search performance in the same running time, it can improve the convergence speed of the algorithm, especially the later search efficiency.

The Möbius domain wall fermion algorithm

NASA Astrophysics Data System (ADS)

Brower, Richard C.; Neff, Harmut; Orginos, Kostas

2017-11-01

We present a review of the properties of generalized domain wall Fermions, based on a (real) Möbius transformation on the Wilson overlap kernel, discussing their algorithmic efficiency, the degree of explicit chiral violations measured by the residual mass (mres) and the Ward-Takahashi identities. The Möbius class interpolates between Shamir's domain wall operator and Boriçi's domain wall implementation of Neuberger's overlap operator without increasing the number of Dirac applications per conjugate gradient iteration. A new scaling parameter (α) reduces chiral violations at finite fifth dimension (Ls) but yields exactly the same overlap action in the limit Ls → ∞. Through the use of 4d Red/Black preconditioning and optimal tuning for the scaling α(Ls) , we show that chiral symmetry violations are typically reduced by an order of magnitude at fixed Ls. We argue that the residual mass for a tuned Möbius algorithm with α = O(1 /Lsγ) for γ < 1 will eventually fall asymptotically as mres = O(1 /Ls1+γ) in the case of a 5D Hamiltonian with out a spectral gap.

Peak Seeking Control for Reduced Fuel Consumption with Preliminary Flight Test Results

NASA Technical Reports Server (NTRS)

Brown, Nelson

2012-01-01

The Environmentally Responsible Aviation project seeks to accomplish the simultaneous reduction of fuel burn, noise, and emissions. A project at NASA Dryden Flight Research Center is contributing to ERAs goals by exploring the practical application of real-time trim configuration optimization for enhanced performance and reduced fuel consumption. This peak-seeking control approach is based on Newton-Raphson algorithm using a time-varying Kalman filter to estimate the gradient of the performance function. In real-time operation, deflection of symmetric ailerons, trailing-edge flaps, and leading-edge flaps of a modified F-18 are directly optimized, and the horizontal stabilators and angle of attack are indirectly optimized. Preliminary results from three research flights are presented herein. The optimization system found a trim configuration that required approximately 3.5% less fuel flow than the baseline trim at the given flight condition. The algorithm consistently rediscovered the solution from several initial conditions. These preliminary results show the algorithm has good performance and is expected to show similar results at other flight conditions and aircraft configurations.

Interpolation bias for the inverse compositional Gauss-Newton algorithm in digital image correlation

NASA Astrophysics Data System (ADS)

Su, Yong; Zhang, Qingchuan; Xu, Xiaohai; Gao, Zeren; Wu, Shangquan

2018-01-01

It is believed that the classic forward additive Newton-Raphson (FA-NR) algorithm and the recently introduced inverse compositional Gauss-Newton (IC-GN) algorithm give rise to roughly equal interpolation bias. Questioning the correctness of this statement, this paper presents a thorough analysis of interpolation bias for the IC-GN algorithm. A theoretical model is built to analytically characterize the dependence of interpolation bias upon speckle image, target image interpolation, and reference image gradient estimation. The interpolation biases of the FA-NR algorithm and the IC-GN algorithm can be significantly different, whose relative difference can exceed 80%. For the IC-GN algorithm, the gradient estimator can strongly affect the interpolation bias; the relative difference can reach 178%. Since the mean bias errors are insensitive to image noise, the theoretical model proposed remains valid in the presence of noise. To provide more implementation details, source codes are uploaded as a supplement.

A novel highly parallel algorithm for linearly unmixing hyperspectral images

NASA Astrophysics Data System (ADS)

Guerra, Raúl; López, Sebastián.; Callico, Gustavo M.; López, Jose F.; Sarmiento, Roberto

2014-10-01

Endmember extraction and abundances calculation represent critical steps within the process of linearly unmixing a given hyperspectral image because of two main reasons. The first one is due to the need of computing a set of accurate endmembers in order to further obtain confident abundance maps. The second one refers to the huge amount of operations involved in these time-consuming processes. This work proposes an algorithm to estimate the endmembers of a hyperspectral image under analysis and its abundances at the same time. The main advantage of this algorithm is its high parallelization degree and the mathematical simplicity of the operations implemented. This algorithm estimates the endmembers as virtual pixels. In particular, the proposed algorithm performs the descent gradient method to iteratively refine the endmembers and the abundances, reducing the mean square error, according with the linear unmixing model. Some mathematical restrictions must be added so the method converges in a unique and realistic solution. According with the algorithm nature, these restrictions can be easily implemented. The results obtained with synthetic images demonstrate the well behavior of the algorithm proposed. Moreover, the results obtained with the well-known Cuprite dataset also corroborate the benefits of our proposal.

Equilibrium Propagation: Bridging the Gap between Energy-Based Models and Backpropagation

PubMed Central

Scellier, Benjamin; Bengio, Yoshua

2017-01-01

We introduce Equilibrium Propagation, a learning framework for energy-based models. It involves only one kind of neural computation, performed in both the first phase (when the prediction is made) and the second phase of training (after the target or prediction error is revealed). Although this algorithm computes the gradient of an objective function just like Backpropagation, it does not need a special computation or circuit for the second phase, where errors are implicitly propagated. Equilibrium Propagation shares similarities with Contrastive Hebbian Learning and Contrastive Divergence while solving the theoretical issues of both algorithms: our algorithm computes the gradient of a well-defined objective function. Because the objective function is defined in terms of local perturbations, the second phase of Equilibrium Propagation corresponds to only nudging the prediction (fixed point or stationary distribution) toward a configuration that reduces prediction error. In the case of a recurrent multi-layer supervised network, the output units are slightly nudged toward their target in the second phase, and the perturbation introduced at the output layer propagates backward in the hidden layers. We show that the signal “back-propagated” during this second phase corresponds to the propagation of error derivatives and encodes the gradient of the objective function, when the synaptic update corresponds to a standard form of spike-timing dependent plasticity. This work makes it more plausible that a mechanism similar to Backpropagation could be implemented by brains, since leaky integrator neural computation performs both inference and error back-propagation in our model. The only local difference between the two phases is whether synaptic changes are allowed or not. We also show experimentally that multi-layer recurrently connected networks with 1, 2, and 3 hidden layers can be trained by Equilibrium Propagation on the permutation-invariant MNIST task. PMID:28522969

The performance of monotonic and new non-monotonic gradient ascent reconstruction algorithms for high-resolution neuroreceptor PET imaging.

PubMed

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

2011-07-07

Iterative expectation maximization (EM) techniques have been extensively used to solve maximum likelihood (ML) problems in positron emission tomography (PET) image reconstruction. Although EM methods offer a robust approach to solving ML problems, they usually suffer from slow convergence rates. The ordered subsets EM (OSEM) algorithm provides significant improvements in the convergence rate, but it can cycle between estimates converging towards the ML solution of each subset. In contrast, gradient-based methods, such as the recently proposed non-monotonic maximum likelihood (NMML) and the more established preconditioned conjugate gradient (PCG), offer a globally convergent, yet equally fast, alternative to OSEM. Reported results showed that NMML provides faster convergence compared to OSEM; however, it has never been compared to other fast gradient-based methods, like PCG. Therefore, in this work we evaluate the performance of two gradient-based methods (NMML and PCG) and investigate their potential as an alternative to the fast and widely used OSEM. All algorithms were evaluated using 2D simulations, as well as a single [(11)C]DASB clinical brain dataset. Results on simulated 2D data show that both PCG and NMML achieve orders of magnitude faster convergence to the ML solution compared to MLEM and exhibit comparable performance to OSEM. Equally fast performance is observed between OSEM and PCG for clinical 3D data, but NMML seems to perform poorly. However, with the addition of a preconditioner term to the gradient direction, the convergence behaviour of NMML can be substantially improved. Although PCG is a fast convergent algorithm, the use of a (bent) line search increases the complexity of the implementation, as well as the computational time involved per iteration. Contrary to previous reports, NMML offers no clear advantage over OSEM or PCG, for noisy PET data. Therefore, we conclude that there is little evidence to replace OSEM as the algorithm of choice for many applications, especially given that in practice convergence is often not desired for algorithms seeking ML estimates.

A Gradient-Based Multistart Algorithm for Multimodal Aerodynamic Shape Optimization Problems Based on Free-Form Deformation

NASA Astrophysics Data System (ADS)

Streuber, Gregg Mitchell

Environmental and economic factors motivate the pursuit of more fuel-efficient aircraft designs. Aerodynamic shape optimization is a powerful tool in this effort, but is hampered by the presence of multimodality in many design spaces. Gradient-based multistart optimization uses a sampling algorithm and multiple parallel optimizations to reliably apply fast gradient-based optimization to moderately multimodal problems. Ensuring that the sampled geometries remain physically realizable requires manually developing specialized linear constraints for each class of problem. Utilizing free-form deformation geometry control allows these linear constraints to be written in a geometry-independent fashion, greatly easing the process of applying the algorithm to new problems. This algorithm was used to assess the presence of multimodality when optimizing a wing in subsonic and transonic flows, under inviscid and viscous conditions, and a blended wing-body under transonic, viscous conditions. Multimodality was present in every wing case, while the blended wing-body was found to be generally unimodal.

WE-AB-209-06: Dynamic Collimator Trajectory Algorithm for Use in VMAT Treatment Deliveries

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

MacDonald, L; Thomas, C; Syme, A

2016-06-15

Purpose: To develop advanced dynamic collimator positioning algorithms for optimal beam’s-eye-view (BEV) fitting of targets in VMAT procedures, including multiple metastases stereotactic radiosurgery procedures. Methods: A trajectory algorithm was developed, which can dynamically modify the angle of the collimator as a function of VMAT control point to provide optimized collimation of target volume(s). Central to this algorithm is a concept denoted “whitespace”, defined as area within the jaw-defined BEV field, outside of the PTV, and not shielded by the MLC when fit to the PTV. Calculating whitespace at all collimator angles and every control point, a two-dimensional topographical map depictingmore » the tightness-of-fit of the MLC was generated. A variety of novel searching algorithms identified a number of candidate trajectories of continuous collimator motion. Ranking these candidate trajectories according to their accrued whitespace value produced an optimal solution for navigation of this map. Results: All trajectories were normalized to minimum possible (i.e. calculated without consideration of collimator motion constraints) accrued whitespace. On an acoustic neuroma case, a random walk algorithm generated a trajectory with 151% whitespace; random walk including a mandatory anchor point improved this to 148%; gradient search produced a trajectory with 137%; and bi-directional gradient search generated a trajectory with 130% whitespace. For comparison, a fixed collimator angle of 30° and 330° accumulated 272% and 228% of whitespace, respectively. The algorithm was tested on a clinical case with two metastases (single isocentre) and identified collimator angles that allow for simultaneous irradiation of the PTVs while minimizing normal tissue irradiation. Conclusion: Dynamic collimator trajectories have the potential to improve VMAT deliveries through increased efficiency and reduced normal tissue dose, especially in treatment of multiple cranial metastases, without significant safety concerns that hinder immediate clinical implementation.« less

Inverse regression-based uncertainty quantification algorithms for high-dimensional models: Theory and practice

NASA Astrophysics Data System (ADS)

Li, Weixuan; Lin, Guang; Li, Bing

2016-09-01

Many uncertainty quantification (UQ) approaches suffer from the curse of dimensionality, that is, their computational costs become intractable for problems involving a large number of uncertainty parameters. In these situations, the classic Monte Carlo often remains the preferred method of choice because its convergence rate O (n - 1 / 2), where n is the required number of model simulations, does not depend on the dimension of the problem. However, many high-dimensional UQ problems are intrinsically low-dimensional, because the variation of the quantity of interest (QoI) is often caused by only a few latent parameters varying within a low-dimensional subspace, known as the sufficient dimension reduction (SDR) subspace in the statistics literature. Motivated by this observation, we propose two inverse regression-based UQ algorithms (IRUQ) for high-dimensional problems. Both algorithms use inverse regression to convert the original high-dimensional problem to a low-dimensional one, which is then efficiently solved by building a response surface for the reduced model, for example via the polynomial chaos expansion. The first algorithm, which is for the situations where an exact SDR subspace exists, is proved to converge at rate O (n-1), hence much faster than MC. The second algorithm, which doesn't require an exact SDR, employs the reduced model as a control variate to reduce the error of the MC estimate. The accuracy gain could still be significant, depending on how well the reduced model approximates the original high-dimensional one. IRUQ also provides several additional practical advantages: it is non-intrusive; it does not require computing the high-dimensional gradient of the QoI; and it reports an error bar so the user knows how reliable the result is.

Non-preconditioned conjugate gradient on cell and FPGA based hybrid supercomputer nodes

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

Dubois, David H; Dubois, Andrew J; Boorman, Thomas M

2009-01-01

This work presents a detailed implementation of a double precision, non-preconditioned, Conjugate Gradient algorithm on a Roadrunner heterogeneous supercomputer node. These nodes utilize the Cell Broadband Engine Architecture{sup TM} in conjunction with x86 Opteron{sup TM} processors from AMD. We implement a common Conjugate Gradient algorithm, on a variety of systems, to compare and contrast performance. Implementation results are presented for the Roadrunner hybrid supercomputer, SRC Computers, Inc. MAPStation SRC-6 FPGA enhanced hybrid supercomputer, and AMD Opteron only. In all hybrid implementations wall clock time is measured, including all transfer overhead and compute timings.

Non-preconditioned conjugate gradient on cell and FPCA-based hybrid supercomputer nodes

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

Dubois, David H; Dubois, Andrew J; Boorman, Thomas M

2009-03-10

This work presents a detailed implementation of a double precision, Non-Preconditioned, Conjugate Gradient algorithm on a Roadrunner heterogeneous supercomputer node. These nodes utilize the Cell Broadband Engine Architecture{trademark} in conjunction with x86 Opteron{trademark} processors from AMD. We implement a common Conjugate Gradient algorithm, on a variety of systems, to compare and contrast performance. Implementation results are presented for the Roadrunner hybrid supercomputer, SRC Computers, Inc. MAPStation SRC-6 FPGA enhanced hybrid supercomputer, and AMD Opteron only. In all hybrid implementations wall clock time is measured, including all transfer overhead and compute timings.

Automatic extraction of planetary image features

NASA Technical Reports Server (NTRS)

LeMoigne-Stewart, Jacqueline J. (Inventor); Troglio, Giulia (Inventor); Benediktsson, Jon A. (Inventor); Serpico, Sebastiano B. (Inventor); Moser, Gabriele (Inventor)

2013-01-01

A method for the extraction of Lunar data and/or planetary features is provided. The feature extraction method can include one or more image processing techniques, including, but not limited to, a watershed segmentation and/or the generalized Hough Transform. According to some embodiments, the feature extraction method can include extracting features, such as, small rocks. According to some embodiments, small rocks can be extracted by applying a watershed segmentation algorithm to the Canny gradient. According to some embodiments, applying a watershed segmentation algorithm to the Canny gradient can allow regions that appear as close contours in the gradient to be segmented.

Filtering Based Adaptive Visual Odometry Sensor Framework Robust to Blurred Images

PubMed Central

Zhao, Haiying; Liu, Yong; Xie, Xiaojia; Liao, Yiyi; Liu, Xixi

2016-01-01

Visual odometry (VO) estimation from blurred image is a challenging problem in practical robot applications, and the blurred images will severely reduce the estimation accuracy of the VO. In this paper, we address the problem of visual odometry estimation from blurred images, and present an adaptive visual odometry estimation framework robust to blurred images. Our approach employs an objective measure of images, named small image gradient distribution (SIGD), to evaluate the blurring degree of the image, then an adaptive blurred image classification algorithm is proposed to recognize the blurred images, finally we propose an anti-blurred key-frame selection algorithm to enable the VO robust to blurred images. We also carried out varied comparable experiments to evaluate the performance of the VO algorithms with our anti-blur framework under varied blurred images, and the experimental results show that our approach can achieve superior performance comparing to the state-of-the-art methods under the condition with blurred images while not increasing too much computation cost to the original VO algorithms. PMID:27399704

Large-Scale Optimization for Bayesian Inference in Complex Systems

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

Willcox, Karen; Marzouk, Youssef

2013-11-12

The SAGUARO (Scalable Algorithms for Groundwater Uncertainty Analysis and Robust Optimization) Project focused on the development of scalable numerical algorithms for large-scale Bayesian inversion in complex systems that capitalize on advances in large-scale simulation-based optimization and inversion methods. The project was a collaborative effort among MIT, the University of Texas at Austin, Georgia Institute of Technology, and Sandia National Laboratories. The research was directed in three complementary areas: efficient approximations of the Hessian operator, reductions in complexity of forward simulations via stochastic spectral approximations and model reduction, and employing large-scale optimization concepts to accelerate sampling. The MIT--Sandia component of themore » SAGUARO Project addressed the intractability of conventional sampling methods for large-scale statistical inverse problems by devising reduced-order models that are faithful to the full-order model over a wide range of parameter values; sampling then employs the reduced model rather than the full model, resulting in very large computational savings. Results indicate little effect on the computed posterior distribution. On the other hand, in the Texas--Georgia Tech component of the project, we retain the full-order model, but exploit inverse problem structure (adjoint-based gradients and partial Hessian information of the parameter-to-observation map) to implicitly extract lower dimensional information on the posterior distribution; this greatly speeds up sampling methods, so that fewer sampling points are needed. We can think of these two approaches as ``reduce then sample'' and ``sample then reduce.'' In fact, these two approaches are complementary, and can be used in conjunction with each other. Moreover, they both exploit deterministic inverse problem structure, in the form of adjoint-based gradient and Hessian information of the underlying parameter-to-observation map, to achieve their speedups.« less

Final Report: Large-Scale Optimization for Bayesian Inference in Complex Systems

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

Ghattas, Omar

2013-10-15

The SAGUARO (Scalable Algorithms for Groundwater Uncertainty Analysis and Robust Optimiza- tion) Project focuses on the development of scalable numerical algorithms for large-scale Bayesian inversion in complex systems that capitalize on advances in large-scale simulation-based optimiza- tion and inversion methods. Our research is directed in three complementary areas: efficient approximations of the Hessian operator, reductions in complexity of forward simulations via stochastic spectral approximations and model reduction, and employing large-scale optimization concepts to accelerate sampling. Our efforts are integrated in the context of a challenging testbed problem that considers subsurface reacting flow and transport. The MIT component of the SAGUAROmore » Project addresses the intractability of conventional sampling methods for large-scale statistical inverse problems by devising reduced-order models that are faithful to the full-order model over a wide range of parameter values; sampling then employs the reduced model rather than the full model, resulting in very large computational savings. Results indicate little effect on the computed posterior distribution. On the other hand, in the Texas-Georgia Tech component of the project, we retain the full-order model, but exploit inverse problem structure (adjoint-based gradients and partial Hessian information of the parameter-to- observation map) to implicitly extract lower dimensional information on the posterior distribution; this greatly speeds up sampling methods, so that fewer sampling points are needed. We can think of these two approaches as "reduce then sample" and "sample then reduce." In fact, these two approaches are complementary, and can be used in conjunction with each other. Moreover, they both exploit deterministic inverse problem structure, in the form of adjoint-based gradient and Hessian information of the underlying parameter-to-observation map, to achieve their speedups.« less

A PDE Sensitivity Equation Method for Optimal Aerodynamic Design

NASA Technical Reports Server (NTRS)

Borggaard, Jeff; Burns, John

1996-01-01

The use of gradient based optimization algorithms in inverse design is well established as a practical approach to aerodynamic design. A typical procedure uses a simulation scheme to evaluate the objective function (from the approximate states) and its gradient, then passes this information to an optimization algorithm. Once the simulation scheme (CFD flow solver) has been selected and used to provide approximate function evaluations, there are several possible approaches to the problem of computing gradients. One popular method is to differentiate the simulation scheme and compute design sensitivities that are then used to obtain gradients. Although this black-box approach has many advantages in shape optimization problems, one must compute mesh sensitivities in order to compute the design sensitivity. In this paper, we present an alternative approach using the PDE sensitivity equation to develop algorithms for computing gradients. This approach has the advantage that mesh sensitivities need not be computed. Moreover, when it is possible to use the CFD scheme for both the forward problem and the sensitivity equation, then there are computational advantages. An apparent disadvantage of this approach is that it does not always produce consistent derivatives. However, for a proper combination of discretization schemes, one can show asymptotic consistency under mesh refinement, which is often sufficient to guarantee convergence of the optimal design algorithm. In particular, we show that when asymptotically consistent schemes are combined with a trust-region optimization algorithm, the resulting optimal design method converges. We denote this approach as the sensitivity equation method. The sensitivity equation method is presented, convergence results are given and the approach is illustrated on two optimal design problems involving shocks.

Convex Optimization over Classes of Multiparticle Entanglement

NASA Astrophysics Data System (ADS)

Shang, Jiangwei; Gühne, Otfried

2018-02-01

A well-known strategy to characterize multiparticle entanglement utilizes the notion of stochastic local operations and classical communication (SLOCC), but characterizing the resulting entanglement classes is difficult. Given a multiparticle quantum state, we first show that Gilbert's algorithm can be adapted to prove separability or membership in a certain entanglement class. We then present two algorithms for convex optimization over SLOCC classes. The first algorithm uses a simple gradient approach, while the other one employs the accelerated projected-gradient method. For demonstration, the algorithms are applied to the likelihood-ratio test using experimental data on bound entanglement of a noisy four-photon Smolin state [Phys. Rev. Lett. 105, 130501 (2010), 10.1103/PhysRevLett.105.130501].

A new edge detection algorithm based on Canny idea

NASA Astrophysics Data System (ADS)

Feng, Yingke; Zhang, Jinmin; Wang, Siming

2017-10-01

The traditional Canny algorithm has poor self-adaptability threshold, and it is more sensitive to noise. In order to overcome these drawbacks, this paper proposed a new edge detection method based on Canny algorithm. Firstly, the media filtering and filtering based on the method of Euclidean distance are adopted to process it; secondly using the Frei-chen algorithm to calculate gradient amplitude; finally, using the Otsu algorithm to calculate partial gradient amplitude operation to get images of thresholds value, then find the average of all thresholds that had been calculated, half of the average is high threshold value, and the half of the high threshold value is low threshold value. Experiment results show that this new method can effectively suppress noise disturbance, keep the edge information, and also improve the edge detection accuracy.

[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.

2.5D complex resistivity modeling and inversion using unstructured grids

NASA Astrophysics Data System (ADS)

Xu, Kaijun; Sun, Jie

2016-04-01

The characteristic of complex resistivity on rock and ore has been recognized by people for a long time. Generally we have used the Cole-Cole Model(CCM) to describe complex resistivity. It has been proved that the electrical anomaly of geologic body can be quantitative estimated by CCM parameters such as direct resistivity(ρ0), chargeability(m), time constant(τ) and frequency dependence(c). Thus it is very important to obtain the complex parameters of geologic body. It is difficult to approximate complex structures and terrain using traditional rectangular grid. In order to enhance the numerical accuracy and rationality of modeling and inversion, we use an adaptive finite-element algorithm for forward modeling of the frequency-domain 2.5D complex resistivity and implement the conjugate gradient algorithm in the inversion of 2.5D complex resistivity. An adaptive finite element method is applied for solving the 2.5D complex resistivity forward modeling of horizontal electric dipole source. First of all, the CCM is introduced into the Maxwell's equations to calculate the complex resistivity electromagnetic fields. Next, the pseudo delta function is used to distribute electric dipole source. Then the electromagnetic fields can be expressed in terms of the primary fields caused by layered structure and the secondary fields caused by inhomogeneities anomalous conductivity. At last, we calculated the electromagnetic fields response of complex geoelectric structures such as anticline, syncline, fault. The modeling results show that adaptive finite-element methods can automatically improve mesh generation and simulate complex geoelectric models using unstructured grids. The 2.5D complex resistivity invertion is implemented based the conjugate gradient algorithm.The conjugate gradient algorithm doesn't need to compute the sensitivity matrix but directly computes the sensitivity matrix or its transpose multiplying vector. In addition, the inversion target zones are segmented with fine grids and the background zones are segmented with big grid, the method can reduce the grid amounts of inversion, it is very helpful to improve the computational efficiency. The inversion results verify the validity and stability of conjugate gradient inversion algorithm. The results of theoretical calculation indicate that the modeling and inversion of 2.5D complex resistivity using unstructured grids are feasible. Using unstructured grids can improve the accuracy of modeling, but the large number of grids inversion is extremely time-consuming, so the parallel computation for the inversion is necessary. Acknowledgments: We thank to the support of the National Natural Science Foundation of China(41304094).

Vehicle tracking using fuzzy-based vehicle detection window with adaptive parameters

NASA Astrophysics Data System (ADS)

Chitsobhuk, Orachat; Kasemsiri, Watjanapong; Glomglome, Sorayut; Lapamonpinyo, Pipatphon

2018-04-01

In this paper, fuzzy-based vehicle tracking system is proposed. The proposed system consists of two main processes: vehicle detection and vehicle tracking. In the first process, the Gradient-based Adaptive Threshold Estimation (GATE) algorithm is adopted to provide the suitable threshold value for the sobel edge detection. The estimated threshold can be adapted to the changes of diverse illumination conditions throughout the day. This leads to greater vehicle detection performance compared to a fixed user's defined threshold. In the second process, this paper proposes the novel vehicle tracking algorithms namely Fuzzy-based Vehicle Analysis (FBA) in order to reduce the false estimation of the vehicle tracking caused by uneven edges of the large vehicles and vehicle changing lanes. The proposed FBA algorithm employs the average edge density and the Horizontal Moving Edge Detection (HMED) algorithm to alleviate those problems by adopting fuzzy rule-based algorithms to rectify the vehicle tracking. The experimental results demonstrate that the proposed system provides the high accuracy of vehicle detection about 98.22%. In addition, it also offers the low false detection rates about 3.92%.

Momentum-weighted conjugate gradient descent algorithm for gradient coil optimization.

PubMed

Lu, Hanbing; Jesmanowicz, Andrzej; Li, Shi-Jiang; Hyde, James S

2004-01-01

MRI gradient coil design is a type of nonlinear constrained optimization. A practical problem in transverse gradient coil design using the conjugate gradient descent (CGD) method is that wire elements move at different rates along orthogonal directions (r, phi, z), and tend to cross, breaking the constraints. A momentum-weighted conjugate gradient descent (MW-CGD) method is presented to overcome this problem. This method takes advantage of the efficiency of the CGD method combined with momentum weighting, which is also an intrinsic property of the Levenberg-Marquardt algorithm, to adjust step sizes along the three orthogonal directions. A water-cooled, 12.8 cm inner diameter, three axis torque-balanced gradient coil for rat imaging was developed based on this method, with an efficiency of 2.13, 2.08, and 4.12 mT.m(-1).A(-1) along X, Y, and Z, respectively. Experimental data demonstrate that this method can improve efficiency by 40% and field uniformity by 27%. This method has also been applied to the design of a gradient coil for the human brain, employing remote current return paths. The benefits of this design include improved gradient field uniformity and efficiency, with a shorter length than gradient coil designs using coaxial return paths. Copyright 2003 Wiley-Liss, Inc.

Solving large test-day models by iteration on data and preconditioned conjugate gradient.

PubMed

Lidauer, M; Strandén, I; Mäntysaari, E A; Pösö, J; Kettunen, A

1999-12-01

A preconditioned conjugate gradient method was implemented into an iteration on a program for data estimation of breeding values, and its convergence characteristics were studied. An algorithm was used as a reference in which one fixed effect was solved by Gauss-Seidel method, and other effects were solved by a second-order Jacobi method. Implementation of the preconditioned conjugate gradient required storing four vectors (size equal to number of unknowns in the mixed model equations) in random access memory and reading the data at each round of iteration. The preconditioner comprised diagonal blocks of the coefficient matrix. Comparison of algorithms was based on solutions of mixed model equations obtained by a single-trait animal model and a single-trait, random regression test-day model. Data sets for both models used milk yield records of primiparous Finnish dairy cows. Animal model data comprised 665,629 lactation milk yields and random regression test-day model data of 6,732,765 test-day milk yields. Both models included pedigree information of 1,099,622 animals. The animal model ¿random regression test-day model¿ required 122 ¿305¿ rounds of iteration to converge with the reference algorithm, but only 88 ¿149¿ were required with the preconditioned conjugate gradient. To solve the random regression test-day model with the preconditioned conjugate gradient required 237 megabytes of random access memory and took 14% of the computation time needed by the reference algorithm.

Implementation and application of a gradient enhanced crystal plasticity model

NASA Astrophysics Data System (ADS)

Soyarslan, C.; Perdahcıoǧlu, E. S.; Aşık, E. E.; van den Boogaard, A. H.; Bargmann, S.

2017-10-01

A rate-independent crystal plasticity model is implemented in which description of the hardening of the material is given as a function of the total dislocation density. The evolution of statistically stored dislocations (SSDs) is described using a saturating type evolution law. The evolution of geometrically necessary dislocations (GNDs) on the other hand is described using the gradient of the plastic strain tensor in a non-local manner. The gradient of the incremental plastic strain tensor is computed explicitly during an implicit FE simulation after each converged step. Using the plastic strain tensor stored as state variables at each integration point and an efficient numerical algorithm to find the gradients, the GND density is obtained. This results in a weak coupling of the equilibrium solution and the gradient enhancement. The algorithm is applied to an academic test problem which considers growth of a cylindrical void in a single crystal matrix.

Hardware friendly probabilistic spiking neural network with long-term and short-term plasticity.

PubMed

Hsieh, Hung-Yi; Tang, Kea-Tiong

2013-12-01

This paper proposes a probabilistic spiking neural network (PSNN) with unimodal weight distribution, possessing long- and short-term plasticity. The proposed algorithm is derived by both the arithmetic gradient decent calculation and bioinspired algorithms. The algorithm is benchmarked by the Iris and Wisconsin breast cancer (WBC) data sets. The network features fast convergence speed and high accuracy. In the experiment, the PSNN took not more than 40 epochs for convergence. The average testing accuracy for Iris and WBC data is 96.7% and 97.2%, respectively. To test the usefulness of the PSNN to real world application, the PSNN was also tested with the odor data, which was collected by our self-developed electronic nose (e-nose). Compared with the algorithm (K-nearest neighbor) that has the highest classification accuracy in the e-nose for the same odor data, the classification accuracy of the PSNN is only 1.3% less but the memory requirement can be reduced at least 40%. All the experiments suggest that the PSNN is hardware friendly. First, it requires only nine-bits weight resolution for training and testing. Second, the PSNN can learn complex data sets with a little number of neurons that in turn reduce the cost of VLSI implementation. In addition, the algorithm is insensitive to synaptic noise and the parameter variation induced by the VLSI fabrication. Therefore, the algorithm can be implemented by either software or hardware, making it suitable for wider application.

Resonator reset in circuit QED by optimal control for large open quantum systems

NASA Astrophysics Data System (ADS)

Boutin, Samuel; Andersen, Christian Kraglund; Venkatraman, Jayameenakshi; Ferris, Andrew J.; Blais, Alexandre

2017-10-01

We study an implementation of the open GRAPE (gradient ascent pulse engineering) algorithm well suited for large open quantum systems. While typical implementations of optimal control algorithms for open quantum systems rely on explicit matrix exponential calculations, our implementation avoids these operations, leading to a polynomial speedup of the open GRAPE algorithm in cases of interest. This speedup, as well as the reduced memory requirements of our implementation, are illustrated by comparison to a standard implementation of open GRAPE. As a practical example, we apply this open-system optimization method to active reset of a readout resonator in circuit QED. In this problem, the shape of a microwave pulse is optimized such as to empty the cavity from measurement photons as fast as possible. Using our open GRAPE implementation, we obtain pulse shapes, leading to a reset time over 4 times faster than passive reset.

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.

Image defog algorithm based on open close filter and gradient domain recursive bilateral filter

NASA Astrophysics Data System (ADS)

Liu, Daqian; Liu, Wanjun; Zhao, Qingguo; Fei, Bowen

2017-11-01

To solve the problems of fuzzy details, color distortion, low brightness of the image obtained by the dark channel prior defog algorithm, an image defog algorithm based on open close filter and gradient domain recursive bilateral filter, referred to as OCRBF, was put forward. The algorithm named OCRBF firstly makes use of weighted quad tree to obtain more accurate the global atmospheric value, then exploits multiple-structure element morphological open and close filter towards the minimum channel map to obtain a rough scattering map by dark channel prior, makes use of variogram to correct the transmittance map,and uses gradient domain recursive bilateral filter for the smooth operation, finally gets recovery images by image degradation model, and makes contrast adjustment to get bright, clear and no fog image. A large number of experimental results show that the proposed defog method in this paper can be good to remove the fog , recover color and definition of the fog image containing close range image, image perspective, the image including the bright areas very well, compared with other image defog algorithms,obtain more clear and natural fog free images with details of higher visibility, what's more, the relationship between the time complexity of SIDA algorithm and the number of image pixels is a linear correlation.

Eye center localization and gaze gesture recognition for human-computer interaction.

PubMed

Zhang, Wenhao; Smith, Melvyn L; Smith, Lyndon N; Farooq, Abdul

2016-03-01

This paper introduces an unsupervised modular approach for accurate and real-time eye center localization in images and videos, thus allowing a coarse-to-fine, global-to-regional scheme. The trajectories of eye centers in consecutive frames, i.e., gaze gestures, are further analyzed, recognized, and employed to boost the human-computer interaction (HCI) experience. This modular approach makes use of isophote and gradient features to estimate the eye center locations. A selective oriented gradient filter has been specifically designed to remove strong gradients from eyebrows, eye corners, and shadows, which sabotage most eye center localization methods. A real-world implementation utilizing these algorithms has been designed in the form of an interactive advertising billboard to demonstrate the effectiveness of our method for HCI. The eye center localization algorithm has been compared with 10 other algorithms on the BioID database and six other algorithms on the GI4E database. It outperforms all the other algorithms in comparison in terms of localization accuracy. Further tests on the extended Yale Face Database b and self-collected data have proved this algorithm to be robust against moderate head poses and poor illumination conditions. The interactive advertising billboard has manifested outstanding usability and effectiveness in our tests and shows great potential for benefiting a wide range of real-world HCI applications.

Spiral trajectory design: a flexible numerical algorithm and base analytical equations.

PubMed

Pipe, James G; Zwart, Nicholas R

2014-01-01

Spiral-based trajectories for magnetic resonance imaging can be advantageous, but are often cumbersome to design or create. This work presents a flexible numerical algorithm for designing trajectories based on explicit definition of radial undersampling, and also gives several analytical expressions for charactering the base (critically sampled) class of these trajectories. Expressions for the gradient waveform, based on slew and amplitude limits, are developed such that a desired pitch in the spiral k-space trajectory is followed. The source code for this algorithm, written in C, is publicly available. Analytical expressions approximating the spiral trajectory (ignoring the radial component) are given to characterize measurement time, gradient heating, maximum gradient amplitude, and off-resonance phase for slew-limited and gradient amplitude-limited cases. Several numerically calculated trajectories are illustrated, and base Archimedean spirals are compared with analytically obtained results. Several different waveforms illustrate that the desired slew and amplitude limits are reached, as are the desired undersampling patterns, using the numerical method. For base Archimedean spirals, the results of the numerical and analytical approaches are in good agreement. A versatile numerical algorithm was developed, and was written in publicly available code. Approximate analytical formulas are given that help characterize spiral trajectories. Copyright © 2013 Wiley Periodicals, Inc.

Far-Infrared Based Pedestrian Detection for Driver-Assistance Systems Based on Candidate Filters, Gradient-Based Feature and Multi-Frame Approval Matching

PubMed Central

Wang, Guohua; Liu, Qiong

2015-01-01

Far-infrared pedestrian detection approaches for advanced driver-assistance systems based on high-dimensional features fail to simultaneously achieve robust and real-time detection. We propose a robust and real-time pedestrian detection system characterized by novel candidate filters, novel pedestrian features and multi-frame approval matching in a coarse-to-fine fashion. Firstly, we design two filters based on the pedestrians’ head and the road to select the candidates after applying a pedestrian segmentation algorithm to reduce false alarms. Secondly, we propose a novel feature encapsulating both the relationship of oriented gradient distribution and the code of oriented gradient to deal with the enormous variance in pedestrians’ size and appearance. Thirdly, we introduce a multi-frame approval matching approach utilizing the spatiotemporal continuity of pedestrians to increase the detection rate. Large-scale experiments indicate that the system works in real time and the accuracy has improved about 9% compared with approaches based on high-dimensional features only. PMID:26703611

Far-Infrared Based Pedestrian Detection for Driver-Assistance Systems Based on Candidate Filters, Gradient-Based Feature and Multi-Frame Approval Matching.

PubMed

Wang, Guohua; Liu, Qiong

2015-12-21

Far-infrared pedestrian detection approaches for advanced driver-assistance systems based on high-dimensional features fail to simultaneously achieve robust and real-time detection. We propose a robust and real-time pedestrian detection system characterized by novel candidate filters, novel pedestrian features and multi-frame approval matching in a coarse-to-fine fashion. Firstly, we design two filters based on the pedestrians' head and the road to select the candidates after applying a pedestrian segmentation algorithm to reduce false alarms. Secondly, we propose a novel feature encapsulating both the relationship of oriented gradient distribution and the code of oriented gradient to deal with the enormous variance in pedestrians' size and appearance. Thirdly, we introduce a multi-frame approval matching approach utilizing the spatiotemporal continuity of pedestrians to increase the detection rate. Large-scale experiments indicate that the system works in real time and the accuracy has improved about 9% compared with approaches based on high-dimensional features only.

Gaussian process regression to accelerate geometry optimizations relying on numerical differentiation

NASA Astrophysics Data System (ADS)

Schmitz, Gunnar; Christiansen, Ove

2018-06-01

We study how with means of Gaussian Process Regression (GPR) geometry optimizations, which rely on numerical gradients, can be accelerated. The GPR interpolates a local potential energy surface on which the structure is optimized. It is found to be efficient to combine results on a low computational level (HF or MP2) with the GPR-calculated gradient of the difference between the low level method and the target method, which is a variant of explicitly correlated Coupled Cluster Singles and Doubles with perturbative Triples correction CCSD(F12*)(T) in this study. Overall convergence is achieved if both the potential and the geometry are converged. Compared to numerical gradient-based algorithms, the number of required single point calculations is reduced. Although introducing an error due to the interpolation, the optimized structures are sufficiently close to the minimum of the target level of theory meaning that the reference and predicted minimum only vary energetically in the μEh regime.

Real-time 2D spatially selective MRI experiments: Comparative analysis of optimal control design methods

NASA Astrophysics Data System (ADS)

Maximov, Ivan I.; Vinding, Mads S.; Tse, Desmond H. Y.; Nielsen, Niels Chr.; Shah, N. Jon

2015-05-01

There is an increasing need for development of advanced radio-frequency (RF) pulse techniques in modern magnetic resonance imaging (MRI) systems driven by recent advancements in ultra-high magnetic field systems, new parallel transmit/receive coil designs, and accessible powerful computational facilities. 2D spatially selective RF pulses are an example of advanced pulses that have many applications of clinical relevance, e.g., reduced field of view imaging, and MR spectroscopy. The 2D spatially selective RF pulses are mostly generated and optimised with numerical methods that can handle vast controls and multiple constraints. With this study we aim at demonstrating that numerical, optimal control (OC) algorithms are efficient for the design of 2D spatially selective MRI experiments, when robustness towards e.g. field inhomogeneity is in focus. We have chosen three popular OC algorithms; two which are gradient-based, concurrent methods using first- and second-order derivatives, respectively; and a third that belongs to the sequential, monotonically convergent family. We used two experimental models: a water phantom, and an in vivo human head. Taking into consideration the challenging experimental setup, our analysis suggests the use of the sequential, monotonic approach and the second-order gradient-based approach as computational speed, experimental robustness, and image quality is key. All algorithms used in this work were implemented in the MATLAB environment and are freely available to the MRI community.

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.

Parallel programming of gradient-based iterative image reconstruction schemes for optical tomography.

PubMed

Hielscher, Andreas H; Bartel, Sebastian

2004-02-01

Optical tomography (OT) is a fast developing novel imaging modality that uses near-infrared (NIR) light to obtain cross-sectional views of optical properties inside the human body. A major challenge remains the time-consuming, computational-intensive image reconstruction problem that converts NIR transmission measurements into cross-sectional images. To increase the speed of iterative image reconstruction schemes that are commonly applied for OT, we have developed and implemented several parallel algorithms on a cluster of workstations. Static process distribution as well as dynamic load balancing schemes suitable for heterogeneous clusters and varying machine performances are introduced and tested. The resulting algorithms are shown to accelerate the reconstruction process to various degrees, substantially reducing the computation times for clinically relevant problems.

Fourier domain preconditioned conjugate gradient algorithm for atmospheric tomography.

PubMed

Yang, Qiang; Vogel, Curtis R; Ellerbroek, Brent L

2006-07-20

By 'atmospheric tomography' we mean the estimation of a layered atmospheric turbulence profile from measurements of the pupil-plane phase (or phase gradients) corresponding to several different guide star directions. We introduce what we believe to be a new Fourier domain preconditioned conjugate gradient (FD-PCG) algorithm for atmospheric tomography, and we compare its performance against an existing multigrid preconditioned conjugate gradient (MG-PCG) approach. Numerical results indicate that on conventional serial computers, FD-PCG is as accurate and robust as MG-PCG, but it is from one to two orders of magnitude faster for atmospheric tomography on 30 m class telescopes. Simulations are carried out for both natural guide stars and for a combination of finite-altitude laser guide stars and natural guide stars to resolve tip-tilt uncertainty.

Learning algorithms for human-machine interfaces.

PubMed

Danziger, Zachary; Fishbach, Alon; Mussa-Ivaldi, Ferdinando A

2009-05-01

The goal of this study is to create and examine machine learning algorithms that adapt in a controlled and cadenced way to foster a harmonious learning environment between the user and the controlled device. To evaluate these algorithms, we have developed a simple experimental framework. Subjects wear an instrumented data glove that records finger motions. The high-dimensional glove signals remotely control the joint angles of a simulated planar two-link arm on a computer screen, which is used to acquire targets. A machine learning algorithm was applied to adaptively change the transformation between finger motion and the simulated robot arm. This algorithm was either LMS gradient descent or the Moore-Penrose (MP) pseudoinverse transformation. Both algorithms modified the glove-to-joint angle map so as to reduce the endpoint errors measured in past performance. The MP group performed worse than the control group (subjects not exposed to any machine learning), while the LMS group outperformed the control subjects. However, the LMS subjects failed to achieve better generalization than the control subjects, and after extensive training converged to the same level of performance as the control subjects. These results highlight the limitations of coadaptive learning using only endpoint error reduction.

Learning Algorithms for Human–Machine Interfaces

PubMed Central

Fishbach, Alon; Mussa-Ivaldi, Ferdinando A.

2012-01-01

The goal of this study is to create and examine machine learning algorithms that adapt in a controlled and cadenced way to foster a harmonious learning environment between the user and the controlled device. To evaluate these algorithms, we have developed a simple experimental framework. Subjects wear an instrumented data glove that records finger motions. The high-dimensional glove signals remotely control the joint angles of a simulated planar two-link arm on a computer screen, which is used to acquire targets. A machine learning algorithm was applied to adaptively change the transformation between finger motion and the simulated robot arm. This algorithm was either LMS gradient descent or the Moore–Penrose (MP) pseudoinverse transformation. Both algorithms modified the glove-to-joint angle map so as to reduce the endpoint errors measured in past performance. The MP group performed worse than the control group (subjects not exposed to any machine learning), while the LMS group outperformed the control subjects. However, the LMS subjects failed to achieve better generalization than the control subjects, and after extensive training converged to the same level of performance as the control subjects. These results highlight the limitations of coadaptive learning using only endpoint error reduction. PMID:19203886

Variational nature, integration, and properties of Newton reaction path

NASA Astrophysics Data System (ADS)

Bofill, Josep Maria; Quapp, Wolfgang

2011-02-01

The distinguished coordinate path and the reduced gradient following path or its equivalent formulation, the Newton trajectory, are analyzed and unified using the theory of calculus of variations. It is shown that their minimum character is related to the fact that the curve is located in a valley region. In this case, we say that the Newton trajectory is a reaction path with the category of minimum energy path. In addition to these findings a Runge-Kutta-Fehlberg algorithm to integrate these curves is also proposed.

Variational nature, integration, and properties of Newton reaction path.

PubMed

Bofill, Josep Maria; Quapp, Wolfgang

2011-02-21

The distinguished coordinate path and the reduced gradient following path or its equivalent formulation, the Newton trajectory, are analyzed and unified using the theory of calculus of variations. It is shown that their minimum character is related to the fact that the curve is located in a valley region. In this case, we say that the Newton trajectory is a reaction path with the category of minimum energy path. In addition to these findings a Runge-Kutta-Fehlberg algorithm to integrate these curves is also proposed.

Analysis and correction of gradient nonlinearity bias in apparent diffusion coefficient measurements.

PubMed

Malyarenko, Dariya I; Ross, Brian D; Chenevert, Thomas L

2014-03-01

Gradient nonlinearity of MRI systems leads to spatially dependent b-values and consequently high non-uniformity errors (10-20%) in apparent diffusion coefficient (ADC) measurements over clinically relevant field-of-views. This work seeks practical correction procedure that effectively reduces observed ADC bias for media of arbitrary anisotropy in the fewest measurements. All-inclusive bias analysis considers spatial and time-domain cross-terms for diffusion and imaging gradients. The proposed correction is based on rotation of the gradient nonlinearity tensor into the diffusion gradient frame where spatial bias of b-matrix can be approximated by its Euclidean norm. Correction efficiency of the proposed procedure is numerically evaluated for a range of model diffusion tensor anisotropies and orientations. Spatial dependence of nonlinearity correction terms accounts for the bulk (75-95%) of ADC bias for FA = 0.3-0.9. Residual ADC non-uniformity errors are amplified for anisotropic diffusion. This approximation obviates need for full diffusion tensor measurement and diagonalization to derive a corrected ADC. Practical scenarios are outlined for implementation of the correction on clinical MRI systems. The proposed simplified correction algorithm appears sufficient to control ADC non-uniformity errors in clinical studies using three orthogonal diffusion measurements. The most efficient reduction of ADC bias for anisotropic medium is achieved with non-lab-based diffusion gradients. Copyright © 2013 Wiley Periodicals, Inc.

Analysis and correction of gradient nonlinearity bias in ADC measurements

PubMed Central

Malyarenko, Dariya I.; Ross, Brian D.; Chenevert, Thomas L.

2013-01-01

Purpose Gradient nonlinearity of MRI systems leads to spatially-dependent b-values and consequently high non-uniformity errors (10–20%) in ADC measurements over clinically relevant field-of-views. This work seeks practical correction procedure that effectively reduces observed ADC bias for media of arbitrary anisotropy in the fewest measurements. Methods All-inclusive bias analysis considers spatial and time-domain cross-terms for diffusion and imaging gradients. The proposed correction is based on rotation of the gradient nonlinearity tensor into the diffusion gradient frame where spatial bias of b-matrix can be approximated by its Euclidean norm. Correction efficiency of the proposed procedure is numerically evaluated for a range of model diffusion tensor anisotropies and orientations. Results Spatial dependence of nonlinearity correction terms accounts for the bulk (75–95%) of ADC bias for FA = 0.3–0.9. Residual ADC non-uniformity errors are amplified for anisotropic diffusion. This approximation obviates need for full diffusion tensor measurement and diagonalization to derive a corrected ADC. Practical scenarios are outlined for implementation of the correction on clinical MRI systems. Conclusions The proposed simplified correction algorithm appears sufficient to control ADC non-uniformity errors in clinical studies using three orthogonal diffusion measurements. The most efficient reduction of ADC bias for anisotropic medium is achieved with non-lab-based diffusion gradients. PMID:23794533

Edge Pushing is Equivalent to Vertex Elimination for Computing Hessians

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

Wang, Mu; Pothen, Alex; Hovland, Paul

We prove the equivalence of two different Hessian evaluation algorithms in AD. The first is the Edge Pushing algorithm of Gower and Mello, which may be viewed as a second order Reverse mode algorithm for computing the Hessian. In earlier work, we have derived the Edge Pushing algorithm by exploiting a Reverse mode invariant based on the concept of live variables in compiler theory. The second algorithm is based on eliminating vertices in a computational graph of the gradient, in which intermediate variables are successively eliminated from the graph, and the weights of the edges are updated suitably. We provemore » that if the vertices are eliminated in a reverse topological order while preserving symmetry in the computational graph of the gradient, then the Vertex Elimination algorithm and the Edge Pushing algorithm perform identical computations. In this sense, the two algorithms are equivalent. This insight that unifies two seemingly disparate approaches to Hessian computations could lead to improved algorithms and implementations for computing Hessians. Read More: http://epubs.siam.org/doi/10.1137/1.9781611974690.ch11« less

A linear recurrent kernel online learning algorithm with sparse updates.

PubMed

Fan, Haijin; Song, Qing

2014-02-01

In this paper, we propose a recurrent kernel algorithm with selectively sparse updates for online learning. The algorithm introduces a linear recurrent term in the estimation of the current output. This makes the past information reusable for updating of the algorithm in the form of a recurrent gradient term. To ensure that the reuse of this recurrent gradient indeed accelerates the convergence speed, a novel hybrid recurrent training is proposed to switch on or off learning the recurrent information according to the magnitude of the current training error. Furthermore, the algorithm includes a data-dependent adaptive learning rate which can provide guaranteed system weight convergence at each training iteration. The learning rate is set as zero when the training violates the derived convergence conditions, which makes the algorithm updating process sparse. Theoretical analyses of the weight convergence are presented and experimental results show the good performance of the proposed algorithm in terms of convergence speed and estimation accuracy. Copyright © 2013 Elsevier Ltd. All rights reserved.

Finite-frequency tomography using adjoint methods-Methodology and examples using membrane surface waves

NASA Astrophysics Data System (ADS)

Tape, Carl; Liu, Qinya; Tromp, Jeroen

2007-03-01

We employ adjoint methods in a series of synthetic seismic tomography experiments to recover surface wave phase-speed models of southern California. Our approach involves computing the Fréchet derivative for tomographic inversions via the interaction between a forward wavefield, propagating from the source to the receivers, and an `adjoint' wavefield, propagating from the receivers back to the source. The forward wavefield is computed using a 2-D spectral-element method (SEM) and a phase-speed model for southern California. A `target' phase-speed model is used to generate the `data' at the receivers. We specify an objective or misfit function that defines a measure of misfit between data and synthetics. For a given receiver, the remaining differences between data and synthetics are time-reversed and used as the source of the adjoint wavefield. For each earthquake, the interaction between the regular and adjoint wavefields is used to construct finite-frequency sensitivity kernels, which we call event kernels. An event kernel may be thought of as a weighted sum of phase-specific (e.g. P) banana-doughnut kernels, with weights determined by the measurements. The overall sensitivity is simply the sum of event kernels, which defines the misfit kernel. The misfit kernel is multiplied by convenient orthonormal basis functions that are embedded in the SEM code, resulting in the gradient of the misfit function, that is, the Fréchet derivative. A non-linear conjugate gradient algorithm is used to iteratively improve the model while reducing the misfit function. We illustrate the construction of the gradient and the minimization algorithm, and consider various tomographic experiments, including source inversions, structural inversions and joint source-structure inversions. Finally, we draw connections between classical Hessian-based tomography and gradient-based adjoint tomography.

Optimal trajectories for aeroassisted orbital transfer

NASA Technical Reports Server (NTRS)

Miele, A.; Venkataraman, P.

1983-01-01

Consideration is given to classical and minimax problems involved in aeroassisted transfer from high earth orbit (HEO) to low earth orbit (LEO). The transfer is restricted to coplanar operation, with trajectory control effected by means of lift modulation. The performance of the maneuver is indexed to the energy expenditure or, alternatively, the time integral of the heating rate. Firist-order optimality conditions are defined for the classical approach, as are a sequential gradient-restoration algorithm and a combined gradient-restoration algorithm. Minimization techniques are presented for the aeroassisted transfer energy consumption and time-delay integral of the heating rate, as well as minimization of the pressure. It is shown that the eigenvalues of the Jacobian matrix of the differential system is both stiff and unstable, implying that the sequential gradient restoration algorithm in its present version is unsuitable. A new method, involving a multipoint approach to the two-poing boundary value problem, is recommended.

River suspended sediment estimation by climatic variables implication: Comparative study among soft computing techniques

NASA Astrophysics Data System (ADS)

Kisi, Ozgur; Shiri, Jalal

2012-06-01

Estimating sediment volume carried by a river is an important issue in water resources engineering. This paper compares the accuracy of three different soft computing methods, Artificial Neural Networks (ANNs), Adaptive Neuro-Fuzzy Inference System (ANFIS), and Gene Expression Programming (GEP), in estimating daily suspended sediment concentration on rivers by using hydro-meteorological data. The daily rainfall, streamflow and suspended sediment concentration data from Eel River near Dos Rios, at California, USA are used as a case study. The comparison results indicate that the GEP model performs better than the other models in daily suspended sediment concentration estimation for the particular data sets used in this study. Levenberg-Marquardt, conjugate gradient and gradient descent training algorithms were used for the ANN models. Out of three algorithms, the Conjugate gradient algorithm was found to be better than the others.

Reduced-Reference Quality Assessment Based on the Entropy of DWT Coefficients of Locally Weighted Gradient Magnitudes.

PubMed

Golestaneh, S Alireza; Karam, Lina

2016-08-24

Perceptual image quality assessment (IQA) attempts to use computational models to estimate the image quality in accordance with subjective evaluations. Reduced-reference (RR) image quality assessment (IQA) methods make use of partial information or features extracted from the reference image for estimating the quality of distorted images. Finding a balance between the number of RR features and accuracy of the estimated image quality is essential and important in IQA. In this paper we propose a training-free low-cost RRIQA method that requires a very small number of RR features (6 RR features). The proposed RRIQA algorithm is based on the discrete wavelet transform (DWT) of locally weighted gradient magnitudes.We apply human visual system's contrast sensitivity and neighborhood gradient information to weight the gradient magnitudes in a locally adaptive manner. The RR features are computed by measuring the entropy of each DWT subband, for each scale, and pooling the subband entropies along all orientations, resulting in L RR features (one average entropy per scale) for an L-level DWT. Extensive experiments performed on seven large-scale benchmark databases demonstrate that the proposed RRIQA method delivers highly competitive performance as compared to the state-of-the-art RRIQA models as well as full reference ones for both natural and texture images. The MATLAB source code of REDLOG and the evaluation results are publicly available online at https://http://lab.engineering.asu.edu/ivulab/software/redlog/.

Control of Complex Dynamic Systems by Neural Networks

NASA Technical Reports Server (NTRS)

Spall, James C.; Cristion, John A.

1993-01-01

This paper considers the use of neural networks (NN's) in controlling a nonlinear, stochastic system with unknown process equations. The NN is used to model the resulting unknown control law. The approach here is based on using the output error of the system to train the NN controller without the need to construct a separate model (NN or other type) for the unknown process dynamics. To implement such a direct adaptive control approach, it is required that connection weights in the NN be estimated while the system is being controlled. As a result of the feedback of the unknown process dynamics, however, it is not possible to determine the gradient of the loss function for use in standard (back-propagation-type) weight estimation algorithms. Therefore, this paper considers the use of a new stochastic approximation algorithm for this weight estimation, which is based on a 'simultaneous perturbation' gradient approximation that only requires the system output error. It is shown that this algorithm can greatly enhance the efficiency over more standard stochastic approximation algorithms based on finite-difference gradient approximations.

Novel artefact removal algorithms for co-registered EEG/fMRI based on selective averaging and subtraction.

PubMed

de Munck, Jan C; van Houdt, Petra J; Gonçalves, Sónia I; van Wegen, Erwin; Ossenblok, Pauly P W

2013-01-01

Co-registered EEG and functional MRI (EEG/fMRI) is a potential clinical tool for planning invasive EEG in patients with epilepsy. In addition, the analysis of EEG/fMRI data provides a fundamental insight into the precise physiological meaning of both fMRI and EEG data. Routine application of EEG/fMRI for localization of epileptic sources is hampered by large artefacts in the EEG, caused by switching of scanner gradients and heartbeat effects. Residuals of the ballistocardiogram (BCG) artefacts are similarly shaped as epileptic spikes, and may therefore cause false identification of spikes. In this study, new ideas and methods are presented to remove gradient artefacts and to reduce BCG artefacts of different shapes that mutually overlap in time. Gradient artefacts can be removed efficiently by subtracting an average artefact template when the EEG sampling frequency and EEG low-pass filtering are sufficient in relation to MR gradient switching (Gonçalves et al., 2007). When this is not the case, the gradient artefacts repeat themselves at time intervals that depend on the remainder between the fMRI repetition time and the closest multiple of the EEG acquisition time. These repetitions are deterministic, but difficult to predict due to the limited precision by which these timings are known. Therefore, we propose to estimate gradient artefact repetitions using a clustering algorithm, combined with selective averaging. Clustering of the gradient artefacts yields cleaner EEG for data recorded during scanning of a 3T scanner when using a sampling frequency of 2048 Hz. It even gives clean EEG when the EEG is sampled with only 256 Hz. Current BCG artefacts-reduction algorithms based on average template subtraction have the intrinsic limitation that they fail to deal properly with artefacts that overlap in time. To eliminate this constraint, the precise timings of artefact overlaps were modelled and represented in a sparse matrix. Next, the artefacts were disentangled with a least squares procedure. The relevance of this approach is illustrated by determining the BCG artefacts in a data set consisting of 29 healthy subjects recorded in a 1.5 T scanner and 15 patients with epilepsy recorded in a 3 T scanner. Analysis of the relationship between artefact amplitude, duration and heartbeat interval shows that in 22% (1.5T data) to 30% (3T data) of the cases BCG artefacts show an overlap. The BCG artefacts of the EEG/fMRI data recorded on the 1.5T scanner show a small negative correlation between HBI and BCG amplitude. In conclusion, the proposed methodology provides a substantial improvement of the quality of the EEG signal without excessive computer power or additional hardware than standard EEG-compatible equipment. Copyright © 2012 Elsevier Inc. All rights reserved.

Autofocus algorithm for synthetic aperture radar imaging with large curvilinear apertures

NASA Astrophysics Data System (ADS)

Bleszynski, E.; Bleszynski, M.; Jaroszewicz, T.

2013-05-01

An approach to autofocusing for large curved synthetic aperture radar (SAR) apertures is presented. Its essential feature is that phase corrections are being extracted not directly from SAR images, but rather from reconstructed SAR phase-history data representing windowed patches of the scene, of sizes sufficiently small to allow the linearization of the forward- and back-projection formulae. The algorithm processes data associated with each patch independently and in two steps. The first step employs a phase-gradient-type method in which phase correction compensating (possibly rapid) trajectory perturbations are estimated from the reconstructed phase history for the dominant scattering point on the patch. The second step uses phase-gradient-corrected data and extracts the absolute phase value, removing in this way phase ambiguities and reducing possible imperfections of the first stage, and providing the distances between the sensor and the scattering point with accuracy comparable to the wavelength. The features of the proposed autofocusing method are illustrated in its applications to intentionally corrupted small-scene 2006 Gotcha data. The examples include the extraction of absolute phases (ranges) for selected prominent point targets. They are then used to focus the scene and determine relative target-target distances.

Fast and accurate detection of spread source in large complex networks.

PubMed

Paluch, Robert; Lu, Xiaoyan; Suchecki, Krzysztof; Szymański, Bolesław K; Hołyst, Janusz A

2018-02-06

Spread over complex networks is a ubiquitous process with increasingly wide applications. Locating spread sources is often important, e.g. finding the patient one in epidemics, or source of rumor spreading in social network. Pinto, Thiran and Vetterli introduced an algorithm (PTVA) to solve the important case of this problem in which a limited set of nodes act as observers and report times at which the spread reached them. PTVA uses all observers to find a solution. Here we propose a new approach in which observers with low quality information (i.e. with large spread encounter times) are ignored and potential sources are selected based on the likelihood gradient from high quality observers. The original complexity of PTVA is O(N α ), where α ∈ (3,4) depends on the network topology and number of observers (N denotes the number of nodes in the network). Our Gradient Maximum Likelihood Algorithm (GMLA) reduces this complexity to O (N 2 log (N)). Extensive numerical tests performed on synthetic networks and real Gnutella network with limitation that id's of spreaders are unknown to observers demonstrate that for scale-free networks with such limitation GMLA yields higher quality localization results than PTVA does.

GPU-based stochastic-gradient optimization for non-rigid medical image registration in time-critical applications

NASA Astrophysics Data System (ADS)

Bhosale, Parag; Staring, Marius; Al-Ars, Zaid; Berendsen, Floris F.

2018-03-01

Currently, non-rigid image registration algorithms are too computationally intensive to use in time-critical applications. Existing implementations that focus on speed typically address this by either parallelization on GPU-hardware, or by introducing methodically novel techniques into CPU-oriented algorithms. Stochastic gradient descent (SGD) optimization and variations thereof have proven to drastically reduce the computational burden for CPU-based image registration, but have not been successfully applied in GPU hardware due to its stochastic nature. This paper proposes 1) NiftyRegSGD, a SGD optimization for the GPU-based image registration tool NiftyReg, 2) random chunk sampler, a new random sampling strategy that better utilizes the memory bandwidth of GPU hardware. Experiments have been performed on 3D lung CT data of 19 patients, which compared NiftyRegSGD (with and without random chunk sampler) with CPU-based elastix Fast Adaptive SGD (FASGD) and NiftyReg. The registration runtime was 21.5s, 4.4s and 2.8s for elastix-FASGD, NiftyRegSGD without, and NiftyRegSGD with random chunk sampling, respectively, while similar accuracy was obtained. Our method is publicly available at https://github.com/SuperElastix/NiftyRegSGD.

Moving force identification based on modified preconditioned conjugate gradient method

NASA Astrophysics Data System (ADS)

Chen, Zhen; Chan, Tommy H. T.; Nguyen, Andy

2018-06-01

This paper develops a modified preconditioned conjugate gradient (M-PCG) method for moving force identification (MFI) by improving the conjugate gradient (CG) and preconditioned conjugate gradient (PCG) methods with a modified Gram-Schmidt algorithm. The method aims to obtain more accurate and more efficient identification results from the responses of bridge deck caused by vehicles passing by, which are known to be sensitive to ill-posed problems that exist in the inverse problem. A simply supported beam model with biaxial time-varying forces is used to generate numerical simulations with various analysis scenarios to assess the effectiveness of the method. Evaluation results show that regularization matrix L and number of iterations j are very important influence factors to identification accuracy and noise immunity of M-PCG. Compared with the conventional counterpart SVD embedded in the time domain method (TDM) and the standard form of CG, the M-PCG with proper regularization matrix has many advantages such as better adaptability and more robust to ill-posed problems. More importantly, it is shown that the average optimal numbers of iterations of M-PCG can be reduced by more than 70% compared with PCG and this apparently makes M-PCG a preferred choice for field MFI applications.

Fast gradient-based algorithm on extended landscapes for wave-front reconstruction of Earth observation satellite

NASA Astrophysics Data System (ADS)

Thiebaut, C.; Perraud, L.; Delvit, J. M.; Latry, C.

2016-07-01

We present an on-board satellite implementation of a gradient-based (optical flows) algorithm for the shifts estimation between images of a Shack-Hartmann wave-front sensor on extended landscapes. The proposed algorithm has low complexity in comparison with classical correlation methods which is a big advantage for being used on-board a satellite at high instrument data rate and in real-time. The electronic board used for this implementation is designed for space applications and is composed of radiation-hardened software and hardware. Processing times of both shift estimations and pre-processing steps are compatible of on-board real-time computation.

The Mobius domain wall fermion algorithm

DOE PAGES

Brower, Richard C.; Neff, Harmut; Orginos, Kostas

2017-07-22

We present a review of the properties of generalized domain wall Fermions, based on a (real) Möbius transformation on the Wilson overlap kernel, discussing their algorithmic efficiency, the degree of explicit chiral violations measured by the residual mass (m res) and the Ward–Takahashi identities. The Möbius class interpolates between Shamir’s domain wall operator and Boriçi’s domain wall implementation of Neuberger’s overlap operator without increasing the number of Dirac applications per conjugate gradient iteration. A new scaling parameter (α) reduces chiral violations at finite fifth dimension (L s) but yields exactly the same overlap action in the limit L s →more » ∞ . Through the use of 4d Red/Black preconditioning and optimal tuning for the scaling α(L s), we show that chiral symmetry violations are typically reduced by an order of magnitude at fixed Ls . Here, we argue that the residual mass for a tuned Möbius algorithm with α = O(1/L s γ) for γ < 1 will eventually fall asymptotically as m res = O(1/L s 1+γ) in the case of a 5D Hamiltonian with out a spectral gap.« less

The Mobius domain wall fermion algorithm

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

Brower, Richard C.; Neff, Harmut; Orginos, Kostas

We present a review of the properties of generalized domain wall Fermions, based on a (real) Möbius transformation on the Wilson overlap kernel, discussing their algorithmic efficiency, the degree of explicit chiral violations measured by the residual mass (m res) and the Ward–Takahashi identities. The Möbius class interpolates between Shamir’s domain wall operator and Boriçi’s domain wall implementation of Neuberger’s overlap operator without increasing the number of Dirac applications per conjugate gradient iteration. A new scaling parameter (α) reduces chiral violations at finite fifth dimension (L s) but yields exactly the same overlap action in the limit L s →more » ∞ . Through the use of 4d Red/Black preconditioning and optimal tuning for the scaling α(L s), we show that chiral symmetry violations are typically reduced by an order of magnitude at fixed Ls . Here, we argue that the residual mass for a tuned Möbius algorithm with α = O(1/L s γ) for γ < 1 will eventually fall asymptotically as m res = O(1/L s 1+γ) in the case of a 5D Hamiltonian with out a spectral gap.« less

Experimental study of stochastic noise propagation in SPECT images reconstructed using the conjugate gradient algorithm.

PubMed

Mariano-Goulart, D; Fourcade, M; Bernon, J L; Rossi, M; Zanca, M

2003-01-01

Thanks to an experimental study based on simulated and physical phantoms, the propagation of the stochastic noise in slices reconstructed using the conjugate gradient algorithm has been analysed versus iterations. After a first increase corresponding to the reconstruction of the signal, the noise stabilises before increasing linearly with iterations. The level of the plateau as well as the slope of the subsequent linear increase depends on the noise in the projection data.

Metabolic Flux Analysis in Isotope Labeling Experiments Using the Adjoint Approach.

PubMed

Mottelet, Stephane; Gaullier, Gil; Sadaka, Georges

2017-01-01

Comprehension of metabolic pathways is considerably enhanced by metabolic flux analysis (MFA-ILE) in isotope labeling experiments. The balance equations are given by hundreds of algebraic (stationary MFA) or ordinary differential equations (nonstationary MFA), and reducing the number of operations is therefore a crucial part of reducing the computation cost. The main bottleneck for deterministic algorithms is the computation of derivatives, particularly for nonstationary MFA. In this article, we explain how the overall identification process may be speeded up by using the adjoint approach to compute the gradient of the residual sum of squares. The proposed approach shows significant improvements in terms of complexity and computation time when it is compared with the usual (direct) approach. Numerical results are obtained for the central metabolic pathways of Escherichia coli and are validated against reference software in the stationary case. The methods and algorithms described in this paper are included in the sysmetab software package distributed under an Open Source license at http://forge.scilab.org/index.php/p/sysmetab/.

An efficient impedance method for induced field evaluation based on a stabilized Bi-conjugate gradient algorithm.

PubMed

Wang, Hua; Liu, Feng; Xia, Ling; Crozier, Stuart

2008-11-21

This paper presents a stabilized Bi-conjugate gradient algorithm (BiCGstab) that can significantly improve the performance of the impedance method, which has been widely applied to model low-frequency field induction phenomena in voxel phantoms. The improved impedance method offers remarkable computational advantages in terms of convergence performance and memory consumption over the conventional, successive over-relaxation (SOR)-based algorithm. The scheme has been validated against other numerical/analytical solutions on a lossy, multilayered sphere phantom excited by an ideal coil loop. To demonstrate the computational performance and application capability of the developed algorithm, the induced fields inside a human phantom due to a low-frequency hyperthermia device is evaluated. The simulation results show the numerical accuracy and superior performance of the method.

Artificial Bee Colony Optimization of Capping Potentials for Hybrid Quantum Mechanical/Molecular Mechanical Calculations.

PubMed

Schiffmann, Christoph; Sebastiani, Daniel

2011-05-10

We present an algorithmic extension of a numerical optimization scheme for analytic capping potentials for use in mixed quantum-classical (quantum mechanical/molecular mechanical, QM/MM) ab initio calculations. Our goal is to minimize bond-cleavage-induced perturbations in the electronic structure, measured by means of a suitable penalty functional. The optimization algorithm-a variant of the artificial bee colony (ABC) algorithm, which relies on swarm intelligence-couples deterministic (downhill gradient) and stochastic elements to avoid local minimum trapping. The ABC algorithm outperforms the conventional downhill gradient approach, if the penalty hypersurface exhibits wiggles that prevent a straight minimization pathway. We characterize the optimized capping potentials by computing NMR chemical shifts. This approach will increase the accuracy of QM/MM calculations of complex biomolecules.

Study of genetic direct search algorithms for function optimization

NASA Technical Reports Server (NTRS)

Zeigler, B. P.

1974-01-01

The results are presented of a study to determine the performance of genetic direct search algorithms in solving function optimization problems arising in the optimal and adaptive control areas. The findings indicate that: (1) genetic algorithms can outperform standard algorithms in multimodal and/or noisy optimization situations, but suffer from lack of gradient exploitation facilities when gradient information can be utilized to guide the search. (2) For large populations, or low dimensional function spaces, mutation is a sufficient operator. However for small populations or high dimensional functions, crossover applied in about equal frequency with mutation is an optimum combination. (3) Complexity, in terms of storage space and running time, is significantly increased when population size is increased or the inversion operator, or the second level adaptation routine is added to the basic structure.

Numerical Aspects of Cone Beam Contour Reconstruction

NASA Astrophysics Data System (ADS)

Louis, Alfred K.

2017-12-01

We describe a method for directly calculating the contours of a function from cone beam data. The algorithm is based on a new inversion formula for the gradient of a function presented in Louis (Inverse Probl 32(11):115005, 2016. http://stacks.iop.org/0266-5611/32/i=11/a=115005). The Radon transform of the gradient is found by using a Grangeat type of formula, reducing the inversion problem to the inversion of the Radon transform. In that way the influence of the scanning curve, vital for all exact inversion formulas for complete data, is avoided Numerical results are presented for the circular scanning geometry which neither fulfills the Tuy-Kirillov condition nor the much weaker condition given by the author in Louis (Inverse Probl 32(11):115005, 2016. http://stacks.iop.org/0266-5611/32/i=11/a=115005).

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

NASA Technical Reports Server (NTRS)

Oliker, Leonid; Heber, Gerd; Biswas, Rupak

2000-01-01

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

Realizable optimal control for a remotely piloted research vehicle. [stability augmentation

NASA Technical Reports Server (NTRS)

Dunn, H. J.

1980-01-01

The design of a control system using the linear-quadratic regulator (LQR) control law theory for time invariant systems in conjunction with an incremental gradient procedure is presented. The incremental gradient technique reduces the full-state feedback controller design, generated by the LQR algorithm, to a realizable design. With a realizable controller, the feedback gains are based only on the available system outputs instead of being based on the full-state outputs. The design is for a remotely piloted research vehicle (RPRV) stability augmentation system. The design includes methods for accounting for noisy measurements, discrete controls with zero-order-hold outputs, and computational delay errors. Results from simulation studies of the response of the RPRV to a step in the elevator and frequency analysis techniques are included to illustrate these abnormalities and their influence on the controller design.

Mixed Transportation Network Design under a Sustainable Development Perspective

PubMed Central

Qin, Jin; Ni, Ling-lin; Shi, Feng

2013-01-01

A mixed transportation network design problem considering sustainable development was studied in this paper. Based on the discretization of continuous link-grade decision variables, a bilevel programming model was proposed to describe the problem, in which sustainability factors, including vehicle exhaust emissions, land-use scale, link load, and financial budget, are considered. The objective of the model is to minimize the total amount of resources exploited under the premise of meeting all the construction goals. A heuristic algorithm, which combined the simulated annealing and path-based gradient projection algorithm, was developed to solve the model. The numerical example shows that the transportation network optimized with the method above not only significantly alleviates the congestion on the link, but also reduces vehicle exhaust emissions within the network by up to 41.56%. PMID:23476142

Mixed transportation network design under a sustainable development perspective.

PubMed

Qin, Jin; Ni, Ling-lin; Shi, Feng

2013-01-01

A mixed transportation network design problem considering sustainable development was studied in this paper. Based on the discretization of continuous link-grade decision variables, a bilevel programming model was proposed to describe the problem, in which sustainability factors, including vehicle exhaust emissions, land-use scale, link load, and financial budget, are considered. The objective of the model is to minimize the total amount of resources exploited under the premise of meeting all the construction goals. A heuristic algorithm, which combined the simulated annealing and path-based gradient projection algorithm, was developed to solve the model. The numerical example shows that the transportation network optimized with the method above not only significantly alleviates the congestion on the link, but also reduces vehicle exhaust emissions within the network by up to 41.56%.

Hybrid Genetic Algorithm - Local Search Method for Ground-Water Management

NASA Astrophysics Data System (ADS)

Chiu, Y.; Nishikawa, T.; Martin, P.

2008-12-01

Ground-water management problems commonly are formulated as a mixed-integer, non-linear programming problem (MINLP). Relying only on conventional gradient-search methods to solve the management problem is computationally fast; however, the methods may become trapped in a local optimum. Global-optimization schemes can identify the global optimum, but the convergence is very slow when the optimal solution approaches the global optimum. In this study, we developed a hybrid optimization scheme, which includes a genetic algorithm and a gradient-search method, to solve the MINLP. The genetic algorithm identifies a near- optimal solution, and the gradient search uses the near optimum to identify the global optimum. Our methodology is applied to a conjunctive-use project in the Warren ground-water basin, California. Hi- Desert Water District (HDWD), the primary water-manager in the basin, plans to construct a wastewater treatment plant to reduce future septic-tank effluent from reaching the ground-water system. The treated wastewater instead will recharge the ground-water basin via percolation ponds as part of a larger conjunctive-use strategy, subject to State regulations (e.g. minimum distances and travel times). HDWD wishes to identify the least-cost conjunctive-use strategies that control ground-water levels, meet regulations, and identify new production-well locations. As formulated, the MINLP objective is to minimize water-delivery costs subject to constraints including pump capacities, available recharge water, water-supply demand, water-level constraints, and potential new-well locations. The methodology was demonstrated by an enumerative search of the entire feasible solution and comparing the optimum solution with results from the branch-and-bound algorithm. The results also indicate that the hybrid method identifies the global optimum within an affordable computation time. Sensitivity analyses, which include testing different recharge-rate scenarios, pond layouts, and water-supply constraints, indicate that the number of new wells is insensitive to water-supply constraints; however, pumping rates and patterns of the existing wells are sensitive. The locations of new wells are mildly sensitive to the pond layout.

No-reference image quality assessment based on natural scene statistics and gradient magnitude similarity

NASA Astrophysics Data System (ADS)

Jia, Huizhen; Sun, Quansen; Ji, Zexuan; Wang, Tonghan; Chen, Qiang

2014-11-01

The goal of no-reference/blind image quality assessment (NR-IQA) is to devise a perceptual model that can accurately predict the quality of a distorted image as human opinions, in which feature extraction is an important issue. However, the features used in the state-of-the-art "general purpose" NR-IQA algorithms are usually natural scene statistics (NSS) based or are perceptually relevant; therefore, the performance of these models is limited. To further improve the performance of NR-IQA, we propose a general purpose NR-IQA algorithm which combines NSS-based features with perceptually relevant features. The new method extracts features in both the spatial and gradient domains. In the spatial domain, we extract the point-wise statistics for single pixel values which are characterized by a generalized Gaussian distribution model to form the underlying features. In the gradient domain, statistical features based on neighboring gradient magnitude similarity are extracted. Then a mapping is learned to predict quality scores using a support vector regression. The experimental results on the benchmark image databases demonstrate that the proposed algorithm correlates highly with human judgments of quality and leads to significant performance improvements over state-of-the-art methods.

Developing operation algorithms for vision subsystems in autonomous mobile robots

NASA Astrophysics Data System (ADS)

Shikhman, M. V.; Shidlovskiy, S. V.

2018-05-01

The paper analyzes algorithms for selecting keypoints on the image for the subsequent automatic detection of people and obstacles. The algorithm is based on the histogram of oriented gradients and the support vector method. The combination of these methods allows successful selection of dynamic and static objects. The algorithm can be applied in various autonomous mobile robots.

Computerized scoring algorithms for the Autobiographical Memory Test.

PubMed

Takano, Keisuke; Gutenbrunner, Charlotte; Martens, Kris; Salmon, Karen; Raes, Filip

2018-02-01

Reduced specificity of autobiographical memories is a hallmark of depressive cognition. Autobiographical memory (AM) specificity is typically measured by the Autobiographical Memory Test (AMT), in which respondents are asked to describe personal memories in response to emotional cue words. Due to this free descriptive responding format, the AMT relies on experts' hand scoring for subsequent statistical analyses. This manual coding potentially impedes research activities in big data analytics such as large epidemiological studies. Here, we propose computerized algorithms to automatically score AM specificity for the Dutch (adult participants) and English (youth participants) versions of the AMT by using natural language processing and machine learning techniques. The algorithms showed reliable performances in discriminating specific and nonspecific (e.g., overgeneralized) autobiographical memories in independent testing data sets (area under the receiver operating characteristic curve > .90). Furthermore, outcome values of the algorithms (i.e., decision values of support vector machines) showed a gradient across similar (e.g., specific and extended memories) and different (e.g., specific memory and semantic associates) categories of AMT responses, suggesting that, for both adults and youth, the algorithms well capture the extent to which a memory has features of specific memories. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Conjugate gradient method for phase retrieval based on the Wirtinger derivative.

PubMed

Wei, Zhun; Chen, Wen; Qiu, Cheng-Wei; Chen, Xudong

2017-05-01

A conjugate gradient Wirtinger flow (CG-WF) algorithm for phase retrieval is proposed in this paper. It is shown that, compared with recently reported Wirtinger flow and its modified methods, the proposed CG-WF algorithm is able to dramatically accelerate the convergence rate while keeping the dominant computational cost of each iteration unchanged. We numerically illustrate the effectiveness of our method in recovering 1D Gaussian signals and 2D natural color images under both Gaussian and coded diffraction pattern models.

Fast optimal wavefront reconstruction for multi-conjugate adaptive optics using the Fourier domain preconditioned conjugate gradient algorithm.

PubMed

Vogel, Curtis R; Yang, Qiang

2006-08-21

We present two different implementations of the Fourier domain preconditioned conjugate gradient algorithm (FD-PCG) to efficiently solve the large structured linear systems that arise in optimal volume turbulence estimation, or tomography, for multi-conjugate adaptive optics (MCAO). We describe how to deal with several critical technical issues, including the cone coordinate transformation problem and sensor subaperture grid spacing. We also extend the FD-PCG approach to handle the deformable mirror fitting problem for MCAO.

Real-time 2D spatially selective MRI experiments: Comparative analysis of optimal control design methods.

PubMed

Maximov, Ivan I; Vinding, Mads S; Tse, Desmond H Y; Nielsen, Niels Chr; Shah, N Jon

2015-05-01

There is an increasing need for development of advanced radio-frequency (RF) pulse techniques in modern magnetic resonance imaging (MRI) systems driven by recent advancements in ultra-high magnetic field systems, new parallel transmit/receive coil designs, and accessible powerful computational facilities. 2D spatially selective RF pulses are an example of advanced pulses that have many applications of clinical relevance, e.g., reduced field of view imaging, and MR spectroscopy. The 2D spatially selective RF pulses are mostly generated and optimised with numerical methods that can handle vast controls and multiple constraints. With this study we aim at demonstrating that numerical, optimal control (OC) algorithms are efficient for the design of 2D spatially selective MRI experiments, when robustness towards e.g. field inhomogeneity is in focus. We have chosen three popular OC algorithms; two which are gradient-based, concurrent methods using first- and second-order derivatives, respectively; and a third that belongs to the sequential, monotonically convergent family. We used two experimental models: a water phantom, and an in vivo human head. Taking into consideration the challenging experimental setup, our analysis suggests the use of the sequential, monotonic approach and the second-order gradient-based approach as computational speed, experimental robustness, and image quality is key. All algorithms used in this work were implemented in the MATLAB environment and are freely available to the MRI community. Copyright © 2015 Elsevier Inc. All rights reserved.

Multidisciplinary design optimization using genetic algorithms

NASA Technical Reports Server (NTRS)

Unal, Resit

1994-01-01

Multidisciplinary design optimization (MDO) is an important step in the conceptual design and evaluation of launch vehicles since it can have a significant impact on performance and life cycle cost. The objective is to search the system design space to determine values of design variables that optimize the performance characteristic subject to system constraints. Gradient-based optimization routines have been used extensively for aerospace design optimization. However, one limitation of gradient based optimizers is their need for gradient information. Therefore, design problems which include discrete variables can not be studied. Such problems are common in launch vehicle design. For example, the number of engines and material choices must be integer values or assume only a few discrete values. In this study, genetic algorithms are investigated as an approach to MDO problems involving discrete variables and discontinuous domains. Optimization by genetic algorithms (GA) uses a search procedure which is fundamentally different from those gradient based methods. Genetic algorithms seek to find good solutions in an efficient and timely manner rather than finding the best solution. GA are designed to mimic evolutionary selection. A population of candidate designs is evaluated at each iteration, and each individual's probability of reproduction (existence in the next generation) depends on its fitness value (related to the value of the objective function). Progress toward the optimum is achieved by the crossover and mutation operations. GA is attractive since it uses only objective function values in the search process, so gradient calculations are avoided. Hence, GA are able to deal with discrete variables. Studies report success in the use of GA for aircraft design optimization studies, trajectory analysis, space structure design and control systems design. In these studies reliable convergence was achieved, but the number of function evaluations was large compared with efficient gradient methods. Applicaiton of GA is underway for a cost optimization study for a launch-vehicle fuel-tank and structural design of a wing. The strengths and limitations of GA for launch vehicle design optimization is studied.

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.

On efficient randomized algorithms for finding the PageRank vector

NASA Astrophysics Data System (ADS)

Gasnikov, A. V.; Dmitriev, D. Yu.

2015-03-01

Two randomized methods are considered for finding the PageRank vector; in other words, the solution of the system p T = p T P with a stochastic n × n matrix P, where n ˜ 107-109, is sought (in the class of probability distributions) with accuracy ɛ: ɛ ≫ n -1. Thus, the possibility of brute-force multiplication of P by the column is ruled out in the case of dense objects. The first method is based on the idea of Markov chain Monte Carlo algorithms. This approach is efficient when the iterative process p {/t+1 T} = p {/t T} P quickly reaches a steady state. Additionally, it takes into account another specific feature of P, namely, the nonzero off-diagonal elements of P are equal in rows (this property is used to organize a random walk over the graph with the matrix P). Based on modern concentration-of-measure inequalities, new bounds for the running time of this method are presented that take into account the specific features of P. In the second method, the search for a ranking vector is reduced to finding the equilibrium in the antagonistic matrix game where S n (1) is a unit simplex in ℝ n and I is the identity matrix. The arising problem is solved by applying a slightly modified Grigoriadis-Khachiyan algorithm (1995). This technique, like the Nazin-Polyak method (2009), is a randomized version of Nemirovski's mirror descent method. The difference is that randomization in the Grigoriadis-Khachiyan algorithm is used when the gradient is projected onto the simplex rather than when the stochastic gradient is computed. For sparse matrices P, the method proposed yields noticeably better results.

An improved approach for the segmentation of starch granules in microscopic images

PubMed Central

2010-01-01

Background Starches are the main storage polysaccharides in plants and are distributed widely throughout plants including seeds, roots, tubers, leaves, stems and so on. Currently, microscopic observation is one of the most important ways to investigate and analyze the structure of starches. The position, shape, and size of the starch granules are the main measurements for quantitative analysis. In order to obtain these measurements, segmentation of starch granules from the background is very important. However, automatic segmentation of starch granules is still a challenging task because of the limitation of imaging condition and the complex scenarios of overlapping granules. Results We propose a novel method to segment starch granules in microscopic images. In the proposed method, we first separate starch granules from background using automatic thresholding and then roughly segment the image using watershed algorithm. In order to reduce the oversegmentation in watershed algorithm, we use the roundness of each segment, and analyze the gradient vector field to find the critical points so as to identify oversegments. After oversegments are found, we extract the features, such as the position and intensity of the oversegments, and use fuzzy c-means clustering to merge the oversegments to the objects with similar features. Experimental results demonstrate that the proposed method can alleviate oversegmentation of watershed segmentation algorithm successfully. Conclusions We present a new scheme for starch granules segmentation. The proposed scheme aims to alleviate the oversegmentation in watershed algorithm. We use the shape information and critical points of gradient vector flow (GVF) of starch granules to identify oversegments, and use fuzzy c-mean clustering based on prior knowledge to merge these oversegments to the objects. Experimental results on twenty microscopic starch images demonstrate the effectiveness of the proposed scheme. PMID:21047380

Peak-Seeking Optimization of Trim for Reduced Fuel Consumption: Architecture and Performance Predictions

NASA Technical Reports Server (NTRS)

Schaefer, Jacob; Brown, Nelson

2013-01-01

A peak-seeking control approach for real-time trim configuration optimization for reduced fuel consumption has been developed by researchers at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center to address the goals of the NASA Environmentally Responsible Aviation project to reduce fuel burn and emissions. The peak-seeking control approach is based on a steepest-descent algorithm using a time-varying Kalman filter to estimate the gradient of a performance function of fuel flow versus control surface positions. In real-time operation, deflections of symmetric ailerons, trailing-edge flaps, and leading-edge flaps of an FA-18 airplane (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) are controlled for optimization of fuel flow. This presentation presents the design and integration of this peak-seeking controller on a modified NASA FA-18 airplane with research flight control computers. A research flight was performed to collect data to build a realistic model of the performance function and characterize measurement noise. This model was then implemented into a nonlinear six-degree-of-freedom FA-18 simulation along with the peak-seeking control algorithm. With the goal of eventual flight tests, the algorithm was first evaluated in the improved simulation environment. Results from the simulation predict good convergence on minimum fuel flow with a 2.5-percent reduction in fuel flow relative to the baseline trim of the aircraft.

Peak-Seeking Optimization of Trim for Reduced Fuel Consumption: Architecture and Performance Predictions

NASA Technical Reports Server (NTRS)

Schaefer, Jacob; Brown, Nelson A.

2013-01-01

A peak-seeking control approach for real-time trim configuration optimization for reduced fuel consumption has been developed by researchers at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center to address the goals of the NASA Environmentally Responsible Aviation project to reduce fuel burn and emissions. The peak-seeking control approach is based on a steepest-descent algorithm using a time-varying Kalman filter to estimate the gradient of a performance function of fuel flow versus control surface positions. In real-time operation, deflections of symmetric ailerons, trailing-edge flaps, and leading-edge flaps of an F/A-18 airplane (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) are controlled for optimization of fuel flow. This paper presents the design and integration of this peak-seeking controller on a modified NASA F/A-18 airplane with research flight control computers. A research flight was performed to collect data to build a realistic model of the performance function and characterize measurement noise. This model was then implemented into a nonlinear six-degree-of-freedom F/A-18 simulation along with the peak-seeking control algorithm. With the goal of eventual flight tests, the algorithm was first evaluated in the improved simulation environment. Results from the simulation predict good convergence on minimum fuel flow with a 2.5-percent reduction in fuel flow relative to the baseline trim of the aircraft.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Application of sensitivity-analysis techniques to the calculation of topological quantities

NASA Astrophysics Data System (ADS)

Gilchrist, Stuart

2017-08-01

Magnetic reconnection in the corona occurs preferentially at sites where the magnetic connectivity is either discontinuous or has a large spatial gradient. Hence there is a general interest in computing quantities (like the squashing factor) that characterize the gradient in the field-line mapping function. Here we present an algorithm for calculating certain (quasi)topological quantities using mathematical techniques from the field of ``sensitivity-analysis''. The method is based on the calculation of a three dimensional field-line mapping Jacobian from which all the present topological quantities of interest can be derived. We will present the algorithm and the details of a publicly available set of libraries that implement the algorithm.

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.

Low Complexity Models to improve Incomplete Sensitivities for Shape Optimization

NASA Astrophysics Data System (ADS)

Stanciu, Mugurel; Mohammadi, Bijan; Moreau, Stéphane

2003-01-01

The present global platform for simulation and design of multi-model configurations treat shape optimization problems in aerodynamics. Flow solvers are coupled with optimization algorithms based on CAD-free and CAD-connected frameworks. Newton methods together with incomplete expressions of gradients are used. Such incomplete sensitivities are improved using reduced models based on physical assumptions. The validity and the application of this approach in real-life problems are presented. The numerical examples concern shape optimization for an airfoil, a business jet and a car engine cooling axial fan.

CPDES3: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in three dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on three-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES3 allows each spatial operator to have 7, 15, 19, or 27 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect induces which is vectorizable on some of the newer scientific computers.

CPDES2: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in two dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on two-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect indices which is vectorizable on some of the newer scientific computers.

Blind retrospective motion correction of MR images.

PubMed

Loktyushin, Alexander; Nickisch, Hannes; Pohmann, Rolf; Schölkopf, Bernhard

2013-12-01

Subject motion can severely degrade MR images. A retrospective motion correction algorithm, Gradient-based motion correction, which significantly reduces ghosting and blurring artifacts due to subject motion was proposed. The technique uses the raw data of standard imaging sequences; no sequence modifications or additional equipment such as tracking devices are required. Rigid motion is assumed. The approach iteratively searches for the motion trajectory yielding the sharpest image as measured by the entropy of spatial gradients. The vast space of motion parameters is efficiently explored by gradient-based optimization with a convergence guarantee. The method has been evaluated on both synthetic and real data in two and three dimensions using standard imaging techniques. MR images are consistently improved over different kinds of motion trajectories. Using a graphics processing unit implementation, computation times are in the order of a few minutes for a full three-dimensional volume. The presented technique can be an alternative or a complement to prospective motion correction methods and is able to improve images with strong motion artifacts from standard imaging sequences without requiring additional data. Copyright © 2013 Wiley Periodicals, Inc., a Wiley company.

Efficient implementation of one- and two-component analytical energy gradients in exact two-component theory

NASA Astrophysics Data System (ADS)

Franzke, Yannick J.; Middendorf, Nils; Weigend, Florian

2018-03-01

We present an efficient algorithm for one- and two-component analytical energy gradients with respect to nuclear displacements in the exact two-component decoupling approach to the one-electron Dirac equation (X2C). Our approach is a generalization of the spin-free ansatz by Cheng and Gauss [J. Chem. Phys. 135, 084114 (2011)], where the perturbed one-electron Hamiltonian is calculated by solving a first-order response equation. Computational costs are drastically reduced by applying the diagonal local approximation to the unitary decoupling transformation (DLU) [D. Peng and M. Reiher, J. Chem. Phys. 136, 244108 (2012)] to the X2C Hamiltonian. The introduced error is found to be almost negligible as the mean absolute error of the optimized structures amounts to only 0.01 pm. Our implementation in TURBOMOLE is also available within the finite nucleus model based on a Gaussian charge distribution. For a X2C/DLU gradient calculation, computational effort scales cubically with the molecular size, while storage increases quadratically. The efficiency is demonstrated in calculations of large silver clusters and organometallic iridium complexes.

Compressing climate model simulations: reducing storage burden while preserving information

NASA Astrophysics Data System (ADS)

Hammerling, Dorit; Baker, Allison; Xu, Haiying; Clyne, John; Li, Samuel

2017-04-01

Climate models, which are run at high spatial and temporal resolutions, generate massive quantities of data. As our computing capabilities continue to increase, storing all of the generated data is becoming a bottleneck, which negatively affects scientific progress. It is thus important to develop methods for representing the full datasets by smaller compressed versions, which still preserve all the critical information and, as an added benefit, allow for faster read and write operations during analysis work. Traditional lossy compression algorithms, as for example used for image files, are not necessarily ideally suited for climate data. While visual appearance is relevant, climate data has additional critical features such as the preservation of extreme values and spatial and temporal gradients. Developing alternative metrics to quantify information loss in a manner that is meaningful to climate scientists is an ongoing process still in its early stages. We will provide an overview of current efforts to develop such metrics to assess existing algorithms and to guide the development of tailored compression algorithms to address this pressing challenge.

Voidage correction algorithm for unresolved Euler-Lagrange simulations

NASA Astrophysics Data System (ADS)

Askarishahi, Maryam; Salehi, Mohammad-Sadegh; Radl, Stefan

2018-04-01

The effect of grid coarsening on the predicted total drag force and heat exchange rate in dense gas-particle flows is investigated using Euler-Lagrange (EL) approach. We demonstrate that grid coarsening may reduce the predicted total drag force and exchange rate. Surprisingly, exchange coefficients predicted by the EL approach deviate more significantly from the exact value compared to results of Euler-Euler (EE)-based calculations. The voidage gradient is identified as the root cause of this peculiar behavior. Consequently, we propose a correction algorithm based on a sigmoidal function to predict the voidage experienced by individual particles. Our correction algorithm can significantly improve the prediction of exchange coefficients in EL models, which is tested for simulations involving Euler grid cell sizes between 2d_p and 12d_p . It is most relevant in simulations of dense polydisperse particle suspensions featuring steep voidage profiles. For these suspensions, classical approaches may result in an error of the total exchange rate of up to 30%.

Exploiting the wavelet structure in compressed sensing MRI.

PubMed

Chen, Chen; Huang, Junzhou

2014-12-01

Sparsity has been widely utilized in magnetic resonance imaging (MRI) to reduce k-space sampling. According to structured sparsity theories, fewer measurements are required for tree sparse data than the data only with standard sparsity. Intuitively, more accurate image reconstruction can be achieved with the same number of measurements by exploiting the wavelet tree structure in MRI. A novel algorithm is proposed in this article to reconstruct MR images from undersampled k-space data. In contrast to conventional compressed sensing MRI (CS-MRI) that only relies on the sparsity of MR images in wavelet or gradient domain, we exploit the wavelet tree structure to improve CS-MRI. This tree-based CS-MRI problem is decomposed into three simpler subproblems then each of the subproblems can be efficiently solved by an iterative scheme. Simulations and in vivo experiments demonstrate the significant improvement of the proposed method compared to conventional CS-MRI algorithms, and the feasibleness on MR data compared to existing tree-based imaging algorithms. Copyright © 2014 Elsevier Inc. All rights reserved.

Dynamic graciloplasty for urinary incontinence: the potential for sequential closed-loop stimulation.

PubMed

Zonnevijlle, Erik D H; Perez-Abadia, Gustavo; Stremel, Richard W; Maldonado, Claudio J; Kon, Moshe; Barker, John H

2003-11-01

Muscle tissue transplantation applied to regain or dynamically assist contractile functions is known as 'dynamic myoplasty'. Success rates of clinical applications are unpredictable, because of lack of endurance, ischemic lesions, abundant scar formation and inadequate performance of tasks due to lack of refined control. Electrical stimulation is used to control dynamic myoplasties and should be improved to reduce some of these drawbacks. Sequential segmental neuromuscular stimulation improves the endurance and closed-loop control offers refinement in rate of contraction of the muscle, while function-controlling stimulator algorithms present the possibility of performing more complex tasks. An acute feasibility study was performed in anaesthetised dogs combining these techniques. Electrically stimulated gracilis-based neo-sphincters were compared to native sphincters with regard to their ability to maintain continence. Measurements were made during fast bladder pressure changes, static high bladder pressure and slow filling of the bladder, mimicking among others posture changes, lifting heavy objects and diuresis. In general, neo-sphincter and native sphincter performance showed no significant difference during these measurements. However, during high bladder pressures reaching 40 cm H(2)O the neo-sphincters maintained positive pressure gradients, whereas most native sphincters relaxed. During slow filling of the bladder the neo-sphincters maintained a controlled positive pressure gradient for a prolonged time without any form of training. Furthermore, the accuracy of these maintained pressure gradients proved to be within the limits set up by the native sphincters. Refinements using more complicated self-learning function-controlling algorithms proved to be effective also and are briefly discussed. In conclusion, a combination of sequential stimulation, closed-loop control and function-controlling algorithms proved feasible in this dynamic graciloplasty-model. Neo-sphincters were created, which would probably provide an acceptable performance, when the stimulation system could be implanted and further tested. Sizing this technique down to implantable proportions seems to be justified and will enable exploration of the possible benefits.

ECP Milestone Report WBS 2.3.4.13 ECP/VTK-m FY18Q1 [MS-18/01-03] Multiblock / Gradients / Release STDA05-5.

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

Moreland, Kenneth D.; Pugmire, David; Geveci, Berk

The FY18Q1 milestone of the ECP/VTK-m project includes the implementation of a multiblock data set, the completion of a gradients filtering operation, and the release of version 1.1 of the VTK-m software. With the completion of this milestone, the new multiblock data set allows us to iteratively schedule algorithms on composite data structures such as assemblies or hierarchies like AMR. The new gradient algorithms approximate derivatives of fields in 3D structures with finite differences. Finally, the release of VTK-m version 1.1 tags a stable release of the software that can more easily be incorporated into external projects.

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.

Spiral bacterial foraging optimization method: Algorithm, evaluation and convergence analysis

NASA Astrophysics Data System (ADS)

Kasaiezadeh, Alireza; Khajepour, Amir; Waslander, Steven L.

2014-04-01

A biologically-inspired algorithm called Spiral Bacterial Foraging Optimization (SBFO) is investigated in this article. SBFO, previously proposed by the same authors, is a multi-agent, gradient-based algorithm that minimizes both the main objective function (local cost) and the distance between each agent and a temporary central point (global cost). A random jump is included normal to the connecting line of each agent to the central point, which produces a vortex around the temporary central point. This random jump is also suitable to cope with premature convergence, which is a feature of swarm-based optimization methods. The most important advantages of this algorithm are as follows: First, this algorithm involves a stochastic type of search with a deterministic convergence. Second, as gradient-based methods are employed, faster convergence is demonstrated over GA, DE, BFO, etc. Third, the algorithm can be implemented in a parallel fashion in order to decentralize large-scale computation. Fourth, the algorithm has a limited number of tunable parameters, and finally SBFO has a strong certainty of convergence which is rare in existing global optimization algorithms. A detailed convergence analysis of SBFO for continuously differentiable objective functions has also been investigated in this article.

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.

MRI diffusion tensor reconstruction with PROPELLER data acquisition.

PubMed

Cheryauka, Arvidas B; Lee, James N; Samsonov, Alexei A; Defrise, Michel; Gullberg, Grant T

2004-02-01

MRI diffusion imaging is effective in measuring the diffusion tensor in brain, cardiac, liver, and spinal tissue. Diffusion tensor tomography MRI (DTT MRI) method is based on reconstructing the diffusion tensor field from measurements of projections of the tensor field. Projections are obtained by appropriate application of rotated diffusion gradients. In the present paper, the potential of a novel data acquisition scheme, PROPELLER (Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction), is examined in combination with DTT MRI for its capability and sufficiency for diffusion imaging. An iterative reconstruction algorithm is used to reconstruct the diffusion tensor field from rotated diffusion weighted blades by appropriate rotated diffusion gradients. DTT MRI with PROPELLER data acquisition shows significant potential to reduce the number of weighted measurements, avoid ambiguity in reconstructing diffusion tensor parameters, increase signal-to-noise ratio, and decrease the influence of signal distortion.

High temperature-ultra performance liquid chromatography-mass spectrometry for the metabonomic analysis of Zucker rat urine.

PubMed

Gika, Helen G; Theodoridis, Georgios; Extance, Jon; Edge, Anthony M; Wilson, Ian D

2008-08-15

The applicability and potential of using elevated temperatures and sub 2-microm porous particles in chromatography for metabonomics/metabolomics was investigated using, for the first time, solvent temperatures higher than the boiling point of water (up to 180 degrees C) and thermal gradients to reduce the use of organic solvents. Ultra performance liquid chromatography, combined with mass spectrometry, was investigated for the global metabolite profiling of the plasma and urine of normal and Zucker (fa/fa) obese rats (a well established disease animal model). "Isobaric" high temperature chromatography, where the temperature and flow rate follow a gradient program, was developed and evaluated against a conventional organic solvent gradient. LC-MS data were first examined by established chromatographic criteria in order to evaluate the chromatographic performance and next were treated by special peak picking algorithms to allow the application of multivariate statistics. These studies showed that, for urine (but not plasma), chromatography at elevated temperatures provided better results than conventional reversed-phase LC with higher peak capacity and better peak asymmetry. From a systems biology point of view, better group clustering and separation was obtained with a larger number of variables of high importance when using high temperature-ultra performance liquid chromatography (HT-UPLC) compared to conventional solvent gradients.

Finite elements and the method of conjugate gradients on a concurrent processor

NASA Technical Reports Server (NTRS)

Lyzenga, G. A.; Raefsky, A.; Hager, G. H.

1985-01-01

An algorithm for the iterative solution of finite element problems on a concurrent processor is presented. The method of conjugate gradients is used to solve the system of matrix equations, which is distributed among the processors of a MIMD computer according to an element-based spatial decomposition. This algorithm is implemented in a two-dimensional elastostatics program on the Caltech Hypercube concurrent processor. The results of tests on up to 32 processors show nearly linear concurrent speedup, with efficiencies over 90 percent for sufficiently large problems.

Hybrid DFP-CG method for solving unconstrained optimization problems

NASA Astrophysics Data System (ADS)

Osman, Wan Farah Hanan Wan; Asrul Hery Ibrahim, Mohd; Mamat, Mustafa

2017-09-01

The conjugate gradient (CG) method and quasi-Newton method are both well known method for solving unconstrained optimization method. In this paper, we proposed a new method by combining the search direction between conjugate gradient method and quasi-Newton method based on BFGS-CG method developed by Ibrahim et al. The Davidon-Fletcher-Powell (DFP) update formula is used as an approximation of Hessian for this new hybrid algorithm. Numerical result showed that the new algorithm perform well than the ordinary DFP method and proven to posses both sufficient descent and global convergence properties.

Finite elements and the method of conjugate gradients on a concurrent processor

NASA Technical Reports Server (NTRS)

Lyzenga, G. A.; Raefsky, A.; Hager, B. H.

1984-01-01

An algorithm for the iterative solution of finite element problems on a concurrent processor is presented. The method of conjugate gradients is used to solve the system of matrix equations, which is distributed among the processors of a MIMD computer according to an element-based spatial decomposition. This algorithm is implemented in a two-dimensional elastostatics program on the Caltech Hypercube concurrent processor. The results of tests on up to 32 processors show nearly linear concurrent speedup, with efficiencies over 90% for sufficiently large problems.

A pipeline leakage locating method based on the gradient descent algorithm

NASA Astrophysics Data System (ADS)

Li, Yulong; Yang, Fan; Ni, Na

2018-04-01

A pipeline leakage locating method based on the gradient descent algorithm is proposed in this paper. The method has low computing complexity, which is suitable for practical application. We have built experimental environment in real underground pipeline network. A lot of real data has been gathered in the past three months. Every leak point has been certificated by excavation. Results show that positioning error is within 0.4 meter. Rate of false alarm and missing alarm are both under 20%. The calculating time is not above 5 seconds.

Phase locking of a seven-channel continuous wave fibre laser system by a stochastic parallel gradient algorithm

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

Volkov, M V; Garanin, S G; Dolgopolov, Yu V

2014-11-30

A seven-channel fibre laser system operated by the master oscillator – multichannel power amplifier scheme is the phase locked using a stochastic parallel gradient algorithm. The phase modulators on lithium niobate crystals are controlled by a multichannel electronic unit with the microcontroller processing signals in real time. The dynamic phase locking of the laser system with the bandwidth of 14 kHz is demonstrated, the time of phasing is 3 – 4 ms. (fibre and integrated-optical structures)

Electrical conductivity imaging using gradient B, decomposition algorithm in magnetic resonance electrical impedance tomography (MREIT).

PubMed

Park, Chunjae; Kwon, Ohin; Woo, Eung Je; Seo, Jin Keun

2004-03-01

In magnetic resonance electrical impedance tomography (MREIT), we try to visualize cross-sectional conductivity (or resistivity) images of a subject. We inject electrical currents into the subject through surface electrodes and measure the z component Bz of the induced internal magnetic flux density using an MRI scanner. Here, z is the direction of the main magnetic field of the MRI scanner. We formulate the conductivity image reconstruction problem in MREIT from a careful analysis of the relationship between the injection current and the induced magnetic flux density Bz. Based on the novel mathematical formulation, we propose the gradient Bz decomposition algorithm to reconstruct conductivity images. This new algorithm needs to differentiate Bz only once in contrast to the previously developed harmonic Bz algorithm where the numerical computation of (inverted delta)2Bz is required. The new algorithm, therefore, has the important advantage of much improved noise tolerance. Numerical simulations with added random noise of realistic amounts show the feasibility of the algorithm in practical applications and also its robustness against measurement noise.

Acceleration of the direct reconstruction of linear parametric images using nested algorithms.

PubMed

Wang, Guobao; Qi, Jinyi

2010-03-07

Parametric imaging using dynamic positron emission tomography (PET) provides important information for biological research and clinical diagnosis. Indirect and direct methods have been developed for reconstructing linear parametric images from dynamic PET data. Indirect methods are relatively simple and easy to implement because the image reconstruction and kinetic modeling are performed in two separate steps. Direct methods estimate parametric images directly from raw PET data and are statistically more efficient. However, the convergence rate of direct algorithms can be slow due to the coupling between the reconstruction and kinetic modeling. Here we present two fast gradient-type algorithms for direct reconstruction of linear parametric images. The new algorithms decouple the reconstruction and linear parametric modeling at each iteration by employing the principle of optimization transfer. Convergence speed is accelerated by running more sub-iterations of linear parametric estimation because the computation cost of the linear parametric modeling is much less than that of the image reconstruction. Computer simulation studies demonstrated that the new algorithms converge much faster than the traditional expectation maximization (EM) and the preconditioned conjugate gradient algorithms for dynamic PET.

Automatic choroid cells segmentation and counting in fluorescence microscopic image

NASA Astrophysics Data System (ADS)

Fei, Jianjun; Zhu, Weifang; Shi, Fei; Xiang, Dehui; Lin, Xiao; Yang, Lei; Chen, Xinjian

2016-03-01

In this paper, we proposed a method to automatically segment and count the rhesus choroid-retinal vascular endothelial cells (RF/6A) in fluorescence microscopic images which is based on shape classification, bottleneck detection and accelerated Dijkstra algorithm. The proposed method includes four main steps. First, a thresholding filter and morphological operations are applied to reduce the noise. Second, a shape classifier is used to decide whether a connected component is needed to be segmented. In this step, the AdaBoost classifier is applied with a set of shape features. Third, the bottleneck positions are found based on the contours of the connected components. Finally, the cells segmentation and counting are completed based on the accelerated Dijkstra algorithm with the gradient information between the bottleneck positions. The results show the feasibility and efficiency of the proposed method.

A hierarchical wavefront reconstruction algorithm for gradient sensors

NASA Astrophysics Data System (ADS)

Bharmal, Nazim; Bitenc, Urban; Basden, Alastair; Myers, Richard

2013-12-01

ELT-scale extreme adaptive optics systems will require new approaches tocompute the wavefront suitably quickly, when the computational burden ofapplying a MVM is no longer practical. An approach is demonstrated here whichis hierarchical in transforming wavefront slopes from a WFS into a wavefront,and then to actuator values. First, simple integration in 1D is used to create1D-wavefront estimates with unknown starting points at the edges of independentspatial domains. Second, these starting points are estimated globally. By thesestarting points are a sub-set of the overall grid where wavefront values are tobe estimated, sparse representations are produced and numerical complexity canbe chosen by the spacing of the starting point grid relative to the overallgrid. Using a combination of algebraic expressions, sparse representation, anda conjugate gradient solver, the number of non-parallelized operations forreconstruction on a 100x100 sub-aperture sized problem is ~600,000 or O(N^3/2),which is approximately the same as for each thread of a MVM solutionparallelized over 100 threads. To reduce the effects of noise propagationwithin each domain, a noise reduction algorithm can be applied which ensuresthe continuity of the wavefront. To apply this additional step has a cost of~1,200,000 operations. We conclude by briefly discussing how the final step ofconverting from wavefront to actuator values can be achieved.

High-Lift Optimization Design Using Neural Networks on a Multi-Element Airfoil

NASA Technical Reports Server (NTRS)

Greenman, Roxana M.; Roth, Karlin R.; Smith, Charles A. (Technical Monitor)

1998-01-01

The high-lift performance of a multi-element airfoil was optimized by using neural-net predictions that were trained using a computational data set. The numerical data was generated using a two-dimensional, incompressible, Navier-Stokes algorithm with the Spalart-Allmaras turbulence model. Because it is difficult to predict maximum lift for high-lift systems, an empirically-based maximum lift criteria was used in this study to determine both the maximum lift and the angle at which it occurs. Multiple input, single output networks were trained using the NASA Ames variation of the Levenberg-Marquardt algorithm for each of the aerodynamic coefficients (lift, drag, and moment). The artificial neural networks were integrated with a gradient-based optimizer. Using independent numerical simulations and experimental data for this high-lift configuration, it was shown that this design process successfully optimized flap deflection, gap, overlap, and angle of attack to maximize lift. Once the neural networks were trained and integrated with the optimizer, minimal additional computer resources were required to perform optimization runs with different initial conditions and parameters. Applying the neural networks within the high-lift rigging optimization process reduced the amount of computational time and resources by 83% compared with traditional gradient-based optimization procedures for multiple optimization runs.

Resonance frequency control of RF normal conducting cavity using gradient estimator of reflected power

NASA Astrophysics Data System (ADS)

Leewe, R.; Shahriari, Z.; Moallem, M.

2017-10-01

Control of the natural resonance frequency of an RF cavity is essential for accelerator structures due to their high cavity sensitivity to internal and external vibrations and the dependency of resonant frequency on temperature changes. Due to the relatively high radio frequencies involved (MHz to GHz), direct measurement of the resonant frequency for real-time control is not possible by using conventional microcontroller hardware. So far, all operational cavities are tuned using phase comparison techniques. The temperature dependent phase measurements render this technique labor and time intensive. To eliminate the phase measurement, reduce man hours and speed up cavity start up time, this paper presents a control theme that relies solely on the reflected power measurement. The control algorithm for the nonlinear system is developed through Lyapunov's method. The controller stabilizes the resonance frequency of the cavity using a nonlinear control algorithm in combination with a gradient estimation method. Experimental results of the proposed system on a test cavity show that the resonance frequency can be tuned to its optimum operating point while the start up time of a single cavity and the accompanied man hours are significantly decreased. A test result of the fully commissioned control system on one of TRIUMF's DTL tanks verifies its performance under real environmental conditions.

A Class of Prediction-Correction Methods for Time-Varying Convex Optimization

NASA Astrophysics Data System (ADS)

Simonetto, Andrea; Mokhtari, Aryan; Koppel, Alec; Leus, Geert; Ribeiro, Alejandro

2016-09-01

This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction steps, while sampling the problem data at a constant rate of $1/h$, where $h$ is the length of the sampling interval. The prediction step is derived by analyzing the iso-residual dynamics of the optimality conditions. The correction step adjusts for the distance between the current prediction and the optimizer at each time step, and consists either of one or multiple gradient steps or Newton steps, which respectively correspond to the gradient trajectory tracking (GTT) or Newton trajectory tracking (NTT) algorithms. Under suitable conditions, we establish that the asymptotic error incurred by both proposed methods behaves as $O(h^2)$, and in some cases as $O(h^4)$, which outperforms the state-of-the-art error bound of $O(h)$ for correction-only methods in the gradient-correction step. Moreover, when the characteristics of the objective function variation are not available, we propose approximate gradient and Newton tracking algorithms (AGT and ANT, respectively) that still attain these asymptotical error bounds. Numerical simulations demonstrate the practical utility of the proposed methods and that they improve upon existing techniques by several orders of magnitude.

MRI brain tumor segmentation based on improved fuzzy c-means method

NASA Astrophysics Data System (ADS)

Deng, Wankai; Xiao, Wei; Pan, Chao; Liu, Jianguo

2009-10-01

This paper focuses on the image segmentation, which is one of the key problems in medical image processing. A new medical image segmentation method is proposed based on fuzzy c- means algorithm and spatial information. Firstly, we classify the image into the region of interest and background using fuzzy c means algorithm. Then we use the information of the tissues' gradient and the intensity inhomogeneities of regions to improve the quality of segmentation. The sum of the mean variance in the region and the reciprocal of the mean gradient along the edge of the region are chosen as an objective function. The minimum of the sum is optimum result. The result shows that the clustering segmentation algorithm is effective.

Panel flutter optimization by gradient projection

NASA Technical Reports Server (NTRS)

Pierson, B. L.

1975-01-01

A gradient projection optimal control algorithm incorporating conjugate gradient directions of search is described and applied to several minimum weight panel design problems subject to a flutter speed constraint. New numerical solutions are obtained for both simply-supported and clamped homogeneous panels of infinite span for various levels of inplane loading and minimum thickness. The minimum thickness inequality constraint is enforced by a simple transformation of variables.

Dynamic phasing of multichannel cw laser radiation by means of a stochastic gradient algorithm

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

Volkov, V A; Volkov, M V; Garanin, S G

2013-09-30

The phasing of a multichannel laser beam by means of an iterative stochastic parallel gradient (SPG) algorithm has been numerically and experimentally investigated. The operation of the SPG algorithm is simulated, the acceptable range of amplitudes of probe phase shifts is found, and the algorithm parameters at which the desired Strehl number can be obtained with a minimum number of iterations are determined. An experimental bench with phase modulators based on lithium niobate, which are controlled by a multichannel electronic unit with a real-time microcontroller, has been designed. Phasing of 16 cw laser beams at a system response bandwidth ofmore » 3.7 kHz and phase thermal distortions in a frequency band of about 10 Hz is experimentally demonstrated. The experimental data are in complete agreement with the calculation results. (control of laser radiation parameters)« less

Accelerating IMRT optimization by voxel sampling

NASA Astrophysics Data System (ADS)

Martin, Benjamin C.; Bortfeld, Thomas R.; Castañon, David A.

2007-12-01

This paper presents a new method for accelerating intensity-modulated radiation therapy (IMRT) optimization using voxel sampling. Rather than calculating the dose to the entire patient at each step in the optimization, the dose is only calculated for some randomly selected voxels. Those voxels are then used to calculate estimates of the objective and gradient which are used in a randomized version of a steepest descent algorithm. By selecting different voxels on each step, we are able to find an optimal solution to the full problem. We also present an algorithm to automatically choose the best sampling rate for each structure within the patient during the optimization. Seeking further improvements, we experimented with several other gradient-based optimization algorithms and found that the delta-bar-delta algorithm performs well despite the randomness. Overall, we were able to achieve approximately an order of magnitude speedup on our test case as compared to steepest descent.

Turbopump Performance Improved by Evolutionary Algorithms

NASA Technical Reports Server (NTRS)

Oyama, Akira; Liou, Meng-Sing

2002-01-01

The development of design optimization technology for turbomachinery has been initiated using the multiobjective evolutionary algorithm under NASA's Intelligent Synthesis Environment and Revolutionary Aeropropulsion Concepts programs. As an alternative to the traditional gradient-based methods, evolutionary algorithms (EA's) are emergent design-optimization algorithms modeled after the mechanisms found in natural evolution. EA's search from multiple points, instead of moving from a single point. In addition, they require no derivatives or gradients of the objective function, leading to robustness and simplicity in coupling any evaluation codes. Parallel efficiency also becomes very high by using a simple master-slave concept for function evaluations, since such evaluations often consume the most CPU time, such as computational fluid dynamics. Application of EA's to multiobjective design problems is also straightforward because EA's maintain a population of design candidates in parallel. Because of these advantages, EA's are a unique and attractive approach to real-world design optimization problems.

A new deadlock resolution protocol and message matching algorithm for the extreme-scale simulator

DOE PAGES

Engelmann, Christian; Naughton, III, Thomas J.

2016-03-22

Investigating the performance of parallel applications at scale on future high-performance computing (HPC) architectures and the performance impact of different HPC architecture choices is an important component of HPC hardware/software co-design. The Extreme-scale Simulator (xSim) is a simulation toolkit for investigating the performance of parallel applications at scale. xSim scales to millions of simulated Message Passing Interface (MPI) processes. The overhead introduced by a simulation tool is an important performance and productivity aspect. This paper documents two improvements to xSim: (1)~a new deadlock resolution protocol to reduce the parallel discrete event simulation overhead and (2)~a new simulated MPI message matchingmore » algorithm to reduce the oversubscription management overhead. The results clearly show a significant performance improvement. The simulation overhead for running the NAS Parallel Benchmark suite was reduced from 102% to 0% for the embarrassingly parallel (EP) benchmark and from 1,020% to 238% for the conjugate gradient (CG) benchmark. xSim offers a highly accurate simulation mode for better tracking of injected MPI process failures. Furthermore, with highly accurate simulation, the overhead was reduced from 3,332% to 204% for EP and from 37,511% to 13,808% for CG.« less

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.

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.

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.

A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization

PubMed Central

Li, Xiangrong; Zhao, Xupei; Duan, Xiabin; Wang, Xiaoliang

2015-01-01

It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence—with at most a linear convergence rate—because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method. PMID:26381742

A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.

PubMed

Li, Xiangrong; Zhao, Xupei; Duan, Xiabin; Wang, Xiaoliang

2015-01-01

It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence--with at most a linear convergence rate--because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method.

An annealed chaotic maximum neural network for bipartite subgraph problem.

PubMed

Wang, Jiahai; Tang, Zheng; Wang, Ronglong

2004-04-01

In this paper, based on maximum neural network, we propose a new parallel algorithm that can help the maximum neural network escape from local minima by including a transient chaotic neurodynamics for bipartite subgraph problem. The goal of the bipartite subgraph problem, which is an NP- complete problem, is to remove the minimum number of edges in a given graph such that the remaining graph is a bipartite graph. Lee et al. presented a parallel algorithm using the maximum neural model (winner-take-all neuron model) for this NP- complete problem. The maximum neural model always guarantees a valid solution and greatly reduces the search space without a burden on the parameter-tuning. However, the model has a tendency to converge to a local minimum easily because it is based on the steepest descent method. By adding a negative self-feedback to the maximum neural network, we proposed a new parallel algorithm that introduces richer and more flexible chaotic dynamics and can prevent the network from getting stuck at local minima. After the chaotic dynamics vanishes, the proposed algorithm is then fundamentally reined by the gradient descent dynamics and usually converges to a stable equilibrium point. The proposed algorithm has the advantages of both the maximum neural network and the chaotic neurodynamics. A large number of instances have been simulated to verify the proposed algorithm. The simulation results show that our algorithm finds the optimum or near-optimum solution for the bipartite subgraph problem superior to that of the best existing parallel algorithms.

Compressive Sensing of Foot Gait Signals and Its Application for the Estimation of Clinically Relevant Time Series.

PubMed

Pant, Jeevan K; Krishnan, Sridhar

2016-07-01

A new signal reconstruction algorithm for compressive sensing based on the minimization of a pseudonorm which promotes block-sparse structure on the first-order difference of the signal is proposed. Involved optimization is carried out by using a sequential version of Fletcher-Reeves' conjugate-gradient algorithm, and the line search is based on Banach's fixed-point theorem. The algorithm is suitable for the reconstruction of foot gait signals which admit block-sparse structure on the first-order difference. An additional algorithm for the estimation of stride-interval, swing-interval, and stance-interval time series from the reconstructed foot gait signals is also proposed. This algorithm is based on finding zero crossing indices of the foot gait signal and using the resulting indices for the computation of time series. Extensive simulation results demonstrate that the proposed signal reconstruction algorithm yields improved signal-to-noise ratio and requires significantly reduced computational effort relative to several competing algorithms over a wide range of compression ratio. For a compression ratio in the range from 88% to 94%, the proposed algorithm is found to offer improved accuracy for the estimation of clinically relevant time-series parameters, namely, the mean value, variance, and spectral index of stride-interval, stance-interval, and swing-interval time series, relative to its nearest competitor algorithm. The improvement in performance for compression ratio as high as 94% indicates that the proposed algorithms would be useful for designing compressive sensing-based systems for long-term telemonitoring of human gait signals.

Accelerated gradient-based free form deformable registration for online adaptive radiotherapy

NASA Astrophysics Data System (ADS)

Yu, Gang; Liang, Yueqiang; Yang, Guanyu; Shu, Huazhong; Li, Baosheng; Yin, Yong; Li, Dengwang

2015-04-01

The registration of planning fan-beam computed tomography (FBCT) and daily cone-beam CT (CBCT) is a crucial step in adaptive radiation therapy. The current intensity-based registration algorithms, such as Demons, may fail when they are used to register FBCT and CBCT, because the CT numbers in CBCT cannot exactly correspond to the electron densities. In this paper, we investigated the effects of CBCT intensity inaccuracy on the registration accuracy and developed an accurate gradient-based free form deformation algorithm (GFFD). GFFD distinguishes itself from other free form deformable registration algorithms by (a) measuring the similarity using the 3D gradient vector fields to avoid the effect of inconsistent intensities between the two modalities; (b) accommodating image sampling anisotropy using the local polynomial approximation-intersection of confidence intervals (LPA-ICI) algorithm to ensure a smooth and continuous displacement field; and (c) introducing a ‘bi-directional’ force along with an adaptive force strength adjustment to accelerate the convergence process. It is expected that such a strategy can decrease the effect of the inconsistent intensities between the two modalities, thus improving the registration accuracy and robustness. Moreover, for clinical application, the algorithm was implemented by graphics processing units (GPU) through OpenCL framework. The registration time of the GFFD algorithm for each set of CT data ranges from 8 to 13 s. The applications of on-line adaptive image-guided radiation therapy, including auto-propagation of contours, aperture-optimization and dose volume histogram (DVH) in the course of radiation therapy were also studied by in-house-developed software.

Improved preconditioned conjugate gradient algorithm and application in 3D inversion of gravity-gradiometry data

NASA Astrophysics Data System (ADS)

Wang, Tai-Han; Huang, Da-Nian; Ma, Guo-Qing; Meng, Zhao-Hai; Li, Ye

2017-06-01

With the continuous development of full tensor gradiometer (FTG) measurement techniques, three-dimensional (3D) inversion of FTG data is becoming increasingly used in oil and gas exploration. In the fast processing and interpretation of large-scale high-precision data, the use of the graphics processing unit process unit (GPU) and preconditioning methods are very important in the data inversion. In this paper, an improved preconditioned conjugate gradient algorithm is proposed by combining the symmetric successive over-relaxation (SSOR) technique and the incomplete Choleksy decomposition conjugate gradient algorithm (ICCG). Since preparing the preconditioner requires extra time, a parallel implement based on GPU is proposed. The improved method is then applied in the inversion of noisecontaminated synthetic data to prove its adaptability in the inversion of 3D FTG data. Results show that the parallel SSOR-ICCG algorithm based on NVIDIA Tesla C2050 GPU achieves a speedup of approximately 25 times that of a serial program using a 2.0 GHz Central Processing Unit (CPU). Real airborne gravity-gradiometry data from Vinton salt dome (southwest Louisiana, USA) are also considered. Good results are obtained, which verifies the efficiency and feasibility of the proposed parallel method in fast inversion of 3D FTG data.

Modified echo peak correction for radial acquisition regime (RADAR).

PubMed

Takizawa, Masahiro; Ito, Taeko; Itagaki, Hiroyuki; Takahashi, Tetsuhiko; Shimizu, Kanichirou; Harada, Junta

2009-01-01

Because radial sampling imposes many limitations on magnetic resonance (MR) imaging hardware, such as on the accuracy of the gradient magnetic field or the homogeneity of B(0), some correction of the echo signal is usually needed before image reconstruction. In our previous study, we developed an echo-peak-shift correction (EPSC) algorithm not easily affected by hardware performance. However, some artifacts remained in lung imaging, where tissue is almost absent, or in cardiac imaging, which is affected by blood flow. In this study, we modified the EPSC algorithm to improve the image quality of the radial aquisition regime (RADAR) and expand its application sequences. We assumed the artifacts were mainly caused by errors in the phase map for EPSC and used a phantom on a 1.5-tesla (T) MR scanner to investigate whether to modify the EPSC algorithm. To evaluate the effectiveness of EPSC, we compared results from T(1)- and T(2)-weighted images of a volunteer's lung region using the current and modified EPSC. We then applied the modified EPSC to RADAR spin echo (SE) and RADAR balanced steady-state acquisition with rewound gradient echo (BASG) sequence. The modified EPSC reduced phase discontinuity in the reference data used for EPSC and improved visualization of blood vessels in the lungs. Motion and blood flow caused no visible artifacts in the resulting images in either RADAR SE or RADAR BASG sequence. Use of the modified EPSC eliminated artifacts caused by signal loss in the reference data for EPSC. In addition, the modified EPSC was applied to RADAR SE and RADAR BASG sequences.

A new algorithm for real-time optimal dispatch of active and reactive power generation retaining nonlinearity

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

Roy, L.; Rao, N.D.

1983-04-01

This paper presents a new method for optimal dispatch of real and reactive power generation which is based on cartesian coordinate formulation of economic dispatch problem and reclassification of state and control variables associated with generator buses. The voltage and power at these buses are classified as parametric and functional inequality constraints, and are handled by reduced gradient technique and penalty factor approach respectively. The advantage of this classification is the reduction in the size of the equality constraint model, leading to less storage requirement. The rectangular coordinate formulation results in an exact equality constraint model in which the coefficientmore » matrix is real, sparse, diagonally dominant, smaller in size and need be computed and factorized once only in each gradient step. In addition, Lagragian multipliers are calculated using a new efficient procedure. A natural outcome of these features is the solution of the economic dispatch problem, faster than other methods available to date in the literature. Rapid and reliable convergence is an additional desirable characteristic of the method. Digital simulation results are presented on several IEEE test systems to illustrate the range of application of the method visa-vis the popular Dommel-Tinney (DT) procedure. It is found that the proposed method is more reliable, 3-4 times faster and requires 20-30 percent less storage compared to the DT algorithm, while being just as general. Thus, owing to its exactness, robust mathematical model and less computational requirements, the method developed in the paper is shown to be a practically feasible algorithm for on-line optimal power dispatch.« less

Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method

NASA Technical Reports Server (NTRS)

Nemec, Marian; Aftosmis, Michael J.

2004-01-01

Adjoint solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape optimization. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (geometric parameters that control the shape). More recently, emerging adjoint applications focus on the analysis problem, where the adjoint solution is used to drive mesh adaptation, as well as to provide estimates of functional error bounds and corrections. The attractive feature of this approach is that the mesh-adaptation procedure targets a specific functional, thereby localizing the mesh refinement and reducing computational cost. Our focus is on the development of adjoint-based optimization techniques for a Cartesian method with embedded boundaries.12 In contrast t o implementations on structured and unstructured grids, Cartesian methods decouple the surface discretization from the volume mesh. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin et developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation. Central to automated shape optimization algorithms is the issue of geometry modeling and control. The need to optimize complex, "real-life" geometry provides a strong incentive for the use of parametric-CAD systems within the optimization procedure. In previous work, we presented an effective optimization framework that incorporates a direct-CAD interface. In this work, we enhance the capabilities of this framework with efficient gradient computations using the discrete adjoint method. We present details of the adjoint numerical implementation, which reuses the domain decomposition, multigrid, and time-marching schemes of the flow solver. Furthermore, we explain and demonstrate the use of CAD in conjunction with the Cartesian adjoint approach. The final paper will contain a number of complex geometry, industrially relevant examples with many design variables to demonstrate the effectiveness of the adjoint method on Cartesian meshes.

Experiment on a three-beam adaptive array for EHF frequency-hopped signals using a fast algorithm, phase-D

NASA Astrophysics Data System (ADS)

Yen, J. L.; Kremer, P.; Amin, N.; Fung, J.

1989-05-01

The Department of National Defence (Canada) has been conducting studies into multi-beam adaptive arrays for extremely high frequency (EHF) frequency hopped signals. A three-beam 43 GHz adaptive antenna and a beam control processor is under development. An interactive software package for the operation of the array, capable of applying different control algorithms is being written. A maximum signal to jammer plus noise ratio (SJNR) was found to provide superior performance in preventing degradation of user signals in the presence of nearby jammers. A new fast algorithm using a modified conjugate gradient approach was found to be a very efficient way to implement anti-jamming arrays based on maximum SJNR criterion. The present study was intended to refine and simplify this algorithm and to implement the algorithm on an experimental array for real-time evaluation of anti-jamming performance. A three-beam adaptive array was used. A simulation package was used in the evaluation of multi-beam systems using more than three beams and different user-jammer scenarios. An attempt to further reduce the computation burden through continued analysis of maximum SJNR met with limited success. A method to acquire and track an incoming laser beam is proposed.

Experiment on a three-beam adaptive array for EHF frequency-hopped signals using a fast algorithm, phase E

NASA Astrophysics Data System (ADS)

Yen, J. L.; Kremer, P.; Fung, J.

1990-05-01

The Department of National Defence (Canada) has been conducting studies into multi-beam adaptive arrays for extremely high frequency (EHF) frequency hopped signals. A three-beam 43 GHz adaptive antenna and a beam control processor is under development. An interactive software package for the operation of the array, capable of applying different control algorithms is being written. A maximum signal to jammer plus noise ratio (SJNR) has been found to provide superior performance in preventing degradation of user signals in the presence of nearby jammers. A new fast algorithm using a modified conjugate gradient approach has been found to be a very efficient way to implement anti-jamming arrays based on maximum SJNR criterion. The present study was intended to refine and simplify this algorithm and to implement the algorithm on an experimental array for real-time evaluation of anti-jamming performance. A three-beam adaptive array was used. A simulation package was used in the evaluation of multi-beam systems using more than three beams and different user-jammer scenarios. An attempt to further reduce the computation burden through further analysis of maximum SJNR met with limited success. The investigation of a new angle detector for spatial tracking in heterodyne laser space communications was completed.

Randomized algorithms for high quality treatment planning in volumetric modulated arc therapy

NASA Astrophysics Data System (ADS)

Yang, Yu; Dong, Bin; Wen, Zaiwen

2017-02-01

In recent years, volumetric modulated arc therapy (VMAT) has been becoming a more and more important radiation technique widely used in clinical application for cancer treatment. One of the key problems in VMAT is treatment plan optimization, which is complicated due to the constraints imposed by the involved equipments. In this paper, we consider a model with four major constraints: the bound on the beam intensity, an upper bound on the rate of the change of the beam intensity, the moving speed of leaves of the multi-leaf collimator (MLC) and its directional-convexity. We solve the model by a two-stage algorithm: performing minimization with respect to the shapes of the aperture and the beam intensities alternatively. Specifically, the shapes of the aperture are obtained by a greedy algorithm whose performance is enhanced by random sampling in the leaf pairs with a decremental rate. The beam intensity is optimized using a gradient projection method with non-monotonic line search. We further improve the proposed algorithm by an incremental random importance sampling of the voxels to reduce the computational cost of the energy functional. Numerical simulations on two clinical cancer date sets demonstrate that our method is highly competitive to the state-of-the-art algorithms in terms of both computational time and quality of treatment planning.

An algorithm for the split-feasibility problems with application to the split-equality problem.

PubMed

Chuang, Chih-Sheng; Chen, Chi-Ming

2017-01-01

In this paper, we study the split-feasibility problem in Hilbert spaces by using the projected reflected gradient algorithm. As applications, we study the convex linear inverse problem and the split-equality problem in Hilbert spaces, and we give new algorithms for these problems. Finally, numerical results are given for our main results.

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.

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.

Planck 2015 results. VI. LFI mapmaking

NASA Astrophysics Data System (ADS)

Planck Collaboration; Ade, P. A. R.; Aghanim, N.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Banday, A. J.; Barreiro, R. B.; Bartolo, N.; Battaner, E.; Benabed, K.; Benoît, A.; Benoit-Lévy, A.; Bernard, J.-P.; Bersanelli, M.; Bielewicz, P.; Bonaldi, A.; Bonavera, L.; Bond, J. R.; Borrill, J.; Bouchet, F. R.; Bucher, M.; Burigana, C.; Butler, R. C.; Calabrese, E.; Cardoso, J.-F.; Catalano, A.; Chamballu, A.; Chary, R.-R.; Christensen, P. R.; Colombi, S.; Colombo, L. P. L.; Crill, B. P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R. D.; Davis, R. J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Dickinson, C.; Diego, J. M.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Ducout, A.; Dupac, X.; Efstathiou, G.; Elsner, F.; Enßlin, T. A.; Eriksen, H. K.; Fergusson, J.; Finelli, F.; Forni, O.; Frailis, M.; Franceschi, E.; Frejsel, A.; Galeotta, S.; Galli, S.; Ganga, K.; Giard, M.; Giraud-Héraud, Y.; Gjerløw, E.; González-Nuevo, J.; Górski, K. M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Hansen, F. K.; Hanson, D.; Harrison, D. L.; Henrot-Versillé, S.; Herranz, D.; Hildebrandt, S. R.; Hivon, E.; Hobson, M.; Holmes, W. A.; Hornstrup, A.; Hovest, W.; Huffenberger, K. M.; Hurier, G.; Jaffe, A. H.; Jaffe, T. R.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kiiveri, K.; Kisner, T. S.; Knoche, J.; Kunz, M.; Kurki-Suonio, H.; Lähteenmäki, A.; Lamarre, J.-M.; Lasenby, A.; Lattanzi, M.; Lawrence, C. R.; Leahy, J. P.; Leonardi, R.; Lesgourgues, J.; Levrier, F.; Liguori, M.; Lilje, P. B.; Linden-Vørnle, M.; Lindholm, V.; López-Caniego, M.; Lubin, P. M.; Macías-Pérez, J. F.; Maggio, G.; Maino, D.; Mandolesi, N.; Mangilli, A.; Martin, P. G.; Martínez-González, E.; Masi, S.; Matarrese, S.; Mazzotta, P.; McGehee, P.; Meinhold, P. R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Murphy, J. A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C. B.; Nørgaard-Nielsen, H. U.; Novikov, D.; Novikov, I.; Paci, F.; Pagano, L.; Paoletti, D.; Partridge, B.; Pasian, F.; Patanchon, G.; Pearson, T. J.; Perdereau, O.; Perotto, L.; Perrotta, F.; Pettorino, V.; Pierpaoli, E.; Pietrobon, D.; Pointecouteau, E.; Polenta, G.; Pratt, G. W.; Prézeau, G.; Prunet, S.; Puget, J.-L.; Rachen, J. P.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renzi, A.; Rocha, G.; Rosset, C.; Rossetti, M.; Roudier, G.; Rubiño-Martín, J. A.; Rusholme, B.; Sandri, M.; Santos, D.; Savelainen, M.; Scott, D.; Seiffert, M. D.; Shellard, E. P. S.; Spencer, L. D.; Stolyarov, V.; Stompor, R.; Sutton, D.; Suur-Uski, A.-S.; Sygnet, J.-F.; Tauber, J. A.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Vassallo, T.; Vielva, P.; Villa, F.; Wade, L. A.; Wandelt, B. D.; Watson, R.; Wehus, I. K.; Yvon, D.; Zacchei, A.; Zonca, A.

2016-09-01

This paper describes the mapmaking procedure applied to Planck Low Frequency Instrument (LFI) data. The mapmaking step takes as input the calibrated timelines and pointing information. The main products are sky maps of I, Q, and U Stokes components. For the first time, we present polarization maps at LFI frequencies. The mapmaking algorithm is based on a destriping technique, which is enhanced with a noise prior. The Galactic region is masked to reduce errors arising from bandpass mismatch and high signal gradients. We apply horn-uniform radiometer weights to reduce the effects of beam-shape mismatch. The algorithm is the same as used for the 2013 release, apart from small changes in parameter settings. We validate the procedure through simulations. Special emphasis is put on the control of systematics, which is particularly important for accurate polarization analysis. We also produce low-resolution versions of the maps and corresponding noise covariance matrices. These serve as input in later analysis steps and parameter estimation. The noise covariance matrices are validated through noise Monte Carlo simulations. The residual noise in the map products is characterized through analysis of half-ring maps, noise covariance matrices, and simulations.

Efficient cooperative compressive spectrum sensing by identifying multi-candidate and exploiting deterministic matrix

NASA Astrophysics Data System (ADS)

Li, Jia; Wang, Qiang; Yan, Wenjie; Shen, Yi

2015-12-01

Cooperative spectrum sensing exploits the spatial diversity to improve the detection of occupied channels in cognitive radio networks (CRNs). Cooperative compressive spectrum sensing (CCSS) utilizing the sparsity of channel occupancy further improves the efficiency by reducing the number of reports without degrading detection performance. In this paper, we firstly and mainly propose the referred multi-candidate orthogonal matrix matching pursuit (MOMMP) algorithms to efficiently and effectively detect occupied channels at fusion center (FC), where multi-candidate identification and orthogonal projection are utilized to respectively reduce the number of required iterations and improve the probability of exact identification. Secondly, two common but different approaches based on threshold and Gaussian distribution are introduced to realize the multi-candidate identification. Moreover, to improve the detection accuracy and energy efficiency, we propose the matrix construction based on shrinkage and gradient descent (MCSGD) algorithm to provide a deterministic filter coefficient matrix of low t-average coherence. Finally, several numerical simulations validate that our proposals provide satisfactory performance with higher probability of detection, lower probability of false alarm and less detection time.

Ultrasound speckle reduction based on fractional order differentiation.

PubMed

Shao, Dangguo; Zhou, Ting; Liu, Fan; Yi, Sanli; Xiang, Yan; Ma, Lei; Xiong, Xin; He, Jianfeng

2017-07-01

Ultrasound images show a granular pattern of noise known as speckle that diminishes their quality and results in difficulties in diagnosis. To preserve edges and features, this paper proposes a fractional differentiation-based image operator to reduce speckle in ultrasound. An image de-noising model based on fractional partial differential equations with balance relation between k (gradient modulus threshold that controls the conduction) and v (the order of fractional differentiation) was constructed by the effective combination of fractional calculus theory and a partial differential equation, and the numerical algorithm of it was achieved using a fractional differential mask operator. The proposed algorithm has better speckle reduction and structure preservation than the three existing methods [P-M model, the speckle reducing anisotropic diffusion (SRAD) technique, and the detail preserving anisotropic diffusion (DPAD) technique]. And it is significantly faster than bilateral filtering (BF) in producing virtually the same experimental results. Ultrasound phantom testing and in vivo imaging show that the proposed method can improve the quality of an ultrasound image in terms of tissue SNR, CNR, and FOM values.

Toward development of mobile application for hand arthritis screening.

PubMed

Akhbardeh, Farhad; Vasefi, Fartash; Tavakolian, Kouhyar; Bradley, David; Fazel-Rezai, Reza

2015-01-01

Arthritis is one of the most common health problems affecting people throughout the world. The goal of the work presented in this paper is to provide individuals, who may be developing or have developed arthritis, with a mobile application to assess and monitor the progress of their disease using their smartphone. The image processing algorithm includes finger border detection algorithm to monitor joint thickness and angular deviation abnormalities, which are common symptoms of arthritis. In this work, we have analyzed and compared gradient, thresholding and Canny algorithms for border detection. The effect of image spatial resolution (down-sampling) is also investigated. The results calculated based on 36 joint measurements show that the mean errors for gradient, thresholding, and Canny methods are 0.20, 2.13, and 2.03 mm, respectively. In addition, the average error for different image resolutions is analyzed and the minimum required resolution is determined for each method. The results confirm that recent smartphone imaging capabilities can provide enough accuracy for hand border detection and finger joint analysis based on gradient method.

Spectral edge: gradient-preserving spectral mapping for image fusion.

PubMed

Connah, David; Drew, Mark S; Finlayson, Graham D

2015-12-01

This paper describes a novel approach to image fusion for color display. Our goal is to generate an output image whose gradient matches that of the input as closely as possible. We achieve this using a constrained contrast mapping paradigm in the gradient domain, where the structure tensor of a high-dimensional gradient representation is mapped exactly to that of a low-dimensional gradient field which is then reintegrated to form an output. Constraints on output colors are provided by an initial RGB rendering. Initially, we motivate our solution with a simple "ansatz" (educated guess) for projecting higher-D contrast onto color gradients, which we expand to a more rigorous theorem to incorporate color constraints. The solution to these constrained optimizations is closed-form, allowing for simple and hence fast and efficient algorithms. The approach can map any N-D image data to any M-D output and can be used in a variety of applications using the same basic algorithm. In this paper, we focus on the problem of mapping N-D inputs to 3D color outputs. We present results in five applications: hyperspectral remote sensing, fusion of color and near-infrared or clear-filter images, multilighting imaging, dark flash, and color visualization of magnetic resonance imaging diffusion-tensor imaging.

An optimal algorithm for reconstructing images from binary measurements

NASA Astrophysics Data System (ADS)

Yang, Feng; Lu, Yue M.; Sbaiz, Luciano; Vetterli, Martin

2010-01-01

We have studied a camera with a very large number of binary pixels referred to as the gigavision camera [1] or the gigapixel digital film camera [2, 3]. Potential advantages of this new camera design include improved dynamic range, thanks to its logarithmic sensor response curve, and reduced exposure time in low light conditions, due to its highly sensitive photon detection mechanism. We use maximum likelihood estimator (MLE) to reconstruct a high quality conventional image from the binary sensor measurements of the gigavision camera. We prove that when the threshold T is "1", the negative loglikelihood function is a convex function. Therefore, optimal solution can be achieved using convex optimization. Base on filter bank techniques, fast algorithms are given for computing the gradient and the multiplication of a vector and Hessian matrix of the negative log-likelihood function. We show that with a minor change, our algorithm also works for estimating conventional images from multiple binary images. Numerical experiments with synthetic 1-D signals and images verify the effectiveness and quality of the proposed algorithm. Experimental results also show that estimation performance can be improved by increasing the oversampling factor or the number of binary images.

Analytic Energy Gradients for Variational Two-Electron Reduced-Density-Matrix-Driven Complete Active Space Self-Consistent Field Theory.

PubMed

Maradzike, Elvis; Gidofalvi, Gergely; Turney, Justin M; Schaefer, Henry F; DePrince, A Eugene

2017-09-12

Analytic energy gradients are presented for a variational two-electron reduced-density-matrix (2-RDM)-driven complete active space self-consistent field (CASSCF) method. The active-space 2-RDM is determined using a semidefinite programing (SDP) algorithm built upon an augmented Lagrangian formalism. Expressions for analytic gradients are simplified by the fact that the Lagrangian is stationary with respect to variations in both the primal and the dual solutions to the SDP problem. Orbital response contributions to the gradient are identical to those that arise in conventional CASSCF methods in which the electronic structure of the active space is described by a full configuration interaction (CI) wave function. We explore the relative performance of variational 2-RDM (v2RDM)- and CI-driven CASSCF for the equilibrium geometries of 20 small molecules. When enforcing two-particle N-representability conditions, full-valence v2RDM-CASSCF-optimized bond lengths display a mean unsigned error of 0.0060 Å and a maximum unsigned error of 0.0265 Å, relative to those obtained from full-valence CI-CASSCF. When enforcing partial three-particle N-representability conditions, the mean and maximum unsigned errors are reduced to only 0.0006 and 0.0054 Å, respectively. For these same molecules, full-valence v2RDM-CASSCF bond lengths computed in the cc-pVQZ basis set deviate from experimentally determined ones on average by 0.017 and 0.011 Å when enforcing two- and three-particle conditions, respectively, whereas CI-CASSCF displays an average deviation of 0.010 Å. The v2RDM-CASSCF approach with two-particle conditions is also applied to the equilibrium geometry of pentacene; optimized bond lengths deviate from those derived from experiment, on average, by 0.015 Å when using a cc-pVDZ basis set and a (22e,22o) active space.

Optimization of Coil Element Configurations for a Matrix Gradient Coil.

PubMed

Kroboth, Stefan; Layton, Kelvin J; Jia, Feng; Littin, Sebastian; Yu, Huijun; Hennig, Jurgen; Zaitsev, Maxim

2018-01-01

Recently, matrix gradient coils (also termed multi-coils or multi-coil arrays) were introduced for imaging and B 0 shimming with 24, 48, and even 84 coil elements. However, in imaging applications, providing one amplifier per coil element is not always feasible due to high cost and technical complexity. In this simulation study, we show that an 84-channel matrix gradient coil (head insert for brain imaging) is able to create a wide variety of field shapes even if the number of amplifiers is reduced. An optimization algorithm was implemented that obtains groups of coil elements, such that a desired target field can be created by driving each group with an amplifier. This limits the number of amplifiers to the number of coil element groups. Simulated annealing is used due to the NP-hard combinatorial nature of the given problem. A spherical harmonic basis set up to the full third order within a sphere of 20-cm diameter in the center of the coil was investigated as target fields. We show that the median normalized least squares error for all target fields is below approximately 5% for 12 or more amplifiers. At the same time, the dissipated power stays within reasonable limits. With a relatively small set of amplifiers, switches can be used to sequentially generate spherical harmonics up to third order. The costs associated with a matrix gradient coil can be lowered, which increases the practical utility of matrix gradient coils.

Linear optics measurements and corrections using an AC dipole in RHIC

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

Wang, G.; Bai, M.; Yang, L.

2010-05-23

We report recent experimental results on linear optics measurements and corrections using ac dipole. In RHIC 2009 run, the concept of the SVD correction algorithm is tested at injection energy for both identifying the artificial gradient errors and correcting it using the trim quadrupoles. The measured phase beatings were reduced by 30% and 40% respectively for two dedicated experiments. In RHIC 2010 run, ac dipole is used to measure {beta}* and chromatic {beta} function. For the 0.65m {beta}* lattice, we observed a factor of 3 discrepancy between model and measured chromatic {beta} function in the yellow ring.

Evaluation and analysis of Seasat-A scanning multichannel Microwave Radiometer (SMMR) Antenna Pattern Correction (APC) algorithm

NASA Technical Reports Server (NTRS)

Kitzis, J. L.; Kitzis, S. N.

1979-01-01

The brightness temperature data produced by the SMMR final Antenna Pattern Correction (APC) algorithm is discussed. The algorithm consisted of: (1) a direct comparison of the outputs of the final and interim APC algorithms; and (2) an analysis of a possible relationship between observed cross track gradients in the interim brightness temperatures and the asymmetry in the antenna temperature data. Results indicate a bias between the brightness temperature produced by the final and interim APC algorithm.

Multimodal medical image fusion by combining gradient minimization smoothing filter and non-subsampled directional filter bank

NASA Astrophysics Data System (ADS)

Zhang, Cheng; Wenbo, Mei; Huiqian, Du; Zexian, Wang

2018-04-01

A new algorithm was proposed for medical images fusion in this paper, which combined gradient minimization smoothing filter (GMSF) with non-sampled directional filter bank (NSDFB). In order to preserve more detail information, a multi scale edge preserving decomposition framework (MEDF) was used to decompose an image into a base image and a series of detail images. For the fusion of base images, the local Gaussian membership function is applied to construct the fusion weighted factor. For the fusion of detail images, NSDFB was applied to decompose each detail image into multiple directional sub-images that are fused by pulse coupled neural network (PCNN) respectively. The experimental results demonstrate that the proposed algorithm is superior to the compared algorithms in both visual effect and objective assessment.

Error analysis of stochastic gradient descent ranking.

PubMed

Chen, Hong; Tang, Yi; Li, Luoqing; Yuan, Yuan; Li, Xuelong; Tang, Yuanyan

2013-06-01

Ranking is always an important task in machine learning and information retrieval, e.g., collaborative filtering, recommender systems, drug discovery, etc. A kernel-based stochastic gradient descent algorithm with the least squares loss is proposed for ranking in this paper. The implementation of this algorithm is simple, and an expression of the solution is derived via a sampling operator and an integral operator. An explicit convergence rate for leaning a ranking function is given in terms of the suitable choices of the step size and the regularization parameter. The analysis technique used here is capacity independent and is novel in error analysis of ranking learning. Experimental results on real-world data have shown the effectiveness of the proposed algorithm in ranking tasks, which verifies the theoretical analysis in ranking error.

A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations

NASA Astrophysics Data System (ADS)

Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten

2018-06-01

This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

An algorithm for automating the registration of USDA segment ground data to LANDSAT MSS data

NASA Technical Reports Server (NTRS)

Graham, M. H. (Principal Investigator)

1981-01-01

The algorithm is referred to as the Automatic Segment Matching Algorithm (ASMA). The ASMA uses control points or the annotation record of a P-format LANDSAT compter compatible tape as the initial registration to relate latitude and longitude to LANDSAT rows and columns. It searches a given area of LANDSAT data with a 2x2 sliding window and computes gradient values for bands 5 and 7 to match the segment boundaries. The gradient values are held in memory during the shifting (or matching) process. The reconstructed segment array, containing ones (1's) for boundaries and zeros elsewhere are computer compared to the LANDSAT array and the best match computed. Initial testing of the ASMA indicates that it has good potential for replacing the manual technique.

Image denoising based on noise detection

NASA Astrophysics Data System (ADS)

Jiang, Yuanxiang; Yuan, Rui; Sun, Yuqiu; Tian, Jinwen

2018-03-01

Because of the noise points in the images, any operation of denoising would change the original information of non-noise pixel. A noise detection algorithm based on fractional calculus was proposed to denoise in this paper. Convolution of the image was made to gain direction gradient masks firstly. Then, the mean gray was calculated to obtain the gradient detection maps. Logical product was made to acquire noise position image next. Comparisons in the visual effect and evaluation parameters after processing, the results of experiment showed that the denoising algorithms based on noise were better than that of traditional methods in both subjective and objective aspects.

Stereo vision with distance and gradient recognition

NASA Astrophysics Data System (ADS)

Kim, Soo-Hyun; Kang, Suk-Bum; Yang, Tae-Kyu

2007-12-01

Robot vision technology is needed for the stable walking, object recognition and the movement to the target spot. By some sensors which use infrared rays and ultrasonic, robot can overcome the urgent state or dangerous time. But stereo vision of three dimensional space would make robot have powerful artificial intelligence. In this paper we consider about the stereo vision for stable and correct movement of a biped robot. When a robot confront with an inclination plane or steps, particular algorithms are needed to go on without failure. This study developed the recognition algorithm of distance and gradient of environment by stereo matching process.

Nonnegative least-squares image deblurring: improved gradient projection approaches

NASA Astrophysics Data System (ADS)

Benvenuto, F.; Zanella, R.; Zanni, L.; Bertero, M.

2010-02-01

The least-squares approach to image deblurring leads to an ill-posed problem. The addition of the nonnegativity constraint, when appropriate, does not provide regularization, even if, as far as we know, a thorough investigation of the ill-posedness of the resulting constrained least-squares problem has still to be done. Iterative methods, converging to nonnegative least-squares solutions, have been proposed. Some of them have the 'semi-convergence' property, i.e. early stopping of the iteration provides 'regularized' solutions. In this paper we consider two of these methods: the projected Landweber (PL) method and the iterative image space reconstruction algorithm (ISRA). Even if they work well in many instances, they are not frequently used in practice because, in general, they require a large number of iterations before providing a sensible solution. Therefore, the main purpose of this paper is to refresh these methods by increasing their efficiency. Starting from the remark that PL and ISRA require only the computation of the gradient of the functional, we propose the application to these algorithms of special acceleration techniques that have been recently developed in the area of the gradient methods. In particular, we propose the application of efficient step-length selection rules and line-search strategies. Moreover, remarking that ISRA is a scaled gradient algorithm, we evaluate its behaviour in comparison with a recent scaled gradient projection (SGP) method for image deblurring. Numerical experiments demonstrate that the accelerated methods still exhibit the semi-convergence property, with a considerable gain both in the number of iterations and in the computational time; in particular, SGP appears definitely the most efficient one.

Subpixel displacement measurement method based on the combination of particle swarm optimization and gradient algorithm

NASA Astrophysics Data System (ADS)

Guang, Chen; Qibo, Feng; Keqin, Ding; Zhan, Gao

2017-10-01

A subpixel displacement measurement method based on the combination of particle swarm optimization (PSO) and gradient algorithm (GA) was proposed for accuracy and speed optimization in GA, which is a subpixel displacement measurement method better applied in engineering practice. An initial integer-pixel value was obtained according to the global searching ability of PSO, and then gradient operators were adopted for a subpixel displacement search. A comparison was made between this method and GA by simulated speckle images and rigid-body displacement in metal specimens. The results showed that the computational accuracy of the combination of PSO and GA method reached 0.1 pixel in the simulated speckle images, or even 0.01 pixels in the metal specimen. Also, computational efficiency and the antinoise performance of the improved method were markedly enhanced.

Algorithm for ion beam figuring of low-gradient mirrors.

PubMed

Jiao, Changjun; Li, Shengyi; Xie, Xuhui

2009-07-20

Ion beam figuring technology for low-gradient mirrors is discussed. Ion beam figuring is a noncontact machining technique in which a beam of high-energy ions is directed toward a target workpiece to remove material in a predetermined and controlled fashion. Owing to this noncontact mode of material removal, problems associated with tool wear and edge effects, which are common in conventional contact polishing processes, are avoided. Based on the Bayesian principle, an iterative dwell time algorithm for planar mirrors is deduced from the computer-controlled optical surfacing (CCOS) principle. With the properties of the removal function, the shaping process of low-gradient mirrors can be approximated by the linear model for planar mirrors. With these discussions, the error surface figuring technology for low-gradient mirrors with a linear path is set up. With the near-Gaussian property of the removal function, the figuring process with a spiral path can be described by the conventional linear CCOS principle, and a Bayesian-based iterative algorithm can be used to deconvolute the dwell time. Moreover, the selection criterion of the spiral parameter is given. Ion beam figuring technology with a spiral scan path based on these methods can be used to figure mirrors with non-axis-symmetrical errors. Experiments on SiC chemical vapor deposition planar and Zerodur paraboloid samples are made, and the final surface errors are all below 1/100 lambda.

Active semi-supervised learning method with hybrid deep belief networks.

PubMed

Zhou, Shusen; Chen, Qingcai; Wang, Xiaolong

2014-01-01

In this paper, we develop a novel semi-supervised learning algorithm called active hybrid deep belief networks (AHD), to address the semi-supervised sentiment classification problem with deep learning. First, we construct the previous several hidden layers using restricted Boltzmann machines (RBM), which can reduce the dimension and abstract the information of the reviews quickly. Second, we construct the following hidden layers using convolutional restricted Boltzmann machines (CRBM), which can abstract the information of reviews effectively. Third, the constructed deep architecture is fine-tuned by gradient-descent based supervised learning with an exponential loss function. Finally, active learning method is combined based on the proposed deep architecture. We did several experiments on five sentiment classification datasets, and show that AHD is competitive with previous semi-supervised learning algorithm. Experiments are also conducted to verify the effectiveness of our proposed method with different number of labeled reviews and unlabeled reviews respectively.

A modified three-term PRP conjugate gradient algorithm for optimization models.

PubMed

Wu, Yanlin

2017-01-01

The nonlinear conjugate gradient (CG) algorithm is a very effective method for optimization, especially for large-scale problems, because of its low memory requirement and simplicity. Zhang et al. (IMA J. Numer. Anal. 26:629-649, 2006) firstly propose a three-term CG algorithm based on the well known Polak-Ribière-Polyak (PRP) formula for unconstrained optimization, where their method has the sufficient descent property without any line search technique. They proved the global convergence of the Armijo line search but this fails for the Wolfe line search technique. Inspired by their method, we will make a further study and give a modified three-term PRP CG algorithm. The presented method possesses the following features: (1) The sufficient descent property also holds without any line search technique; (2) the trust region property of the search direction is automatically satisfied; (3) the steplengh is bounded from below; (4) the global convergence will be established under the Wolfe line search. Numerical results show that the new algorithm is more effective than that of the normal method.

Hysteresis modeling of magnetic shape memory alloy actuator based on Krasnosel'skii-Pokrovskii model.

PubMed

Zhou, Miaolei; Wang, Shoubin; Gao, Wei

2013-01-01

As a new type of intelligent material, magnetically shape memory alloy (MSMA) has a good performance in its applications in the actuator manufacturing. Compared with traditional actuators, MSMA actuator has the advantages as fast response and large deformation; however, the hysteresis nonlinearity of the MSMA actuator restricts its further improving of control precision. In this paper, an improved Krasnosel'skii-Pokrovskii (KP) model is used to establish the hysteresis model of MSMA actuator. To identify the weighting parameters of the KP operators, an improved gradient correction algorithm and a variable step-size recursive least square estimation algorithm are proposed in this paper. In order to demonstrate the validity of the proposed modeling approach, simulation experiments are performed, simulations with improved gradient correction algorithm and variable step-size recursive least square estimation algorithm are studied, respectively. Simulation results of both identification algorithms demonstrate that the proposed modeling approach in this paper can establish an effective and accurate hysteresis model for MSMA actuator, and it provides a foundation for improving the control precision of MSMA actuator.

Hysteresis Modeling of Magnetic Shape Memory Alloy Actuator Based on Krasnosel'skii-Pokrovskii Model

PubMed Central

Wang, Shoubin; Gao, Wei

2013-01-01

As a new type of intelligent material, magnetically shape memory alloy (MSMA) has a good performance in its applications in the actuator manufacturing. Compared with traditional actuators, MSMA actuator has the advantages as fast response and large deformation; however, the hysteresis nonlinearity of the MSMA actuator restricts its further improving of control precision. In this paper, an improved Krasnosel'skii-Pokrovskii (KP) model is used to establish the hysteresis model of MSMA actuator. To identify the weighting parameters of the KP operators, an improved gradient correction algorithm and a variable step-size recursive least square estimation algorithm are proposed in this paper. In order to demonstrate the validity of the proposed modeling approach, simulation experiments are performed, simulations with improved gradient correction algorithm and variable step-size recursive least square estimation algorithm are studied, respectively. Simulation results of both identification algorithms demonstrate that the proposed modeling approach in this paper can establish an effective and accurate hysteresis model for MSMA actuator, and it provides a foundation for improving the control precision of MSMA actuator. PMID:23737730

Medial-based deformable models in nonconvex shape-spaces for medical image segmentation.

PubMed

McIntosh, Chris; Hamarneh, Ghassan

2012-01-01

We explore the application of genetic algorithms (GA) to deformable models through the proposition of a novel method for medical image segmentation that combines GA with nonconvex, localized, medial-based shape statistics. We replace the more typical gradient descent optimizer used in deformable models with GA, and the convex, implicit, global shape statistics with nonconvex, explicit, localized ones. Specifically, we propose GA to reduce typical deformable model weaknesses pertaining to model initialization, pose estimation and local minima, through the simultaneous evolution of a large number of models. Furthermore, we constrain the evolution, and thus reduce the size of the search-space, by using statistically-based deformable models whose deformations are intuitive (stretch, bulge, bend) and are driven in terms of localized principal modes of variation, instead of modes of variation across the entire shape that often fail to capture localized shape changes. Although GA are not guaranteed to achieve the global optima, our method compares favorably to the prevalent optimization techniques, convex/nonconvex gradient-based optimizers and to globally optimal graph-theoretic combinatorial optimization techniques, when applied to the task of corpus callosum segmentation in 50 mid-sagittal brain magnetic resonance images.

Analysis of Artificial Neural Network Backpropagation Using Conjugate Gradient Fletcher Reeves In The Predicting Process

NASA Astrophysics Data System (ADS)

Wanto, Anjar; Zarlis, Muhammad; Sawaluddin; Hartama, Dedy

2017-12-01

Backpropagation is a good artificial neural network algorithm used to predict, one of which is to predict the rate of Consumer Price Index (CPI) based on the foodstuff sector. While conjugate gradient fletcher reeves is a suitable optimization method when juxtaposed with backpropagation method, because this method can shorten iteration without reducing the quality of training and testing result. Consumer Price Index (CPI) data that will be predicted to come from the Central Statistics Agency (BPS) Pematangsiantar. The results of this study will be expected to contribute to the government in making policies to improve economic growth. In this study, the data obtained will be processed by conducting training and testing with artificial neural network backpropagation by using parameter learning rate 0,01 and target error minimum that is 0.001-0,09. The training network is built with binary and bipolar sigmoid activation functions. After the results with backpropagation are obtained, it will then be optimized using the conjugate gradient fletcher reeves method by conducting the same training and testing based on 5 predefined network architectures. The result, the method used can increase the speed and accuracy result.

Optimization-based image reconstruction in x-ray computed tomography by sparsity exploitation of local continuity and nonlocal spatial self-similarity

NASA Astrophysics Data System (ADS)

Han-Ming, Zhang; Lin-Yuan, Wang; Lei, Li; Bin, Yan; Ai-Long, Cai; Guo-En, Hu

2016-07-01

The additional sparse prior of images has been the subject of much research in problems of sparse-view computed tomography (CT) reconstruction. A method employing the image gradient sparsity is often used to reduce the sampling rate and is shown to remove the unwanted artifacts while preserve sharp edges, but may cause blocky or patchy artifacts. To eliminate this drawback, we propose a novel sparsity exploitation-based model for CT image reconstruction. In the presented model, the sparse representation and sparsity exploitation of both gradient and nonlocal gradient are investigated. The new model is shown to offer the potential for better results by introducing a similarity prior information of the image structure. Then, an effective alternating direction minimization algorithm is developed to optimize the objective function with a robust convergence result. Qualitative and quantitative evaluations have been carried out both on the simulation and real data in terms of accuracy and resolution properties. The results indicate that the proposed method can be applied for achieving better image-quality potential with the theoretically expected detailed feature preservation. Project supported by the National Natural Science Foundation of China (Grant No. 61372172).

GPU-accelerated adjoint algorithmic differentiation

NASA Astrophysics Data System (ADS)

Gremse, Felix; Höfter, Andreas; Razik, Lukas; Kiessling, Fabian; Naumann, Uwe

2016-03-01

Many scientific problems such as classifier training or medical image reconstruction can be expressed as minimization of differentiable real-valued cost functions and solved with iterative gradient-based methods. Adjoint algorithmic differentiation (AAD) enables automated computation of gradients of such cost functions implemented as computer programs. To backpropagate adjoint derivatives, excessive memory is potentially required to store the intermediate partial derivatives on a dedicated data structure, referred to as the ;tape;. Parallelization is difficult because threads need to synchronize their accesses during taping and backpropagation. This situation is aggravated for many-core architectures, such as Graphics Processing Units (GPUs), because of the large number of light-weight threads and the limited memory size in general as well as per thread. We show how these limitations can be mediated if the cost function is expressed using GPU-accelerated vector and matrix operations which are recognized as intrinsic functions by our AAD software. We compare this approach with naive and vectorized implementations for CPUs. We use four increasingly complex cost functions to evaluate the performance with respect to memory consumption and gradient computation times. Using vectorization, CPU and GPU memory consumption could be substantially reduced compared to the naive reference implementation, in some cases even by an order of complexity. The vectorization allowed usage of optimized parallel libraries during forward and reverse passes which resulted in high speedups for the vectorized CPU version compared to the naive reference implementation. The GPU version achieved an additional speedup of 7.5 ± 4.4, showing that the processing power of GPUs can be utilized for AAD using this concept. Furthermore, we show how this software can be systematically extended for more complex problems such as nonlinear absorption reconstruction for fluorescence-mediated tomography.

GRAPPA reconstructed wave-CAIPI MP-RAGE at 7 Tesla.

PubMed

Schwarz, Jolanda M; Pracht, Eberhard D; Brenner, Daniel; Reuter, Martin; Stöcker, Tony

2018-04-16

The aim of this project was to develop a GRAPPA-based reconstruction for wave-CAIPI data. Wave-CAIPI fully exploits the 3D coil sensitivity variations by combining corkscrew k-space trajectories with CAIPIRINHA sampling. It reduces artifacts and limits reconstruction induced spatially varying noise enhancement. The GRAPPA-based wave-CAIPI method is robust and does not depend on the accuracy of coil sensitivity estimations. We developed a GRAPPA-based, noniterative wave-CAIPI reconstruction algorithm utilizing multiple GRAPPA kernels. For data acquisition, we implemented a fast 3D magnetization-prepared rapid gradient-echo wave-CAIPI sequence tailored for ultra-high field application. The imaging results were evaluated by comparing the g-factor and the root mean square error to Cartesian CAIPIRINHA acquisitions. Additionally, to assess the performance of subcortical segmentations (calculated by FreeSurfer), the data were analyzed across five subjects. Sixteen-fold accelerated whole brain magnetization-prepared rapid gradient-echo data (1 mm isotropic resolution) were acquired in 40 seconds at 7T. A clear improvement in image quality compared to Cartesian CAIPIRINHA sampling was observed. For the chosen imaging protocol, the results of 16-fold accelerated wave-CAIPI acquisitions were comparable to results of 12-fold accelerated Cartesian CAIPIRINHA. In comparison to the originally proposed SENSitivity Encoding reconstruction of Wave-CAIPI data, the GRAPPA approach provided similar image quality. High-quality, wave-CAIPI magnetization-prepared rapid gradient-echo images can be reconstructed by means of a GRAPPA-based reconstruction algorithm. Even for high acceleration factors, the noniterative reconstruction is robust and does not require coil sensitivity estimations. By altering the aliasing pattern, ultra-fast whole-brain structural imaging becomes feasible. © 2018 International Society for Magnetic Resonance in Medicine.

GPU-Accelerated Adjoint Algorithmic Differentiation.

PubMed

Gremse, Felix; Höfter, Andreas; Razik, Lukas; Kiessling, Fabian; Naumann, Uwe

2016-03-01

Many scientific problems such as classifier training or medical image reconstruction can be expressed as minimization of differentiable real-valued cost functions and solved with iterative gradient-based methods. Adjoint algorithmic differentiation (AAD) enables automated computation of gradients of such cost functions implemented as computer programs. To backpropagate adjoint derivatives, excessive memory is potentially required to store the intermediate partial derivatives on a dedicated data structure, referred to as the "tape". Parallelization is difficult because threads need to synchronize their accesses during taping and backpropagation. This situation is aggravated for many-core architectures, such as Graphics Processing Units (GPUs), because of the large number of light-weight threads and the limited memory size in general as well as per thread. We show how these limitations can be mediated if the cost function is expressed using GPU-accelerated vector and matrix operations which are recognized as intrinsic functions by our AAD software. We compare this approach with naive and vectorized implementations for CPUs. We use four increasingly complex cost functions to evaluate the performance with respect to memory consumption and gradient computation times. Using vectorization, CPU and GPU memory consumption could be substantially reduced compared to the naive reference implementation, in some cases even by an order of complexity. The vectorization allowed usage of optimized parallel libraries during forward and reverse passes which resulted in high speedups for the vectorized CPU version compared to the naive reference implementation. The GPU version achieved an additional speedup of 7.5 ± 4.4, showing that the processing power of GPUs can be utilized for AAD using this concept. Furthermore, we show how this software can be systematically extended for more complex problems such as nonlinear absorption reconstruction for fluorescence-mediated tomography.

GPU-Accelerated Adjoint Algorithmic Differentiation

PubMed Central

Gremse, Felix; Höfter, Andreas; Razik, Lukas; Kiessling, Fabian; Naumann, Uwe

2015-01-01

Many scientific problems such as classifier training or medical image reconstruction can be expressed as minimization of differentiable real-valued cost functions and solved with iterative gradient-based methods. Adjoint algorithmic differentiation (AAD) enables automated computation of gradients of such cost functions implemented as computer programs. To backpropagate adjoint derivatives, excessive memory is potentially required to store the intermediate partial derivatives on a dedicated data structure, referred to as the “tape”. Parallelization is difficult because threads need to synchronize their accesses during taping and backpropagation. This situation is aggravated for many-core architectures, such as Graphics Processing Units (GPUs), because of the large number of light-weight threads and the limited memory size in general as well as per thread. We show how these limitations can be mediated if the cost function is expressed using GPU-accelerated vector and matrix operations which are recognized as intrinsic functions by our AAD software. We compare this approach with naive and vectorized implementations for CPUs. We use four increasingly complex cost functions to evaluate the performance with respect to memory consumption and gradient computation times. Using vectorization, CPU and GPU memory consumption could be substantially reduced compared to the naive reference implementation, in some cases even by an order of complexity. The vectorization allowed usage of optimized parallel libraries during forward and reverse passes which resulted in high speedups for the vectorized CPU version compared to the naive reference implementation. The GPU version achieved an additional speedup of 7.5 ± 4.4, showing that the processing power of GPUs can be utilized for AAD using this concept. Furthermore, we show how this software can be systematically extended for more complex problems such as nonlinear absorption reconstruction for fluorescence-mediated tomography. PMID:26941443

Optimal trajectories of aircraft and spacecraft

NASA Technical Reports Server (NTRS)

Miele, A.

1990-01-01

Work done on algorithms for the numerical solutions of optimal control problems and their application to the computation of optimal flight trajectories of aircraft and spacecraft is summarized. General considerations on calculus of variations, optimal control, numerical algorithms, and applications of these algorithms to real-world problems are presented. The sequential gradient-restoration algorithm (SGRA) is examined for the numerical solution of optimal control problems of the Bolza type. Both the primal formulation and the dual formulation are discussed. Aircraft trajectories, in particular, the application of the dual sequential gradient-restoration algorithm (DSGRA) to the determination of optimal flight trajectories in the presence of windshear are described. Both take-off trajectories and abort landing trajectories are discussed. Take-off trajectories are optimized by minimizing the peak deviation of the absolute path inclination from a reference value. Abort landing trajectories are optimized by minimizing the peak drop of altitude from a reference value. Abort landing trajectories are optimized by minimizing the peak drop of altitude from a reference value. The survival capability of an aircraft in a severe windshear is discussed, and the optimal trajectories are found to be superior to both constant pitch trajectories and maximum angle of attack trajectories. Spacecraft trajectories, in particular, the application of the primal sequential gradient-restoration algorithm (PSGRA) to the determination of optimal flight trajectories for aeroassisted orbital transfer are examined. Both the coplanar case and the noncoplanar case are discussed within the frame of three problems: minimization of the total characteristic velocity; minimization of the time integral of the square of the path inclination; and minimization of the peak heating rate. The solution of the second problem is called nearly-grazing solution, and its merits are pointed out as a useful engineering compromise between energy requirements and aerodynamics heating requirements.

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.

Improvement of resolution in full-view linear-array photoacoustic computed tomography using a novel adaptive weighting method

NASA Astrophysics Data System (ADS)

Omidi, Parsa; Diop, Mamadou; Carson, Jeffrey; Nasiriavanaki, Mohammadreza

2017-03-01

Linear-array-based photoacoustic computed tomography is a popular methodology for deep and high resolution imaging. However, issues such as phase aberration, side-lobe effects, and propagation limitations deteriorate the resolution. The effect of phase aberration due to acoustic attenuation and constant assumption of the speed of sound (SoS) can be reduced by applying an adaptive weighting method such as the coherence factor (CF). Utilizing an adaptive beamforming algorithm such as the minimum variance (MV) can improve the resolution at the focal point by eliminating the side-lobes. Moreover, invisibility of directional objects emitting parallel to the detection plane, such as vessels and other absorbing structures stretched in the direction perpendicular to the detection plane can degrade resolution. In this study, we propose a full-view array level weighting algorithm in which different weighs are assigned to different positions of the linear array based on an orientation algorithm which uses the histogram of oriented gradient (HOG). Simulation results obtained from a synthetic phantom show the superior performance of the proposed method over the existing reconstruction methods.

A combined finite element-boundary integral formulation for solution of two-dimensional scattering problems via CGFFT. [Conjugate Gradient Fast Fourier Transformation

NASA Technical Reports Server (NTRS)

Collins, Jeffery D.; Volakis, John L.; Jin, Jian-Ming

1990-01-01

A new technique is presented for computing the scattering by 2-D structures of arbitrary composition. The proposed solution approach combines the usual finite element method with the boundary-integral equation to formulate a discrete system. This is subsequently solved via the conjugate gradient (CG) algorithm. A particular characteristic of the method is the use of rectangular boundaries to enclose the scatterer. Several of the resulting boundary integrals are therefore convolutions and may be evaluated via the fast Fourier transform (FFT) in the implementation of the CG algorithm. The solution approach offers the principal advantage of having O(N) memory demand and employs a 1-D FFT versus a 2-D FFT as required with a traditional implementation of the CGFFT algorithm. The speed of the proposed solution method is compared with that of the traditional CGFFT algorithm, and results for rectangular bodies are given and shown to be in excellent agreement with the moment method.

Coordinated Beamforming for MISO Interference Channel: Complexity Analysis and Efficient Algorithms

DTIC Science & Technology

2010-01-01

Algorithm The cyclic coordinate descent algorithm is also known as the nonlinear Gauss - Seidel iteration [32]. There are several studies of this type of...vkρ(vi−1). It can be shown that the above BB gradient projection direction is always a descent direction. The R-linear convergence of the BB method has...KKT solution ) of the inexact pricing algorithm for MISO interference channel. The latter is interesting since the convergence of the original pricing

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.

Filtering Airborne LIDAR Data by AN Improved Morphological Method Based on Multi-Gradient Analysis

NASA Astrophysics Data System (ADS)

Li, Y.

2013-05-01

The technology of airborne Light Detection And Ranging (LIDAR) is capable of acquiring dense and accurate 3D geospatial data. Although many related efforts have been made by a lot of researchers in the last few years, LIDAR data filtering is still a challenging task, especially for area with high relief or hybrid geographic features. In order to address the bare-ground extraction from LIDAR point clouds of complex landscapes, a novel morphological filtering algorithm is proposed based on multi-gradient analysis in terms of the characteristic of LIDAR data distribution in this paper. Firstly, point clouds are organized by an index mesh. Then, the multigradient of each point is calculated using the morphological method. And, objects are removed gradually by choosing some points to carry on an improved opening operation constrained by multi-gradient iteratively. 15 sample data provided by ISPRS Working Group III/3 are employed to test the filtering algorithm proposed. These sample data include those environments that may lead to filtering difficulty. Experimental results show that filtering algorithm proposed by this paper is of high adaptability to various scenes including urban and rural areas. Omission error, commission error and total error can be simultaneously controlled in a relatively small interval. This algorithm can efficiently remove object points while preserves ground points to a great degree.

Iterative reconstruction methods in atmospheric tomography: FEWHA, Kaczmarz and Gradient-based algorithm

NASA Astrophysics Data System (ADS)

Ramlau, R.; Saxenhuber, D.; Yudytskiy, M.

2014-07-01

The problem of atmospheric tomography arises in ground-based telescope imaging with adaptive optics (AO), where one aims to compensate in real-time for the rapidly changing optical distortions in the atmosphere. Many of these systems depend on a sufficient reconstruction of the turbulence profiles in order to obtain a good correction. Due to steadily growing telescope sizes, there is a strong increase in the computational load for atmospheric reconstruction with current methods, first and foremost the MVM. In this paper we present and compare three novel iterative reconstruction methods. The first iterative approach is the Finite Element- Wavelet Hybrid Algorithm (FEWHA), which combines wavelet-based techniques and conjugate gradient schemes to efficiently and accurately tackle the problem of atmospheric reconstruction. The method is extremely fast, highly flexible and yields superior quality. Another novel iterative reconstruction algorithm is the three step approach which decouples the problem in the reconstruction of the incoming wavefronts, the reconstruction of the turbulent layers (atmospheric tomography) and the computation of the best mirror correction (fitting step). For the atmospheric tomography problem within the three step approach, the Kaczmarz algorithm and the Gradient-based method have been developed. We present a detailed comparison of our reconstructors both in terms of quality and speed performance in the context of a Multi-Object Adaptive Optics (MOAO) system for the E-ELT setting on OCTOPUS, the ESO end-to-end simulation tool.

MO-F-CAMPUS-T-01: Radiosurgery of Multiple Brain Metastases with Single-Isocenter VMAT: Optimizing Treatment Geometry to Reduce Normal Brain Dose

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

Wu, Q; Snyder, K; Liu, C

Purpose: To develop an optimization algorithm to reduce normal brain dose by optimizing couch and collimator angles for single isocenter multiple targets treatment of stereotactic radiosurgery. Methods: Three metastatic brain lesions were retrospectively planned using single-isocenter volumetric modulated arc therapy (VMAT). Three matrices were developed to calculate the projection of each lesion on Beam’s Eye View (BEV) by the rotating couch, collimator and gantry respectively. The island blocking problem was addressed by computing the total area of open space between any two lesions with shared MLC leaf pairs. The couch and collimator angles resulting in the smallest open areas weremore » the optimized angles for each treatment arc. Two treatment plans with and without couch and collimator angle optimization were developed using the same objective functions and to achieve 99% of each target volume receiving full prescription dose of 18Gy. Plan quality was evaluated by calculating each target’s Conformity Index (CI), Gradient Index (GI), and Homogeneity index (HI), and absolute volume of normal brain V8Gy, V10Gy, V12Gy, and V14Gy. Results: Using the new couch/collimator optimization strategy, dose to normal brain tissue was reduced substantially. V8, V10, V12, and V14 decreased by 2.3%, 3.6%, 3.5%, and 6%, respectively. There were no significant differences in the conformity index, gradient index, and homogeneity index between two treatment plans with and without the new optimization algorithm. Conclusion: We have developed a solution to the island blocking problem in delivering radiation to multiple brain metastases with shared isocenter. Significant reduction in dose to normal brain was achieved by using optimal couch and collimator angles that minimize total area of open space between any of the two lesions with shared MLC leaf pairs. This technique has been integrated into Eclipse treatment system using scripting API.« less

Algorithm for the Evaluation of Imperfections in Auto Bodywork Using Profiles from a Retroreflective Image

PubMed Central

Barber, Ramon; Zwilling, Valerie; Salichs, Miguel A.

2014-01-01

Nowadays the automobile industry is becoming more and more demanding as far as quality is concerned. Within the wide variety of processes in which this quality must be ensured, those regarding the squeezing of the auto bodywork are especially important due to the fact that the quality of the resulting product is tested manually by experts, leading to inaccuracies of all types. In this paper, an algorithm is proposed for the automated evaluation of the imperfections in the sheets of the bodywork after the squeezing process. The algorithm processes the profile signals from a retroreflective image and characterizes an imperfection. It is based on a convergence criterion that follows the line of the maximum gradient of the imperfection and gives its geometrical characteristics as a result: maximum gradient, length, width, and area. PMID:24504105

Algorithm for the evaluation of imperfections in auto bodywork using profiles from a retroreflective image.

PubMed

Barber, Ramon; Zwilling, Valerie; Salichs, Miguel A

2014-02-05

Nowadays the automobile industry is becoming more and more demanding as far as quality is concerned. Within the wide variety of processes in which this quality must be ensured, those regarding the squeezing of the auto bodywork are especially important due to the fact that the quality of the resulting product is tested manually by experts, leading to inaccuracies of all types. In this paper, an algorithm is proposed for the automated evaluation of the imperfections in the sheets of the bodywork after the squeezing process. The algorithm processes the profile signals from a retroreflective image and characterizes an imperfection. It is based on a convergence criterion that follows the line of the maximum gradient of the imperfection and gives its geometrical characteristics as a result: maximum gradient, length, width, and area.

Multi-sensor image fusion algorithm based on multi-objective particle swarm optimization algorithm

NASA Astrophysics Data System (ADS)

Xie, Xia-zhu; Xu, Ya-wei

2017-11-01

On the basis of DT-CWT (Dual-Tree Complex Wavelet Transform - DT-CWT) theory, an approach based on MOPSO (Multi-objective Particle Swarm Optimization Algorithm) was proposed to objectively choose the fused weights of low frequency sub-bands. High and low frequency sub-bands were produced by DT-CWT. Absolute value of coefficients was adopted as fusion rule to fuse high frequency sub-bands. Fusion weights in low frequency sub-bands were used as particles in MOPSO. Spatial Frequency and Average Gradient were adopted as two kinds of fitness functions in MOPSO. The experimental result shows that the proposed approach performances better than Average Fusion and fusion methods based on local variance and local energy respectively in brightness, clarity and quantitative evaluation which includes Entropy, Spatial Frequency, Average Gradient and QAB/F.

Accelerated gradient based diffuse optical tomographic image reconstruction.

PubMed

Biswas, Samir Kumar; Rajan, K; Vasu, R M

2011-01-01

Fast reconstruction of interior optical parameter distribution using a new approach called Broyden-based model iterative image reconstruction (BMOBIIR) and adjoint Broyden-based MOBIIR (ABMOBIIR) of a tissue and a tissue mimicking phantom from boundary measurement data in diffuse optical tomography (DOT). DOT is a nonlinear and ill-posed inverse problem. Newton-based MOBIIR algorithm, which is generally used, requires repeated evaluation of the Jacobian which consumes bulk of the computation time for reconstruction. In this study, we propose a Broyden approach-based accelerated scheme for Jacobian computation and it is combined with conjugate gradient scheme (CGS) for fast reconstruction. The method makes explicit use of secant and adjoint information that can be obtained from forward solution of the diffusion equation. This approach reduces the computational time many fold by approximating the system Jacobian successively through low-rank updates. Simulation studies have been carried out with single as well as multiple inhomogeneities. Algorithms are validated using an experimental study carried out on a pork tissue with fat acting as an inhomogeneity. The results obtained through the proposed BMOBIIR and ABMOBIIR approaches are compared with those of Newton-based MOBIIR algorithm. The mean squared error and execution time are used as metrics for comparing the results of reconstruction. We have shown through experimental and simulation studies that Broyden-based MOBIIR and adjoint Broyden-based methods are capable of reconstructing single as well as multiple inhomogeneities in tissue and a tissue-mimicking phantom. Broyden MOBIIR and adjoint Broyden MOBIIR methods are computationally simple and they result in much faster implementations because they avoid direct evaluation of Jacobian. The image reconstructions have been carried out with different initial values using Newton, Broyden, and adjoint Broyden approaches. These algorithms work well when the initial guess is close to the true solution. However, when initial guess is far away from true solution, Newton-based MOBIIR gives better reconstructed images. The proposed methods are found to be stable with noisy measurement data.

Fast inversion of gravity data using the symmetric successive over-relaxation (SSOR) preconditioned conjugate gradient algorithm

NASA Astrophysics Data System (ADS)

Meng, Zhaohai; Li, Fengting; Xu, Xuechun; Huang, Danian; Zhang, Dailei

2017-02-01

The subsurface three-dimensional (3D) model of density distribution is obtained by solving an under-determined linear equation that is established by gravity data. Here, we describe a new fast gravity inversion method to recover a 3D density model from gravity data. The subsurface will be divided into a large number of rectangular blocks, each with an unknown constant density. The gravity inversion method introduces a stabiliser model norm with a depth weighting function to produce smooth models. The depth weighting function is combined with the model norm to counteract the skin effect of the gravity potential field. As the numbers of density model parameters is NZ (the number of layers in the vertical subsurface domain) times greater than the observed gravity data parameters, the inverse density parameter is larger than the observed gravity data parameters. Solving the full set of gravity inversion equations is very time-consuming, and applying a new algorithm to estimate gravity inversion can significantly reduce the number of iterations and the computational time. In this paper, a new symmetric successive over-relaxation (SSOR) iterative conjugate gradient (CG) method is shown to be an appropriate algorithm to solve this Tikhonov cost function (gravity inversion equation). The new, faster method is applied on Gaussian noise-contaminated synthetic data to demonstrate its suitability for 3D gravity inversion. To demonstrate the performance of the new algorithm on actual gravity data, we provide a case study that includes ground-based measurement of residual Bouguer gravity anomalies over the Humble salt dome near Houston, Gulf Coast Basin, off the shore of Louisiana. A 3D distribution of salt rock concentration is used to evaluate the inversion results recovered by the new SSOR iterative method. In the test model, the density values in the constructed model coincide with the known location and depth of the salt dome.

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.

Fast conjugate phase image reconstruction based on a Chebyshev approximation to correct for B0 field inhomogeneity and concomitant gradients.

PubMed

Chen, Weitian; Sica, Christopher T; Meyer, Craig H

2008-11-01

Off-resonance effects can cause image blurring in spiral scanning and various forms of image degradation in other MRI methods. Off-resonance effects can be caused by both B0 inhomogeneity and concomitant gradient fields. Previously developed off-resonance correction methods focus on the correction of a single source of off-resonance. This work introduces a computationally efficient method of correcting for B0 inhomogeneity and concomitant gradients simultaneously. The method is a fast alternative to conjugate phase reconstruction, with the off-resonance phase term approximated by Chebyshev polynomials. The proposed algorithm is well suited for semiautomatic off-resonance correction, which works well even with an inaccurate or low-resolution field map. The proposed algorithm is demonstrated using phantom and in vivo data sets acquired by spiral scanning. Semiautomatic off-resonance correction alone is shown to provide a moderate amount of correction for concomitant gradient field effects, in addition to B0 imhomogeneity effects. However, better correction is provided by the proposed combined method. The best results were produced using the semiautomatic version of the proposed combined method.

An ``Openable,'' High-Strength Gradient Set for Orthopedic MRI

NASA Astrophysics Data System (ADS)

Crozier, Stuart; Roffmann, Wolfgang U.; Luescher, Kurt; Snape-Jenkinson, Christopher; Forbes, Lawrence K.; Doddrell, David M.

1999-07-01

A novel three-axis gradient set and RF resonator for orthopedic MRI has been designed and constructed. The set is openable and may be wrapped around injured joints. The design methodology used was the minimization of magnetic field spherical harmonics by simulated annealing. Splitting of the longitudinal coil presents the major design challenge to a fully openable gradient set and in order to efficiently design such coils, we have developed a new fast algorithm for determining the magnetic field spherical harmonics generated by an arc of multiturn wire. The algorithm allows a realistic impression of the effect of split longitudinal designs. A prototype set was constructed based on the new designs and tested in a 2-T clinical research system. The set generated 12 mT/m/A with a linear region of 12 cm and a switching time of 100 μs, conforming closely with theoretical predictions. Preliminary images from the set are presented.

Investigation on improved infrared image detail enhancement algorithm based on adaptive histogram statistical stretching and gradient filtering

NASA Astrophysics Data System (ADS)

Zeng, Bangze; Zhu, Youpan; Li, Zemin; Hu, Dechao; Luo, Lin; Zhao, Deli; Huang, Juan

2014-11-01

Duo to infrared image with low contrast, big noise and unclear visual effect, target is very difficult to observed and identified. This paper presents an improved infrared image detail enhancement algorithm based on adaptive histogram statistical stretching and gradient filtering (AHSS-GF). Based on the fact that the human eyes are very sensitive to the edges and lines, the author proposed to extract the details and textures by using the gradient filtering. New histogram could be acquired by calculating the sum of original histogram based on fixed window. With the minimum value for cut-off point, author carried on histogram statistical stretching. After the proper weights given to the details and background, the detail-enhanced results could be acquired finally. The results indicate image contrast could be improved and the details and textures could be enhanced effectively as well.

Optimization of diffusion-weighted single-refocused spin-echo EPI by reducing eddy-current artifacts and shortening the echo time.

PubMed

Shrestha, Manoj; Hok, Pavel; Nöth, Ulrike; Lienerth, Bianca; Deichmann, Ralf

2018-03-30

The purpose of this work was to optimize the acquisition of diffusion-weighted (DW) single-refocused spin-echo (srSE) data without intrinsic eddy-current compensation (ECC) for an improved performance of ECC postprocessing. The rationale is that srSE sequences without ECC may yield shorter echo times (TE) and thus higher signal-to-noise ratios (SNR) than srSE or twice-refocused spin-echo (trSE) schemes with intrinsic ECC. The proposed method employs dummy scans with DW gradients to drive eddy currents into a steady state before data acquisition. Parameters of the ECC postprocessing algorithm were also optimized. Simulations were performed to obtain minimum TE values for the proposed sequence and sequences with intrinsic ECC. Experimentally, the proposed method was compared with standard DW-trSE imaging, both in vitro and in vivo. Simulations showed substantially shorter TE for the proposed method than for methods with intrinsic ECC when using shortened echo readouts. Data of the proposed method showed a marked increase in SNR. A dummy scan duration of at least 1.5 s improved performance of the ECC postprocessing algorithm. Changes proposed for the DW-srSE sequence and for the parameter setting of the postprocessing ECC algorithm considerably reduced eddy-current artifacts and provided a higher SNR.

An objective algorithm for reconstructing the three-dimensional ocean temperature field based on Argo profiles and SST data

NASA Astrophysics Data System (ADS)

Zhou, Chaojie; Ding, Xiaohua; Zhang, Jie; Yang, Jungang; Ma, Qiang

2017-12-01

While global oceanic surface information with large-scale, real-time, high-resolution data is collected by satellite remote sensing instrumentation, three-dimensional (3D) observations are usually obtained from in situ measurements, but with minimal coverage and spatial resolution. To meet the needs of 3D ocean investigations, we have developed a new algorithm to reconstruct the 3D ocean temperature field based on the Array for Real-time Geostrophic Oceanography (Argo) profiles and sea surface temperature (SST) data. The Argo temperature profiles are first optimally fitted to generate a series of temperature functions of depth, with the vertical temperature structure represented continuously. By calculating the derivatives of the fitted functions, the calculation of the vertical temperature gradient of the Argo profiles at an arbitrary depth is accomplished. A gridded 3D temperature gradient field is then found by applying inverse distance weighting interpolation in the horizontal direction. Combined with the processed SST, the 3D temperature field reconstruction is realized below the surface using the gridded temperature gradient. Finally, to confirm the effectiveness of the algorithm, an experiment in the Pacific Ocean south of Japan is conducted, for which a 3D temperature field is generated. Compared with other similar gridded products, the reconstructed 3D temperature field derived by the proposed algorithm achieves satisfactory accuracy, with correlation coefficients of 0.99 obtained, including a higher spatial resolution (0.25° × 0.25°), resulting in the capture of smaller-scale characteristics. Finally, both the accuracy and the superiority of the algorithm are validated.

Influence of measuring algorithm on shape accuracy in the compensating turning of high gradient thin-wall parts

NASA Astrophysics Data System (ADS)

Wang, Tao; Wang, Guilin; Zhu, Dengchao; Li, Shengyi

2015-02-01

In order to meet the requirement of aerodynamics, the infrared domes or windows with conformal and thin-wall structure becomes the development trend of high-speed aircrafts in the future. But these parts usually have low stiffness, the cutting force will change along with the axial position, and it is very difficult to meet the requirement of shape accuracy by single machining. Therefore, on-machine measurement and compensating turning are used to control the shape errors caused by the fluctuation of cutting force and the change of stiffness. In this paper, on the basis of ultra precision diamond lathe, a contact measuring system with five DOFs is developed to achieve on-machine measurement of conformal thin-wall parts with high accuracy. According to high gradient surface, the optimizing algorithm is designed on the distribution of measuring points by using the data screening method. The influence rule of sampling frequency is analyzed on measuring errors, the best sampling frequency is found out based on planning algorithm, the effect of environmental factors and the fitting errors are controlled within lower range, and the measuring accuracy of conformal dome is greatly improved in the process of on-machine measurement. According to MgF2 conformal dome with high gradient, the compensating turning is implemented by using the designed on-machine measuring algorithm. The shape error is less than PV 0.8μm, greatly superior compared with PV 3μm before compensating turning, which verifies the correctness of measuring algorithm.

Numerical simulations of detonation propagation in gaseous fuel-air mixtures

NASA Astrophysics Data System (ADS)

Honhar, Praveen; Kaplan, Carolyn; Houim, Ryan; Oran, Elaine

2017-11-01

Unsteady multidimensional numerical simulations of detonation propagation and survival in mixtures of fuel (hydrogen or methane) diluted with air were carried out with a fully compressible Navier-Stokes solver using a simplified chemical-diffusive model (CDM). The CDM was derived using a genetic algorithm combined with the Nelder-Mead optimization algorithm and reproduces physically correct laminar flame and detonation properties. Cases studied are overdriven detonations propagating through confined mediums, with or without gradients in composition. Results from simulations confirm that the survival of the detonation depends on the channel heights. In addition, the simulations show that the propagation of the detonation waves depends on the steepness in composition gradients.

A new optimal seam method for seamless image stitching

NASA Astrophysics Data System (ADS)

Xue, Jiale; Chen, Shengyong; Cheng, Xu; Han, Ying; Zhao, Meng

2017-07-01

A novel optimal seam method which aims to stitch those images with overlapping area more seamlessly has been propos ed. Considering the traditional gradient domain optimal seam method and fusion algorithm result in bad color difference measurement and taking a long time respectively, the input images would be converted to HSV space and a new energy function is designed to seek optimal stitching path. To smooth the optimal stitching path, a simplified pixel correction and weighted average method are utilized individually. The proposed methods exhibit performance in eliminating the stitching seam compared with the traditional gradient optimal seam and high efficiency with multi-band blending algorithm.

Stan : A Probabilistic Programming Language

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

Carpenter, Bob; Gelman, Andrew; Hoffman, Matthew D.

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Stan is also a platform for computing log densities and their gradients and Hessians, which can be used in alternative algorithms such as variational Bayes, expectationmore » propagation, and marginal inference using approximate integration. To this end, Stan is set up so that the densities, gradients, and Hessians, along with intermediate quantities of the algorithm such as acceptance probabilities, are easily accessible. Stan can also be called from the command line using the cmdstan package, through R using the rstan package, and through Python using the pystan package. All three interfaces support sampling and optimization-based inference with diagnostics and posterior analysis. rstan and pystan also provide access to log probabilities, gradients, Hessians, parameter transforms, and specialized plotting.« less

Blind separation of positive sources by globally convergent gradient search.

PubMed

Oja, Erkki; Plumbley, Mark

2004-09-01

The instantaneous noise-free linear mixing model in independent component analysis is largely a solved problem under the usual assumption of independent nongaussian sources and full column rank mixing matrix. However, with some prior information on the sources, like positivity, new analysis and perhaps simplified solution methods may yet become possible. In this letter, we consider the task of independent component analysis when the independent sources are known to be nonnegative and well grounded, which means that they have a nonzero pdf in the region of zero. It can be shown that in this case, the solution method is basically very simple: an orthogonal rotation of the whitened observation vector into nonnegative outputs will give a positive permutation of the original sources. We propose a cost function whose minimum coincides with nonnegativity and derive the gradient algorithm under the whitening constraint, under which the separating matrix is orthogonal. We further prove that in the Stiefel manifold of orthogonal matrices, the cost function is a Lyapunov function for the matrix gradient flow, implying global convergence. Thus, this algorithm is guaranteed to find the nonnegative well-grounded independent sources. The analysis is complemented by a numerical simulation, which illustrates the algorithm.

Pixel-By Estimation of Scene Motion in Video

NASA Astrophysics Data System (ADS)

Tashlinskii, A. G.; Smirnov, P. V.; Tsaryov, M. G.

2017-05-01

The paper considers the effectiveness of motion estimation in video using pixel-by-pixel recurrent algorithms. The algorithms use stochastic gradient decent to find inter-frame shifts of all pixels of a frame. These vectors form shift vectors' field. As estimated parameters of the vectors the paper studies their projections and polar parameters. It considers two methods for estimating shift vectors' field. The first method uses stochastic gradient descent algorithm to sequentially process all nodes of the image row-by-row. It processes each row bidirectionally i.e. from the left to the right and from the right to the left. Subsequent joint processing of the results allows compensating inertia of the recursive estimation. The second method uses correlation between rows to increase processing efficiency. It processes rows one after the other with the change in direction after each row and uses obtained values to form resulting estimate. The paper studies two criteria of its formation: gradient estimation minimum and correlation coefficient maximum. The paper gives examples of experimental results of pixel-by-pixel estimation for a video with a moving object and estimation of a moving object trajectory using shift vectors' field.

Stan : A Probabilistic Programming Language

DOE PAGES

Carpenter, Bob; Gelman, Andrew; Hoffman, Matthew D.; ...

2017-01-01

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Stan is also a platform for computing log densities and their gradients and Hessians, which can be used in alternative algorithms such as variational Bayes, expectationmore » propagation, and marginal inference using approximate integration. To this end, Stan is set up so that the densities, gradients, and Hessians, along with intermediate quantities of the algorithm such as acceptance probabilities, are easily accessible. Stan can also be called from the command line using the cmdstan package, through R using the rstan package, and through Python using the pystan package. All three interfaces support sampling and optimization-based inference with diagnostics and posterior analysis. rstan and pystan also provide access to log probabilities, gradients, Hessians, parameter transforms, and specialized plotting.« less

A passive microwave snow depth algorithm with a proxy for snow metamorphism

USGS Publications Warehouse

Josberger, E.G.; Mognard, N.M.

2002-01-01

Passive microwave brightness temperatures of snowpacks depend not only on the snow depth, but also on the internal snowpack properties, particularly the grain size, which changes through the winter. Algorithms that assume a constant grain size can yield erroneous estimates of snow depth or water equivalent. For snowpacks that are subject to temperatures well below freezing, the bulk temperature gradient through the snowpack controls the metamorphosis of the snow grains. This study used National Weather Service (NWS) station measurements of snow depth and air temperature from the Northern US Great Plains to determine temporal and spatial variability of the snow depth and bulk snowpack temperature gradient. This region is well suited for this study because it consists primarily of open farmland or prairie, has little relief, is subject to very cold temperatures, and has more than 280 reporting stations. A geostatistical technique called Kriging was used to grid the randomly spaced snow depth measurements. The resulting snow depth maps were then compared with the passive microwave observations from the Special Sensor Microwave Imager (SSM/I). Two snow seasons were examined: 1988-89, a typical snow year, and 1996-97, a record year for snow that was responsible for extensive flooding in the Red River Basin. Inspection of the time series of snow depth and microwave spectral gradient (the difference between the 19 and 37 GHz bands) showed that while the snowpack was constant, the spectral gradient continued to increase. However, there was a strong correlation (0.6 < R2 < 0.9) between the spectral gradient and the cumulative bulk temperature gradient through the snowpack (TGI). Hence, TGI is an index of grain size metamorphism that has occurred within the snowpack. TGI time series from 21 representative sites across the region and the corresponding SSM/I observations were used to develop an algorithm for snow depth that requires daily air temperatures. Copyright ?? 2002 John Wiley & Sons, Ltd.

Smart Phase Tuning in Microwave Photonic Integrated Circuits Toward Automated Frequency Multiplication by Design

NASA Astrophysics Data System (ADS)

Nabavi, N.

2018-07-01

The author investigates the monitoring methods for fine adjustment of the previously proposed on-chip architecture for frequency multiplication and translation of harmonics by design. Digital signal processing (DSP) algorithms are utilized to create an optimized microwave photonic integrated circuit functionality toward automated frequency multiplication. The implemented DSP algorithms are formed on discrete Fourier transform and optimization-based algorithms (Greedy and gradient-based algorithms), which are analytically derived and numerically compared based on the accuracy and speed of convergence criteria.

Method of determining effects of heat-induced irregular refractive index on an optical system.

PubMed

Song, Xifa; Li, Lin; Huang, Yifan

2015-09-01

The effects of an irregular refractive index on optical performance are examined. A method was developed to express a lens's irregular refractive index distribution. An optical system and its mountings were modeled by a thermomechanical finite element (FE) program in the predicted operating temperature range, -45°C-50°C. FE outputs were elaborated using a MATLAB optimization routine; a nonlinear least squares algorithm was adopted to determine which gradient equation best fit each lens's refractive index distribution. The obtained gradient data were imported into Zemax for sequential ray-tracing analysis. The root mean square spot diameter, modulation transfer function, and diffraction ensquared energy were computed for an optical system under an irregular refractive index and under thermoelastic deformation. These properties are greatly reduced by the irregular refractive index effect, which is one-third to five-sevenths the size of the thermoelastic deformation effect. Thus, thermal analyses of optical systems should consider not only thermoelastic deformation but also refractive index irregularities caused by inhomogeneous temperature.

An endoscopic diffuse optical tomographic method with high resolution based on the improved FOCUSS method

NASA Astrophysics Data System (ADS)

Qin, Zhuanping; Ma, Wenjuan; Ren, Shuyan; Geng, Liqing; Li, Jing; Yang, Ying; Qin, Yingmei

2017-02-01

Endoscopic DOT has the potential to apply to cancer-related imaging in tubular organs. Although the DOT has relatively large tissue penetration depth, the endoscopic DOT is limited by the narrow space of the internal tubular tissue, so as to the relatively small penetration depth. Because some adenocarcinomas including cervical adenocarcinoma are located in deep canal, it is necessary to improve the imaging resolution under the limited measurement condition. To improve the resolution, a new FOCUSS algorithm along with the image reconstruction algorithm based on the effective detection range (EDR) is developed. This algorithm is based on the region of interest (ROI) to reduce the dimensions of the matrix. The shrinking method cuts down the computation burden. To reduce the computational complexity, double conjugate gradient method is used in the matrix inversion. For a typical inner size and optical properties of the cervix-like tubular tissue, reconstructed images from the simulation data demonstrate that the proposed method achieves equivalent image quality to that obtained from the method based on EDR when the target is close the inner boundary of the model, and with higher spatial resolution and quantitative ratio when the targets are far from the inner boundary of the model. The quantitative ratio of reconstructed absorption and reduced scattering coefficient can be up to 70% and 80% under 5mm depth, respectively. Furthermore, the two close targets with different depths can be separated from each other. The proposed method will be useful to the development of endoscopic DOT technologies in tubular organs.

Evaluation and reformulation of the maximum peak height algorithm (MPH) and application in a hypertrophic lagoon

NASA Astrophysics Data System (ADS)

Pitarch, Jaime; Ruiz-Verdú, Antonio; Sendra, María. D.; Santoleri, Rosalia

2017-02-01

We studied the performance of the MERIS maximum peak height (MPH) algorithm in the retrieval of chlorophyll-a concentration (CHL), using a matchup data set of Bottom-of-Rayleigh Reflectances (BRR) and CHL from a hypertrophic lake (Albufera de Valencia). The MPH algorithm produced a slight underestimation of CHL in the pixels classified as cyanobacteria (83% of the total) and a strong overestimation in those classified as eukaryotic phytoplankton (17%). In situ biomass data showed that the binary classification of MPH was not appropriate for mixed phytoplankton populations, producing also unrealistic discontinuities in the CHL maps. We recalibrated MPH using our matchup data set and found that a single calibration curve of third degree fitted equally well to all matchups regardless of how they were classified. As a modification to the former approach, we incorporated the Phycocyanin Index (PCI) in the formula, thus taking into account the gradient of phytoplankton composition, which reduced the CHL retrieval errors. By using in situ biomass data, we also proved that PCI was indeed an indicator of cyanobacterial dominance. We applied our recalibration of the MPH algorithm to the whole MERIS data set (2002-2012). Results highlight the usefulness of the MPH algorithm as a tool to monitor eutrophication. The relevance of this fact is higher since MPH does not require a complete atmospheric correction, which often fails over such waters. An adequate flagging or correction of sun glint is advisable though, since the MPH algorithm was sensitive to sun glint.

An enhanced artificial bee colony algorithm (EABC) for solving dispatching of hydro-thermal system (DHTS) problem.

PubMed

Yu, Yi; Wu, Yonggang; Hu, Binqi; Liu, Xinglong

2018-01-01

The dispatching of hydro-thermal system is a nonlinear programming problem with multiple constraints and high dimensions and the solution techniques of the model have been a hotspot in research. Based on the advantage of that the artificial bee colony algorithm (ABC) can efficiently solve the high-dimensional problem, an improved artificial bee colony algorithm has been proposed to solve DHTS problem in this paper. The improvements of the proposed algorithm include two aspects. On one hand, local search can be guided in efficiency by the information of the global optimal solution and its gradient in each generation. The global optimal solution improves the search efficiency of the algorithm but loses diversity, while the gradient can weaken the loss of diversity caused by the global optimal solution. On the other hand, inspired by genetic algorithm, the nectar resource which has not been updated in limit generation is transformed to a new one by using selection, crossover and mutation, which can ensure individual diversity and make full use of prior information for improving the global search ability of the algorithm. The two improvements of ABC algorithm are proved to be effective via a classical numeral example at last. Among which the genetic operator for the promotion of the ABC algorithm's performance is significant. The results are also compared with those of other state-of-the-art algorithms, the enhanced ABC algorithm has general advantages in minimum cost, average cost and maximum cost which shows its usability and effectiveness. The achievements in this paper provide a new method for solving the DHTS problems, and also offer a novel reference for the improvement of mechanism and the application of algorithms.

Constraint treatment techniques and parallel algorithms for multibody dynamic analysis. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Chiou, Jin-Chern

1990-01-01

Computational procedures for kinematic and dynamic analysis of three-dimensional multibody dynamic (MBD) systems are developed from the differential-algebraic equations (DAE's) viewpoint. Constraint violations during the time integration process are minimized and penalty constraint stabilization techniques and partitioning schemes are developed. The governing equations of motion, a two-stage staggered explicit-implicit numerical algorithm, are treated which takes advantage of a partitioned solution procedure. A robust and parallelizable integration algorithm is developed. This algorithm uses a two-stage staggered central difference algorithm to integrate the translational coordinates and the angular velocities. The angular orientations of bodies in MBD systems are then obtained by using an implicit algorithm via the kinematic relationship between Euler parameters and angular velocities. It is shown that the combination of the present solution procedures yields a computationally more accurate solution. To speed up the computational procedures, parallel implementation of the present constraint treatment techniques, the two-stage staggered explicit-implicit numerical algorithm was efficiently carried out. The DAE's and the constraint treatment techniques were transformed into arrowhead matrices to which Schur complement form was derived. By fully exploiting the sparse matrix structural analysis techniques, a parallel preconditioned conjugate gradient numerical algorithm is used to solve the systems equations written in Schur complement form. A software testbed was designed and implemented in both sequential and parallel computers. This testbed was used to demonstrate the robustness and efficiency of the constraint treatment techniques, the accuracy of the two-stage staggered explicit-implicit numerical algorithm, and the speed up of the Schur-complement-based parallel preconditioned conjugate gradient algorithm on a parallel computer.

The evolving approach to the evaluation of low-gradient aortic stenosis.

PubMed

Cutting, William B; Bavry, Anthony A

2018-04-07

Severe aortic stenosis (AS) is typically identified by a low valve area (≤1.0 cm 2 ) and high mean gradient (≥40 mm Hg). A subset of patients are found to have a less than severe mean gradient (<40 mm Hg) despite a low valve area. These latter types can present as either low ejection fraction with low-gradient AS (stage D2) or normal ejection fraction with low-gradient AS (stage D3). Determining the true severity of disease within these categories has proved difficult. In this review we illustrate both traditional and novel techniques that can be used for further valvular assessment. We also propose a simple algorithm that can be used to evaluate low-gradient AS. Published by Elsevier Inc.

An image morphing technique based on optimal mass preserving mapping.

PubMed

Zhu, Lei; Yang, Yan; Haker, Steven; Tannenbaum, Allen

2007-06-01

Image morphing, or image interpolation in the time domain, deals with the metamorphosis of one image into another. In this paper, a new class of image morphing algorithms is proposed based on the theory of optimal mass transport. The L(2) mass moving energy functional is modified by adding an intensity penalizing term, in order to reduce the undesired double exposure effect. It is an intensity-based approach and, thus, is parameter free. The optimal warping function is computed using an iterative gradient descent approach. This proposed morphing method is also extended to doubly connected domains using a harmonic parameterization technique, along with finite-element methods.

An Image Morphing Technique Based on Optimal Mass Preserving Mapping

PubMed Central

Zhu, Lei; Yang, Yan; Haker, Steven; Tannenbaum, Allen

2013-01-01

Image morphing, or image interpolation in the time domain, deals with the metamorphosis of one image into another. In this paper, a new class of image morphing algorithms is proposed based on the theory of optimal mass transport. The L2 mass moving energy functional is modified by adding an intensity penalizing term, in order to reduce the undesired double exposure effect. It is an intensity-based approach and, thus, is parameter free. The optimal warping function is computed using an iterative gradient descent approach. This proposed morphing method is also extended to doubly connected domains using a harmonic parameterization technique, along with finite-element methods. PMID:17547128

Aerodynamic Design on Unstructured Grids for Turbulent Flows

NASA Technical Reports Server (NTRS)

Anderson, W. Kyle; Bonhaus, Daryl L.

1997-01-01

An aerodynamic design algorithm for turbulent flows using unstructured grids is described. The current approach uses adjoint (costate) variables for obtaining derivatives of the cost function. The solution of the adjoint equations is obtained using an implicit formulation in which the turbulence model is fully coupled with the flow equations when solving for the costate variables. The accuracy of the derivatives is demonstrated by comparison with finite-difference gradients and a few example computations are shown. In addition, a user interface is described which significantly reduces the time required for setting up the design problems. Recommendations on directions of further research into the Navier Stokes design process are made.

Development of Artificial Neural Network Model for Diesel Fuel Properties Prediction using Vibrational Spectroscopy.

PubMed

Bolanča, Tomislav; Marinović, Slavica; Ukić, Sime; Jukić, Ante; Rukavina, Vinko

2012-06-01

This paper describes development of artificial neural network models which can be used to correlate and predict diesel fuel properties from several FTIR-ATR absorbances and Raman intensities as input variables. Multilayer feed forward and radial basis function neural networks have been used to rapid and simultaneous prediction of cetane number, cetane index, density, viscosity, distillation temperatures at 10% (T10), 50% (T50) and 90% (T90) recovery, contents of total aromatics and polycyclic aromatic hydrocarbons of commercial diesel fuels. In this study two-phase training procedures for multilayer feed forward networks were applied. While first phase training algorithm was constantly the back propagation one, two second phase training algorithms were varied and compared, namely: conjugate gradient and quasi Newton. In case of radial basis function network, radial layer was trained using K-means radial assignment algorithm and three different radial spread algorithms: explicit, isotropic and K-nearest neighbour. The number of hidden layer neurons and experimental data points used for the training set have been optimized for both neural networks in order to insure good predictive ability by reducing unnecessary experimental work. This work shows that developed artificial neural network models can determine main properties of diesel fuels simultaneously based on a single and fast IR or Raman measurement.

Incomplete projection reconstruction of computed tomography based on the modified discrete algebraic reconstruction technique

NASA Astrophysics Data System (ADS)

Yang, Fuqiang; Zhang, Dinghua; Huang, Kuidong; Gao, Zongzhao; Yang, YaFei

2018-02-01

Based on the discrete algebraic reconstruction technique (DART), this study aims to address and test a new improved algorithm applied to incomplete projection data to generate a high quality reconstruction image by reducing the artifacts and noise in computed tomography. For the incomplete projections, an augmented Lagrangian based on compressed sensing is first used in the initial reconstruction for segmentation of the DART to get higher contrast graphics for boundary and non-boundary pixels. Then, the block matching 3D filtering operator was used to suppress the noise and to improve the gray distribution of the reconstructed image. Finally, simulation studies on the polychromatic spectrum were performed to test the performance of the new algorithm. Study results show a significant improvement in the signal-to-noise ratios (SNRs) and average gradients (AGs) of the images reconstructed from incomplete data. The SNRs and AGs of the new images reconstructed by DART-ALBM were on average 30%-40% and 10% higher than the images reconstructed by DART algorithms. Since the improved DART-ALBM algorithm has a better robustness to limited-view reconstruction, which not only makes the edge of the image clear but also makes the gray distribution of non-boundary pixels better, it has the potential to improve image quality from incomplete projections or sparse projections.

A hybrid multi-objective evolutionary algorithm for wind-turbine blade optimization

NASA Astrophysics Data System (ADS)

Sessarego, M.; Dixon, K. R.; Rival, D. E.; Wood, D. H.

2015-08-01

A concurrent-hybrid non-dominated sorting genetic algorithm (hybrid NSGA-II) has been developed and applied to the simultaneous optimization of the annual energy production, flapwise root-bending moment and mass of the NREL 5 MW wind-turbine blade. By hybridizing a multi-objective evolutionary algorithm (MOEA) with gradient-based local search, it is believed that the optimal set of blade designs could be achieved in lower computational cost than for a conventional MOEA. To measure the convergence between the hybrid and non-hybrid NSGA-II on a wind-turbine blade optimization problem, a computationally intensive case was performed using the non-hybrid NSGA-II. From this particular case, a three-dimensional surface representing the optimal trade-off between the annual energy production, flapwise root-bending moment and blade mass was achieved. The inclusion of local gradients in the blade optimization, however, shows no improvement in the convergence for this three-objective problem.

Planck 2015 results: VI. LFI mapmaking

DOE PAGES

Ade, P. A. R.; Aghanim, N.; Ashdown, M.; ...

2016-09-20

This article describes the mapmaking procedure applied to Planck Low Frequency Instrument (LFI) data. The mapmaking step takes as input the calibrated timelines and pointing information. The main products are sky maps of I, Q, and U Stokes components. For the first time, we present polarization maps at LFI frequencies. The mapmaking algorithm is based on a destriping technique, which is enhanced with a noise prior. The Galactic region is masked to reduce errors arising from bandpass mismatch and high signal gradients. We apply horn-uniform radiometer weights to reduce the effects of beam-shape mismatch. The algorithm is the same asmore » used for the 2013 release, apart from small changes in parameter settings. We validate the procedure through simulations. Special emphasis is put on the control of systematics, which is particularly important for accurate polarization analysis. We also produce low-resolution versions of the maps and corresponding noise covariance matrices. These serve as input in later analysis steps and parameter estimation. The noise covariance matrices are validated through noise Monte Carlo simulations. The residual noise in the map products is characterized through analysis of half-ring maps, noise covariance matrices, and simulations.« less

Teaching a Machine to Feel Postoperative Pain: Combining High-Dimensional Clinical Data with Machine Learning Algorithms to Forecast Acute Postoperative Pain

PubMed Central

Tighe, Patrick J.; Harle, Christopher A.; Hurley, Robert W.; Aytug, Haldun; Boezaart, Andre P.; Fillingim, Roger B.

2015-01-01

Background Given their ability to process highly dimensional datasets with hundreds of variables, machine learning algorithms may offer one solution to the vexing challenge of predicting postoperative pain. Methods Here, we report on the application of machine learning algorithms to predict postoperative pain outcomes in a retrospective cohort of 8071 surgical patients using 796 clinical variables. Five algorithms were compared in terms of their ability to forecast moderate to severe postoperative pain: Least Absolute Shrinkage and Selection Operator (LASSO), gradient-boosted decision tree, support vector machine, neural network, and k-nearest neighbor, with logistic regression included for baseline comparison. Results In forecasting moderate to severe postoperative pain for postoperative day (POD) 1, the LASSO algorithm, using all 796 variables, had the highest accuracy with an area under the receiver-operating curve (ROC) of 0.704. Next, the gradient-boosted decision tree had an ROC of 0.665 and the k-nearest neighbor algorithm had an ROC of 0.643. For POD 3, the LASSO algorithm, using all variables, again had the highest accuracy, with an ROC of 0.727. Logistic regression had a lower ROC of 0.5 for predicting pain outcomes on POD 1 and 3. Conclusions Machine learning algorithms, when combined with complex and heterogeneous data from electronic medical record systems, can forecast acute postoperative pain outcomes with accuracies similar to methods that rely only on variables specifically collected for pain outcome prediction. PMID:26031220

Bin Packing, Number Balancing, and Rescaling Linear Programs

NASA Astrophysics Data System (ADS)

Hoberg, Rebecca

This thesis deals with several important algorithmic questions using techniques from diverse areas including discrepancy theory, machine learning and lattice theory. In Chapter 2, we construct an improved approximation algorithm for a classical NP-complete problem, the bin packing problem. In this problem, the goal is to pack items of sizes si ∈ [0,1] into as few bins as possible, where a set of items fits into a bin provided the sum of the item sizes is at most one. We give a polynomial-time rounding scheme for a standard linear programming relaxation of the problem, yielding a packing that uses at most OPT + O(log OPT) bins. This makes progress towards one of the "10 open problems in approximation algorithms" stated in the book of Shmoys and Williamson. In fact, based on related combinatorial lower bounds, Rothvoss conjectures that theta(logOPT) may be a tight bound on the additive integrality gap of this LP relaxation. In Chapter 3, we give a new polynomial-time algorithm for linear programming. Our algorithm is based on the multiplicative weights update (MWU) method, which is a general framework that is currently of great interest in theoretical computer science. An algorithm for linear programming based on MWU was known previously, but was not polynomial time--we remedy this by alternating between a MWU phase and a rescaling phase. The rescaling methods we introduce improve upon previous methods by reducing the number of iterations needed until one can rescale, and they can be used for any algorithm with a similar rescaling structure. Finally, we note that the MWU phase of the algorithm has a simple interpretation as gradient descent of a particular potential function, and we show we can speed up this phase by walking in a direction that decreases both the potential function and its gradient. In Chapter 4, we show that an approximate oracle for Minkowski's Theorem gives an approximate oracle for the number balancing problem, and conversely. Number balancing is the problem of minimizing | 〈a,x〉 | over x ∈ {-1,0,1}n \\ { 0}, given a ∈ [0,1]n. While an application of the pigeonhole principle shows that there always exists x with | 〈a,x〉| ≤ O(√ n/2n), the best known algorithm only guarantees |〈a,x〉| ≤ 2-ntheta(log n). We show that an oracle for Minkowski's Theorem with approximation factor rho would give an algorithm for NBP that guarantees | 〈a,x〉 | ≤ 2-ntheta(1/rho). In particular, this would beat the bound of Karmarkar and Karp provided rho ≤ O(logn/loglogn). In the other direction, we prove that any polynomial time algorithm for NBP that guarantees a solution of difference at most 2√n/2 n would give a polynomial approximation for Minkowski as well as a polynomial factor approximation algorithm for the Shortest Vector Problem.

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.

An enhanced artificial bee colony algorithm (EABC) for solving dispatching of hydro-thermal system (DHTS) problem

PubMed Central

Yu, Yi; Hu, Binqi; Liu, Xinglong

2018-01-01

The dispatching of hydro-thermal system is a nonlinear programming problem with multiple constraints and high dimensions and the solution techniques of the model have been a hotspot in research. Based on the advantage of that the artificial bee colony algorithm (ABC) can efficiently solve the high-dimensional problem, an improved artificial bee colony algorithm has been proposed to solve DHTS problem in this paper. The improvements of the proposed algorithm include two aspects. On one hand, local search can be guided in efficiency by the information of the global optimal solution and its gradient in each generation. The global optimal solution improves the search efficiency of the algorithm but loses diversity, while the gradient can weaken the loss of diversity caused by the global optimal solution. On the other hand, inspired by genetic algorithm, the nectar resource which has not been updated in limit generation is transformed to a new one by using selection, crossover and mutation, which can ensure individual diversity and make full use of prior information for improving the global search ability of the algorithm. The two improvements of ABC algorithm are proved to be effective via a classical numeral example at last. Among which the genetic operator for the promotion of the ABC algorithm’s performance is significant. The results are also compared with those of other state-of-the-art algorithms, the enhanced ABC algorithm has general advantages in minimum cost, average cost and maximum cost which shows its usability and effectiveness. The achievements in this paper provide a new method for solving the DHTS problems, and also offer a novel reference for the improvement of mechanism and the application of algorithms. PMID:29324743

Truncated Conjugate Gradient: An Optimal Strategy for the Analytical Evaluation of the Many-Body Polarization Energy and Forces in Molecular Simulations.

PubMed

Aviat, Félix; Levitt, Antoine; Stamm, Benjamin; Maday, Yvon; Ren, Pengyu; Ponder, Jay W; Lagardère, Louis; Piquemal, Jean-Philip

2017-01-10

We introduce a new class of methods, denoted as Truncated Conjugate Gradient(TCG), to solve the many-body polarization energy and its associated forces in molecular simulations (i.e. molecular dynamics (MD) and Monte Carlo). The method consists in a fixed number of Conjugate Gradient (CG) iterations. TCG approaches provide a scalable solution to the polarization problem at a user-chosen cost and a corresponding optimal accuracy. The optimality of the CG-method guarantees that the number of the required matrix-vector products are reduced to a minimum compared to other iterative methods. This family of methods is non-empirical, fully adaptive, and provides analytical gradients, avoiding therefore any energy drift in MD as compared to popular iterative solvers. Besides speed, one great advantage of this class of approximate methods is that their accuracy is systematically improvable. Indeed, as the CG-method is a Krylov subspace method, the associated error is monotonically reduced at each iteration. On top of that, two improvements can be proposed at virtually no cost: (i) the use of preconditioners can be employed, which leads to the Truncated Preconditioned Conjugate Gradient (TPCG); (ii) since the residual of the final step of the CG-method is available, one additional Picard fixed point iteration ("peek"), equivalent to one step of Jacobi Over Relaxation (JOR) with relaxation parameter ω, can be made at almost no cost. This method is denoted by TCG-n(ω). Black-box adaptive methods to find good choices of ω are provided and discussed. Results show that TPCG-3(ω) is converged to high accuracy (a few kcal/mol) for various types of systems including proteins and highly charged systems at the fixed cost of four matrix-vector products: three CG iterations plus the initial CG descent direction. Alternatively, T(P)CG-2(ω) provides robust results at a reduced cost (three matrix-vector products) and offers new perspectives for long polarizable MD as a production algorithm. The T(P)CG-1(ω) level provides less accurate solutions for inhomogeneous systems, but its applicability to well-conditioned problems such as water is remarkable, with only two matrix-vector product evaluations.

Truncated Conjugate Gradient: An Optimal Strategy for the Analytical Evaluation of the Many-Body Polarization Energy and Forces in Molecular Simulations

PubMed Central

2016-01-01

We introduce a new class of methods, denoted as Truncated Conjugate Gradient(TCG), to solve the many-body polarization energy and its associated forces in molecular simulations (i.e. molecular dynamics (MD) and Monte Carlo). The method consists in a fixed number of Conjugate Gradient (CG) iterations. TCG approaches provide a scalable solution to the polarization problem at a user-chosen cost and a corresponding optimal accuracy. The optimality of the CG-method guarantees that the number of the required matrix-vector products are reduced to a minimum compared to other iterative methods. This family of methods is non-empirical, fully adaptive, and provides analytical gradients, avoiding therefore any energy drift in MD as compared to popular iterative solvers. Besides speed, one great advantage of this class of approximate methods is that their accuracy is systematically improvable. Indeed, as the CG-method is a Krylov subspace method, the associated error is monotonically reduced at each iteration. On top of that, two improvements can be proposed at virtually no cost: (i) the use of preconditioners can be employed, which leads to the Truncated Preconditioned Conjugate Gradient (TPCG); (ii) since the residual of the final step of the CG-method is available, one additional Picard fixed point iteration (“peek”), equivalent to one step of Jacobi Over Relaxation (JOR) with relaxation parameter ω, can be made at almost no cost. This method is denoted by TCG-n(ω). Black-box adaptive methods to find good choices of ω are provided and discussed. Results show that TPCG-3(ω) is converged to high accuracy (a few kcal/mol) for various types of systems including proteins and highly charged systems at the fixed cost of four matrix-vector products: three CG iterations plus the initial CG descent direction. Alternatively, T(P)CG-2(ω) provides robust results at a reduced cost (three matrix-vector products) and offers new perspectives for long polarizable MD as a production algorithm. The T(P)CG-1(ω) level provides less accurate solutions for inhomogeneous systems, but its applicability to well-conditioned problems such as water is remarkable, with only two matrix-vector product evaluations. PMID:28068773

Image Motion Detection And Estimation: The Modified Spatio-Temporal Gradient Scheme

NASA Astrophysics Data System (ADS)

Hsin, Cheng-Ho; Inigo, Rafael M.

1990-03-01

The detection and estimation of motion are generally involved in computing a velocity field of time-varying images. A completely new modified spatio-temporal gradient scheme to determine motion is proposed. This is derived by using gradient methods and properties of biological vision. A set of general constraints is proposed to derive motion constraint equations. The constraints are that the second directional derivatives of image intensity at an edge point in the smoothed image will be constant at times t and t+L . This scheme basically has two stages: spatio-temporal filtering, and velocity estimation. Initially, image sequences are processed by a set of oriented spatio-temporal filters which are designed using a Gaussian derivative model. The velocity is then estimated for these filtered image sequences based on the gradient approach. From a computational stand point, this scheme offers at least three advantages over current methods. The greatest advantage of the modified spatio-temporal gradient scheme over the traditional ones is that an infinite number of motion constraint equations are derived instead of only one. Therefore, it solves the aperture problem without requiring any additional assumptions and is simply a local process. The second advantage is that because of the spatio-temporal filtering, the direct computation of image gradients (discrete derivatives) is avoided. Therefore the error in gradients measurement is reduced significantly. The third advantage is that during the processing of motion detection and estimation algorithm, image features (edges) are produced concurrently with motion information. The reliable range of detected velocity is determined by parameters of the oriented spatio-temporal filters. Knowing the velocity sensitivity of a single motion detection channel, a multiple-channel mechanism for estimating image velocity, seldom addressed by other motion schemes in machine vision, can be constructed by appropriately choosing and combining different sets of parameters. By applying this mechanism, a great range of velocity can be detected. The scheme has been tested for both synthetic and real images. The results of simulations are very satisfactory.

Evaluating some computer exhancement algorithms that improve the visibility of cometary morphology

NASA Technical Reports Server (NTRS)

Larson, Stephen M.; Slaughter, Charles D.

1992-01-01

Digital enhancement of cometary images is a necessary tool in studying cometary morphology. Many image processing algorithms, some developed specifically for comets, have been used to enhance the subtle, low contrast coma and tail features. We compare some of the most commonly used algorithms on two different images to evaluate their strong and weak points, and conclude that there currently exists no single 'ideal' algorithm, although the radial gradient spatial filter gives the best overall result. This comparison should aid users in selecting the best algorithm to enhance particular features of interest.

Scope of Gradient and Genetic Algorithms in Multivariable Function Optimization

NASA Technical Reports Server (NTRS)

Shaykhian, Gholam Ali; Sen, S. K.

2007-01-01

Global optimization of a multivariable function - constrained by bounds specified on each variable and also unconstrained - is an important problem with several real world applications. Deterministic methods such as the gradient algorithms as well as the randomized methods such as the genetic algorithms may be employed to solve these problems. In fact, there are optimization problems where a genetic algorithm/an evolutionary approach is preferable at least from the quality (accuracy) of the results point of view. From cost (complexity) point of view, both gradient and genetic approaches are usually polynomial-time; there are no serious differences in this regard, i.e., the computational complexity point of view. However, for certain types of problems, such as those with unacceptably erroneous numerical partial derivatives and those with physically amplified analytical partial derivatives whose numerical evaluation involves undesirable errors and/or is messy, a genetic (stochastic) approach should be a better choice. We have presented here the pros and cons of both the approaches so that the concerned reader/user can decide which approach is most suited for the problem at hand. Also for the function which is known in a tabular form, instead of an analytical form, as is often the case in an experimental environment, we attempt to provide an insight into the approaches focusing our attention toward accuracy. Such an insight will help one to decide which method, out of several available methods, should be employed to obtain the best (least error) output. *

A quasi-Newton algorithm for large-scale nonlinear equations.

PubMed

Huang, Linghua

2017-01-01

In this paper, the algorithm for large-scale nonlinear equations is designed by the following steps: (i) a conjugate gradient (CG) algorithm is designed as a sub-algorithm to obtain the initial points of the main algorithm, where the sub-algorithm's initial point does not have any restrictions; (ii) a quasi-Newton algorithm with the initial points given by sub-algorithm is defined as main algorithm, where a new nonmonotone line search technique is presented to get the step length [Formula: see text]. The given nonmonotone line search technique can avoid computing the Jacobian matrix. The global convergence and the [Formula: see text]-order convergent rate of the main algorithm are established under suitable conditions. Numerical results show that the proposed method is competitive with a similar method for large-scale problems.

Preconditioned conjugate gradient methods for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.

1990-01-01

The compressible Navier-Stokes equations are solved for a variety of two-dimensional inviscid and viscous problems by preconditioned conjugate gradient-like algorithms. Roe's flux difference splitting technique is used to discretize the inviscid fluxes. The viscous terms are discretized by using central differences. An algebraic turbulence model is also incorporated. The system of linear equations which arises out of the linearization of a fully implicit scheme is solved iteratively by the well known methods of GMRES (Generalized Minimum Residual technique) and Chebyschev iteration. Incomplete LU factorization and block diagonal factorization are used as preconditioners. The resulting algorithm is competitive with the best current schemes, but has wide applications in parallel computing and unstructured mesh computations.

The effect of model uncertainty on some optimal routing problems

NASA Technical Reports Server (NTRS)

Mohanty, Bibhu; Cassandras, Christos G.

1991-01-01

The effect of model uncertainties on optimal routing in a system of parallel queues is examined. The uncertainty arises in modeling the service time distribution for the customers (jobs, packets) to be served. For a Poisson arrival process and Bernoulli routing, the optimal mean system delay generally depends on the variance of this distribution. However, as the input traffic load approaches the system capacity the optimal routing assignment and corresponding mean system delay are shown to converge to a variance-invariant point. The implications of these results are examined in the context of gradient-based routing algorithms. An example of a model-independent algorithm using online gradient estimation is also included.

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.

A modified conjugate gradient coefficient with inexact line search for unconstrained optimization

NASA Astrophysics Data System (ADS)

Aini, Nurul; Rivaie, Mohd; Mamat, Mustafa

2016-11-01

Conjugate gradient (CG) method is a line search algorithm mostly known for its wide application in solving unconstrained optimization problems. Its low memory requirements and global convergence properties makes it one of the most preferred method in real life application such as in engineering and business. In this paper, we present a new CG method based on AMR* and CD method for solving unconstrained optimization functions. The resulting algorithm is proven to have both the sufficient descent and global convergence properties under inexact line search. Numerical tests are conducted to assess the effectiveness of the new method in comparison to some previous CG methods. The results obtained indicate that our method is indeed superior.

A hybrid linear/nonlinear training algorithm for feedforward neural networks.

PubMed

McLoone, S; Brown, M D; Irwin, G; Lightbody, A

1998-01-01

This paper presents a new hybrid optimization strategy for training feedforward neural networks. The algorithm combines gradient-based optimization of nonlinear weights with singular value decomposition (SVD) computation of linear weights in one integrated routine. It is described for the multilayer perceptron (MLP) and radial basis function (RBF) networks and then extended to the local model network (LMN), a new feedforward structure in which a global nonlinear model is constructed from a set of locally valid submodels. Simulation results are presented demonstrating the superiority of the new hybrid training scheme compared to second-order gradient methods. It is particularly effective for the LMN architecture where the linear to nonlinear parameter ratio is large.

WS-BP: An efficient wolf search based back-propagation algorithm

NASA Astrophysics Data System (ADS)

Nawi, Nazri Mohd; Rehman, M. Z.; Khan, Abdullah

2015-05-01

Wolf Search (WS) is a heuristic based optimization algorithm. Inspired by the preying and survival capabilities of the wolves, this algorithm is highly capable to search large spaces in the candidate solutions. This paper investigates the use of WS algorithm in combination with back-propagation neural network (BPNN) algorithm to overcome the local minima problem and to improve convergence in gradient descent. The performance of the proposed Wolf Search based Back-Propagation (WS-BP) algorithm is compared with Artificial Bee Colony Back-Propagation (ABC-BP), Bat Based Back-Propagation (Bat-BP), and conventional BPNN algorithms. Specifically, OR and XOR datasets are used for training the network. The simulation results show that the WS-BP algorithm effectively avoids the local minima and converge to global minima.

New Techniques in Numerical Analysis and Their Application to Aerospace Systems.

DTIC Science & Technology

1979-01-01

employment of the sequential gradient-restoration algorithm and the modified quasilineari- zation algorithm in some problems of structural analysis (Refs. 6...and a state inequa - lity constraint. The state inequality constraint is of a special type, namely, it is linear in some or all of the com- ponents of

Sparse matrix methods based on orthogonality and conjugacy

NASA Technical Reports Server (NTRS)

Lawson, C. L.

1973-01-01

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

Self-calibrated multiple-echo acquisition with radial trajectories using the conjugate gradient method (SMART-CG).

PubMed

Jung, Youngkyoo; Samsonov, Alexey A; Bydder, Mark; Block, Walter F

2011-04-01

To remove phase inconsistencies between multiple echoes, an algorithm using a radial acquisition to provide inherent phase and magnitude information for self correction was developed. The information also allows simultaneous support for parallel imaging for multiple coil acquisitions. Without a separate field map acquisition, a phase estimate from each echo in multiple echo train was generated. When using a multiple channel coil, magnitude and phase estimates from each echo provide in vivo coil sensitivities. An algorithm based on the conjugate gradient method uses these estimates to simultaneously remove phase inconsistencies between echoes, and in the case of multiple coil acquisition, simultaneously provides parallel imaging benefits. The algorithm is demonstrated on single channel, multiple channel, and undersampled data. Substantial image quality improvements were demonstrated. Signal dropouts were completely removed and undersampling artifacts were well suppressed. The suggested algorithm is able to remove phase cancellation and undersampling artifacts simultaneously and to improve image quality of multiecho radial imaging, the important technique for fast three-dimensional MRI data acquisition. Copyright © 2011 Wiley-Liss, Inc.

Self-calibrated Multiple-echo Acquisition with Radial Trajectories using the Conjugate Gradient Method (SMART-CG)

PubMed Central

Jung, Youngkyoo; Samsonov, Alexey A; Bydder, Mark; Block, Walter F.

2011-01-01

Purpose To remove phase inconsistencies between multiple echoes, an algorithm using a radial acquisition to provide inherent phase and magnitude information for self correction was developed. The information also allows simultaneous support for parallel imaging for multiple coil acquisitions. Materials and Methods Without a separate field map acquisition, a phase estimate from each echo in multiple echo train was generated. When using a multiple channel coil, magnitude and phase estimates from each echo provide in-vivo coil sensitivities. An algorithm based on the conjugate gradient method uses these estimates to simultaneously remove phase inconsistencies between echoes, and in the case of multiple coil acquisition, simultaneously provides parallel imaging benefits. The algorithm is demonstrated on single channel, multiple channel, and undersampled data. Results Substantial image quality improvements were demonstrated. Signal dropouts were completely removed and undersampling artifacts were well suppressed. Conclusion The suggested algorithm is able to remove phase cancellation and undersampling artifacts simultaneously and to improve image quality of multiecho radial imaging, the important technique for fast 3D MRI data acquisition. PMID:21448967

Linearized motion estimation for articulated planes.

PubMed

Datta, Ankur; Sheikh, Yaser; Kanade, Takeo

2011-04-01

In this paper, we describe the explicit application of articulation constraints for estimating the motion of a system of articulated planes. We relate articulations to the relative homography between planes and show that these articulations translate into linearized equality constraints on a linear least-squares system, which can be solved efficiently using a Karush-Kuhn-Tucker system. The articulation constraints can be applied for both gradient-based and feature-based motion estimation algorithms and to illustrate this, we describe a gradient-based motion estimation algorithm for an affine camera and a feature-based motion estimation algorithm for a projective camera that explicitly enforces articulation constraints. We show that explicit application of articulation constraints leads to numerically stable estimates of motion. The simultaneous computation of motion estimates for all of the articulated planes in a scene allows us to handle scene areas where there is limited texture information and areas that leave the field of view. Our results demonstrate the wide applicability of the algorithm in a variety of challenging real-world cases such as human body tracking, motion estimation of rigid, piecewise planar scenes, and motion estimation of triangulated meshes.

Experimental determination of pore shapes using phase retrieval from q -space NMR diffraction

NASA Astrophysics Data System (ADS)

Demberg, Kerstin; Laun, Frederik Bernd; Bertleff, Marco; Bachert, Peter; Kuder, Tristan Anselm

2018-05-01

This paper presents an approach to solving the phase problem in nuclear magnetic resonance (NMR) diffusion pore imaging, a method that allows imaging the shape of arbitrary closed pores filled with an NMR-detectable medium for investigation of the microstructure of biological tissue and porous materials. Classical q -space imaging composed of two short diffusion-encoding gradient pulses yields, analogously to diffraction experiments, the modulus squared of the Fourier transform of the pore image which entails an inversion problem: An unambiguous reconstruction of the pore image requires both magnitude and phase. Here the phase information is recovered from the Fourier modulus by applying a phase retrieval algorithm. This allows omitting experimentally challenging phase measurements using specialized temporal gradient profiles. A combination of the hybrid input-output algorithm and the error reduction algorithm was used with dynamically adapting support (shrinkwrap extension). No a priori knowledge on the pore shape was fed to the algorithm except for a finite pore extent. The phase retrieval approach proved successful for simulated data with and without noise and was validated in phantom experiments with well-defined pores using hyperpolarized xenon gas.

Experimental determination of pore shapes using phase retrieval from q-space NMR diffraction.

PubMed

Demberg, Kerstin; Laun, Frederik Bernd; Bertleff, Marco; Bachert, Peter; Kuder, Tristan Anselm

2018-05-01

This paper presents an approach to solving the phase problem in nuclear magnetic resonance (NMR) diffusion pore imaging, a method that allows imaging the shape of arbitrary closed pores filled with an NMR-detectable medium for investigation of the microstructure of biological tissue and porous materials. Classical q-space imaging composed of two short diffusion-encoding gradient pulses yields, analogously to diffraction experiments, the modulus squared of the Fourier transform of the pore image which entails an inversion problem: An unambiguous reconstruction of the pore image requires both magnitude and phase. Here the phase information is recovered from the Fourier modulus by applying a phase retrieval algorithm. This allows omitting experimentally challenging phase measurements using specialized temporal gradient profiles. A combination of the hybrid input-output algorithm and the error reduction algorithm was used with dynamically adapting support (shrinkwrap extension). No a priori knowledge on the pore shape was fed to the algorithm except for a finite pore extent. The phase retrieval approach proved successful for simulated data with and without noise and was validated in phantom experiments with well-defined pores using hyperpolarized xenon gas.

Sea surface velocities from visible and infrared multispectral atmospheric mapping sensor imagery

NASA Technical Reports Server (NTRS)

Pope, P. A.; Emery, W. J.; Radebaugh, M.

1992-01-01

High resolution (100 m), sequential Multispectral Atmospheric Mapping Sensor (MAMS) images were used in a study to calculate advective surface velocities using the Maximum Cross Correlation (MCC) technique. Radiance and brightness temperature gradient magnitude images were formed from visible (0.48 microns) and infrared (11.12 microns) image pairs, respectively, of Chandeleur Sound, which is a shallow body of water northeast of the Mississippi delta, at 145546 GMT and 170701 GMT on 30 Mar. 1989. The gradient magnitude images enhanced the surface water feature boundaries, and a lower cutoff on the gradient magnitudes calculated allowed the undesirable sunglare and backscatter gradients in the visible images, and the water vapor absorption gradients in the infrared images, to be reduced in strength. Requiring high (greater than 0.4) maximum cross correlation coefficients and spatial coherence of the vector field aided in the selection of an optimal template size of 10 x 10 pixels (first image) and search limit of 20 pixels (second image) to use in the MCC technique. Use of these optimum input parameters to the MCC algorithm, and high correlation and spatial coherence filtering of the resulting velocity field from the MCC calculation yielded a clustered velocity distribution over the visible and infrared gradient images. The velocity field calculated from the visible gradient image pair agreed well with a subjective analysis of the motion, but the velocity field from the infrared gradient image pair did not. This was attributed to the changing shapes of the gradient features, their nonuniqueness, and large displacements relative to the mean distance between them. These problems implied a lower repeat time for the imagery was needed in order to improve the velocity field derived from gradient imagery. Suggestions are given for optimizing the repeat time of sequential imagery when using the MCC method for motion studies. Applying the MCC method to the infrared brightness temperature imagery yielded a velocity field which did agree with the subjective analysis of the motion and that derived from the visible gradient imagery. Differences between the visible and infrared derived velocities were 14.9 cm/s in speed and 56.7 degrees in direction. Both of these velocity fields also agreed well with the motion expected from considerations of the ocean bottom topography and wind and tidal forcing in the study area during the 2.175 hour time interval.

A modified conjugate gradient method based on the Tikhonov system for computerized tomography (CT).

PubMed

Wang, Qi; Wang, Huaxiang

2011-04-01

During the past few decades, computerized tomography (CT) was widely used for non-destructive testing (NDT) and non-destructive examination (NDE) in the industrial area because of its characteristics of non-invasiveness and visibility. Recently, CT technology has been applied to multi-phase flow measurement. Using the principle of radiation attenuation measurements along different directions through the investigated object with a special reconstruction algorithm, cross-sectional information of the scanned object can be worked out. It is a typical inverse problem and has always been a challenge for its nonlinearity and ill-conditions. The Tikhonov regulation method is widely used for similar ill-posed problems. However, the conventional Tikhonov method does not provide reconstructions with qualities good enough, the relative errors between the reconstructed images and the real distribution should be further reduced. In this paper, a modified conjugate gradient (CG) method is applied to a Tikhonov system (MCGT method) for reconstructing CT images. The computational load is dominated by the number of independent measurements m, and a preconditioner is imported to lower the condition number of the Tikhonov system. Both simulation and experiment results indicate that the proposed method can reduce the computational time and improve the quality of image reconstruction. Copyright © 2010 ISA. Published by Elsevier Ltd. All rights reserved.

Fast conjugate phase image reconstruction based on a Chebyshev approximation to correct for B0 field inhomogeneity and concomitant gradients

PubMed Central

Chen, Weitian; Sica, Christopher T.; Meyer, Craig H.

2008-01-01

Off-resonance effects can cause image blurring in spiral scanning and various forms of image degradation in other MRI methods. Off-resonance effects can be caused by both B0 inhomogeneity and concomitant gradient fields. Previously developed off-resonance correction methods focus on the correction of a single source of off-resonance. This work introduces a computationally efficient method of correcting for B0 inhomogeneity and concomitant gradients simultaneously. The method is a fast alternative to conjugate phase reconstruction, with the off-resonance phase term approximated by Chebyshev polynomials. The proposed algorithm is well suited for semiautomatic off-resonance correction, which works well even with an inaccurate or low-resolution field map. The proposed algorithm is demonstrated using phantom and in vivo data sets acquired by spiral scanning. Semiautomatic off-resonance correction alone is shown to provide a moderate amount of correction for concomitant gradient field effects, in addition to B0 imhomogeneity effects. However, better correction is provided by the proposed combined method. The best results were produced using the semiautomatic version of the proposed combined method. PMID:18956462

Gradient descent for robust kernel-based regression

NASA Astrophysics Data System (ADS)

Guo, Zheng-Chu; Hu, Ting; Shi, Lei

2018-06-01

In this paper, we study the gradient descent algorithm generated by a robust loss function over a reproducing kernel Hilbert space (RKHS). The loss function is defined by a windowing function G and a scale parameter σ, which can include a wide range of commonly used robust losses for regression. There is still a gap between theoretical analysis and optimization process of empirical risk minimization based on loss: the estimator needs to be global optimal in the theoretical analysis while the optimization method can not ensure the global optimality of its solutions. In this paper, we aim to fill this gap by developing a novel theoretical analysis on the performance of estimators generated by the gradient descent algorithm. We demonstrate that with an appropriately chosen scale parameter σ, the gradient update with early stopping rules can approximate the regression function. Our elegant error analysis can lead to convergence in the standard L 2 norm and the strong RKHS norm, both of which are optimal in the mini-max sense. We show that the scale parameter σ plays an important role in providing robustness as well as fast convergence. The numerical experiments implemented on synthetic examples and real data set also support our theoretical results.

Improving a maximum horizontal gradient algorithm to determine geological body boundaries and fault systems based on gravity data

NASA Astrophysics Data System (ADS)

Van Kha, Tran; Van Vuong, Hoang; Thanh, Do Duc; Hung, Duong Quoc; Anh, Le Duc

2018-05-01

The maximum horizontal gradient method was first proposed by Blakely and Simpson (1986) for determining the boundaries between geological bodies with different densities. The method involves the comparison of a center point with its eight nearest neighbors in four directions within each 3 × 3 calculation grid. The horizontal location and magnitude of the maximum values are found by interpolating a second-order polynomial through the trio of points provided that the magnitude of the middle point is greater than its two nearest neighbors in one direction. In theoretical models of multiple sources, however, the above condition does not allow the maximum horizontal locations to be fully located, and it could be difficult to correlate the edges of complicated sources. In this paper, the authors propose an additional condition to identify more maximum horizontal locations within the calculation grid. This additional condition will improve the method algorithm for interpreting the boundaries of magnetic and/or gravity sources. The improved algorithm was tested on gravity models and applied to gravity data for the Phu Khanh basin on the continental shelf of the East Vietnam Sea. The results show that the additional locations of the maximum horizontal gradient could be helpful for connecting the edges of complicated source bodies.

A framework for comparing different image segmentation methods and its use in studying equivalences between level set and fuzzy connectedness frameworks

PubMed Central

Ciesielski, Krzysztof Chris; Udupa, Jayaram K.

2011-01-01

In the current vast image segmentation literature, there seems to be considerable redundancy among algorithms, while there is a serious lack of methods that would allow their theoretical comparison to establish their similarity, equivalence, or distinctness. In this paper, we make an attempt to fill this gap. To accomplish this goal, we argue that: (1) every digital segmentation algorithm A should have a well defined continuous counterpart MA, referred to as its model, which constitutes an asymptotic of A when image resolution goes to infinity; (2) the equality of two such models MA and MA′ establishes a theoretical (asymptotic) equivalence of their digital counterparts A and A′. Such a comparison is of full theoretical value only when, for each involved algorithm A, its model MA is proved to be an asymptotic of A. So far, such proofs do not appear anywhere in the literature, even in the case of algorithms introduced as digitizations of continuous models, like level set segmentation algorithms. The main goal of this article is to explore a line of investigation for formally pairing the digital segmentation algorithms with their asymptotic models, justifying such relations with mathematical proofs, and using the results to compare the segmentation algorithms in this general theoretical framework. As a first step towards this general goal, we prove here that the gradient based thresholding model M∇ is the asymptotic for the fuzzy connectedness Udupa and Samarasekera segmentation algorithm used with gradient based affinity A∇. We also argue that, in a sense, M∇ is the asymptotic for the original front propagation level set algorithm of Malladi, Sethian, and Vemuri, thus establishing a theoretical equivalence between these two specific algorithms. Experimental evidence of this last equivalence is also provided. PMID:21442014

Three-dimensional Gravity Inversion with a New Gradient Scheme on Unstructured Grids

NASA Astrophysics Data System (ADS)

Sun, S.; Yin, C.; Gao, X.; Liu, Y.; Zhang, B.

2017-12-01

Stabilized gradient-based methods have been proved to be efficient for inverse problems. Based on these methods, setting gradient close to zero can effectively minimize the objective function. Thus the gradient of objective function determines the inversion results. By analyzing the cause of poor resolution on depth in gradient-based gravity inversion methods, we find that imposing depth weighting functional in conventional gradient can improve the depth resolution to some extent. However, the improvement is affected by the regularization parameter and the effect of the regularization term becomes smaller with increasing depth (shown as Figure 1 (a)). In this paper, we propose a new gradient scheme for gravity inversion by introducing a weighted model vector. The new gradient can improve the depth resolution more efficiently, which is independent of the regularization parameter, and the effect of regularization term will not be weakened when depth increases. Besides, fuzzy c-means clustering method and smooth operator are both used as regularization terms to yield an internal consecutive inverse model with sharp boundaries (Sun and Li, 2015). We have tested our new gradient scheme with unstructured grids on synthetic data to illustrate the effectiveness of the algorithm. Gravity forward modeling with unstructured grids is based on the algorithm proposed by Okbe (1979). We use a linear conjugate gradient inversion scheme to solve the inversion problem. The numerical experiments show a great improvement in depth resolution compared with regular gradient scheme, and the inverse model is compact at all depths (shown as Figure 1 (b)). AcknowledgeThis research is supported by Key Program of National Natural Science Foundation of China (41530320), China Natural Science Foundation for Young Scientists (41404093), and Key National Research Project of China (2016YFC0303100, 2017YFC0601900). ReferencesSun J, Li Y. 2015. Multidomain petrophysically constrained inversion and geology differentiation using guided fuzzy c-means clustering. Geophysics, 80(4): ID1-ID18. Okabe M. 1979. Analytical expressions for gravity anomalies due to homogeneous polyhedral bodies and translations into magnetic anomalies. Geophysics, 44(4), 730-741.

Automatic facial animation parameters extraction in MPEG-4 visual communication

NASA Astrophysics Data System (ADS)

Yang, Chenggen; Gong, Wanwei; Yu, Lu

2002-01-01

Facial Animation Parameters (FAPs) are defined in MPEG-4 to animate a facial object. The algorithm proposed in this paper to extract these FAPs is applied to very low bit-rate video communication, in which the scene is composed of a head-and-shoulder object with complex background. This paper addresses the algorithm to automatically extract all FAPs needed to animate a generic facial model, estimate the 3D motion of head by points. The proposed algorithm extracts human facial region by color segmentation and intra-frame and inter-frame edge detection. Facial structure and edge distribution of facial feature such as vertical and horizontal gradient histograms are used to locate the facial feature region. Parabola and circle deformable templates are employed to fit facial feature and extract a part of FAPs. A special data structure is proposed to describe deformable templates to reduce time consumption for computing energy functions. Another part of FAPs, 3D rigid head motion vectors, are estimated by corresponding-points method. A 3D head wire-frame model provides facial semantic information for selection of proper corresponding points, which helps to increase accuracy of 3D rigid object motion estimation.

The pulse-pair algorithm as a robust estimator of turbulent weather spectral parameters using airborne pulse Doppler radar

NASA Technical Reports Server (NTRS)

Baxa, Ernest G., Jr.; Lee, Jonggil

1991-01-01

The pulse pair method for spectrum parameter estimation is commonly used in pulse Doppler weather radar signal processing since it is economical to implement and can be shown to be a maximum likelihood estimator. With the use of airborne weather radar for windshear detection, the turbulent weather and strong ground clutter return spectrum differs from that assumed in its derivation, so the performance robustness of the pulse pair technique must be understood. Here, the effect of radar system pulse to pulse phase jitter and signal spectrum skew on the pulse pair algorithm performance is discussed. Phase jitter effect may be significant when the weather return signal to clutter ratio is very low and clutter rejection filtering is attempted. The analysis can be used to develop design specifications for airborne radar system phase stability. It is also shown that the weather return spectrum skew can cause a significant bias in the pulse pair mean windspeed estimates, and that the poly pulse pair algorithm can reduce this bias. It is suggested that use of a spectrum mode estimator may be more appropriate in characterizing the windspeed within a radar range resolution cell for detection of hazardous windspeed gradients.

Detection of buried magnetic objects by a SQUID gradiometer system

NASA Astrophysics Data System (ADS)

Meyer, Hans-Georg; Hartung, Konrad; Linzen, Sven; Schneider, Michael; Stolz, Ronny; Fried, Wolfgang; Hauspurg, Sebastian

2009-05-01

We present a magnetic detection system based on superconducting gradiometric sensors (SQUID gradiometers). The system provides a unique fast mapping of large areas with a high resolution of the magnetic field gradient as well as the local position. A main part of this work is the localization and classification of magnetic objects in the ground by automatic interpretation of geomagnetic field gradients, measured by the SQUID system. In accordance with specific features the field is decomposed into segments, which allow inferences to possible objects in the ground. The global consideration of object describing properties and their optimization using error minimization methods allows the reconstruction of superimposed features and detection of buried objects. The analysis system of measured geomagnetic fields works fully automatically. By a given surface of area-measured gradients the algorithm determines within numerical limits the absolute position of objects including depth with sub-pixel accuracy and allows an arbitrary position and attitude of sources. Several SQUID gradiometer data sets were used to show the applicability of the analysis algorithm.

GPU computing with Kaczmarz’s and other iterative algorithms for linear systems

PubMed Central

Elble, Joseph M.; Sahinidis, Nikolaos V.; Vouzis, Panagiotis

2009-01-01

The graphics processing unit (GPU) is used to solve large linear systems derived from partial differential equations. The differential equations studied are strongly convection-dominated, of various sizes, and common to many fields, including computational fluid dynamics, heat transfer, and structural mechanics. The paper presents comparisons between GPU and CPU implementations of several well-known iterative methods, including Kaczmarz’s, Cimmino’s, component averaging, conjugate gradient normal residual (CGNR), symmetric successive overrelaxation-preconditioned conjugate gradient, and conjugate-gradient-accelerated component-averaged row projections (CARP-CG). Computations are preformed with dense as well as general banded systems. The results demonstrate that our GPU implementation outperforms CPU implementations of these algorithms, as well as previously studied parallel implementations on Linux clusters and shared memory systems. While the CGNR method had begun to fall out of favor for solving such problems, for the problems studied in this paper, the CGNR method implemented on the GPU performed better than the other methods, including a cluster implementation of the CARP-CG method. PMID:20526446

Optimization of neural network architecture for classification of radar jamming FM signals

NASA Astrophysics Data System (ADS)

Soto, Alberto; Mendoza, Ariadna; Flores, Benjamin C.

2017-05-01

The purpose of this study is to investigate several artificial Neural Network (NN) architectures in order to design a cognitive radar system capable of optimally distinguishing linear Frequency-Modulated (FM) signals from bandlimited Additive White Gaussian Noise (AWGN). The goal is to create a theoretical framework to determine an optimal NN architecture to achieve a Probability of Detection (PD) of 95% or higher and a Probability of False Alarm (PFA) of 1.5% or lower at 5 dB Signal to Noise Ratio (SNR). Literature research reveals that the frequency-domain power spectral densities characterize a signal more efficiently than its time-domain counterparts. Therefore, the input data is preprocessed by calculating the magnitude square of the Discrete Fourier Transform of the digitally sampled bandlimited AWGN and linear FM signals to populate a matrix containing N number of samples and M number of spectra. This matrix is used as input for the NN, and the spectra are divided as follows: 70% for training, 15% for validation, and 15% for testing. The study begins by experimentally deducing the optimal number of hidden neurons (1-40 neurons), then the optimal number of hidden layers (1-5 layers), and lastly, the most efficient learning algorithm. The training algorithms examined are: Resilient Backpropagation, Scaled Conjugate Gradient, Conjugate Gradient with Powell/Beale Restarts, Polak-Ribiére Conjugate Gradient, and Variable Learning Rate Backpropagation. We determine that an architecture with ten hidden neurons (or higher), one hidden layer, and a Scaled Conjugate Gradient for training algorithm encapsulates an optimal architecture for our application.

A hybrid neural learning algorithm using evolutionary learning and derivative free local search method.

PubMed

Ghosh, Ranadhir; Yearwood, John; Ghosh, Moumita; Bagirov, Adil

2006-06-01

In this paper we investigate a hybrid model based on the Discrete Gradient method and an evolutionary strategy for determining the weights in a feed forward artificial neural network. Also we discuss different variants for hybrid models using the Discrete Gradient method and an evolutionary strategy for determining the weights in a feed forward artificial neural network. The Discrete Gradient method has the advantage of being able to jump over many local minima and find very deep local minima. However, earlier research has shown that a good starting point for the discrete gradient method can improve the quality of the solution point. Evolutionary algorithms are best suited for global optimisation problems. Nevertheless they are cursed with longer training times and often unsuitable for real world application. For optimisation problems such as weight optimisation for ANNs in real world applications the dimensions are large and time complexity is critical. Hence the idea of a hybrid model can be a suitable option. In this paper we propose different fusion strategies for hybrid models combining the evolutionary strategy with the discrete gradient method to obtain an optimal solution much quicker. Three different fusion strategies are discussed: a linear hybrid model, an iterative hybrid model and a restricted local search hybrid model. Comparative results on a range of standard datasets are provided for different fusion hybrid models.

A parallel algorithm for 2D visco-acoustic frequency-domain full-waveform inversion: application to a dense OBS data set

NASA Astrophysics Data System (ADS)

Sourbier, F.; Operto, S.; Virieux, J.

2006-12-01

We present a distributed-memory parallel algorithm for 2D visco-acoustic full-waveform inversion of wide-angle seismic data. Our code is written in fortran90 and use MPI for parallelism. The algorithm was applied to real wide-angle data set recorded by 100 OBSs with a 1-km spacing in the eastern-Nankai trough (Japan) to image the deep structure of the subduction zone. Full-waveform inversion is applied sequentially to discrete frequencies by proceeding from the low to the high frequencies. The inverse problem is solved with a classic gradient method. Full-waveform modeling is performed with a frequency-domain finite-difference method. In the frequency-domain, solving the wave equation requires resolution of a large unsymmetric system of linear equations. We use the massively parallel direct solver MUMPS (http://www.enseeiht.fr/irit/apo/MUMPS) for distributed-memory computer to solve this system. The MUMPS solver is based on a multifrontal method for the parallel factorization. The MUMPS algorithm is subdivided in 3 main steps: a symbolic analysis step that performs re-ordering of the matrix coefficients to minimize the fill-in of the matrix during the subsequent factorization and an estimation of the assembly tree of the matrix. Second, the factorization is performed with dynamic scheduling to accomodate numerical pivoting and provides the LU factors distributed over all the processors. Third, the resolution is performed for multiple sources. To compute the gradient of the cost function, 2 simulations per shot are required (one to compute the forward wavefield and one to back-propagate residuals). The multi-source resolutions can be performed in parallel with MUMPS. In the end, each processor stores in core a sub-domain of all the solutions. These distributed solutions can be exploited to compute in parallel the gradient of the cost function. Since the gradient of the cost function is a weighted stack of the shot and residual solutions of MUMPS, each processor computes the corresponding sub-domain of the gradient. In the end, the gradient is centralized on the master processor using a collective communation. The gradient is scaled by the diagonal elements of the Hessian matrix. This scaling is computed only once per frequency before the first iteration of the inversion. Estimation of the diagonal terms of the Hessian requires performing one simulation per non redondant shot and receiver position. The same strategy that the one used for the gradient is used to compute the diagonal Hessian in parallel. This algorithm was applied to a dense wide-angle data set recorded by 100 OBSs in the eastern Nankai trough, offshore Japan. Thirteen frequencies ranging from 3 and 15 Hz were inverted. Tweny iterations per frequency were computed leading to 260 tomographic velocity models of increasing resolution. The velocity model dimensions are 105 km x 25 km corresponding to a finite-difference grid of 4201 x 1001 grid with a 25-m grid interval. The number of shot was 1005 and the number of inverted OBS gathers was 93. The inversion requires 20 days on 6 32-bits bi-processor nodes with 4 Gbytes of RAM memory per node when only the LU factorization is performed in parallel. Preliminary estimations of the time required to perform the inversion with the fully-parallelized code is 6 and 4 days using 20 and 50 processors respectively.

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

Wannamaker, Philip E.

We have developed an algorithm for the inversion of magnetotelluric (MT) data to a 3D earth resistivity model based upon the finite element method. Hexahedral edge finite elements are implemented to accommodate discontinuities in the electric field across resistivity boundaries, and to accurately simulate topographic variations. All matrices are reduced and solved using direct solution modules which avoids ill-conditioning endemic to iterative solvers such as conjugate gradients, principally PARDISO for the finite element system and PLASMA for the parameter step estimate. Large model parameterizations can be handled by transforming the Gauss-Newton estimator to data-space form. Accuracy of the forward problemmore » and jacobians has been checked by comparison to integral equations results and by limiting asymptotes. Inverse accuracy and performance has been verified against the public Dublin Secret Test Model 2 and the well-known Mount St Helens 3D MT data set. This algorithm we believe is the most capable yet for forming 3D images of earth resistivity structure and their implications for geothermal fluids and pathways.« less

Melanoma segmentation based on deep learning.

PubMed

Zhang, Xiaoqing

2017-12-01

Malignant melanoma is one of the most deadly forms of skin cancer, which is one of the world's fastest-growing cancers. Early diagnosis and treatment is critical. In this study, a neural network structure is utilized to construct a broad and accurate basis for the diagnosis of skin cancer, thereby reducing screening errors. The technique is able to improve the efficacy for identification of normally indistinguishable lesions (such as pigment spots) versus clinically unknown lesions, and to ultimately improve the diagnostic accuracy. In the field of medical imaging, in general, using neural networks for image segmentation is relatively rare. The existing traditional machine-learning neural network algorithms still cannot completely solve the problem of information loss, nor detect the precise division of the boundary area. We use an improved neural network framework, described herein, to achieve efficacious feature learning, and satisfactory segmentation of melanoma images. The architecture of the network includes multiple convolution layers, dropout layers, softmax layers, multiple filters, and activation functions. The number of data sets can be increased via rotation of the training set. A non-linear activation function (such as ReLU and ELU) is employed to alleviate the problem of gradient disappearance, and RMSprop/Adam are incorporated to optimize the loss algorithm. A batch normalization layer is added between the convolution layer and the activation layer to solve the problem of gradient disappearance and explosion. Experiments, described herein, show that our improved neural network architecture achieves higher accuracy for segmentation of melanoma images as compared with existing processes.

Numerical preservation of symmetry properties of continuum problems

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

Caramana, E.J.; Whalen, P.

1997-12-31

The authors investigate the problem of perfectly preserving a symmetry associated naturally with one coordinate system when calculated in a different coordinate system. This allows a much wider range of problems that may be viewed as perturbations of the given symmetry to be investigated. They study the problem of preserving cylindrical symmetry in two-dimensional cartesian geometry and spherical symmetry in two-dimensional cylindrical geometry. They show that this can be achieved by a simple modification of the gradient operator used to compute the force in a staggered grid Lagrangian hydrodynamics algorithm. In the absence of the supposed symmetry they show thatmore » the new operator produces almost no change in the results because it is always close to the original gradient operator. Their technique this results in a subtle manipulation of the spatial truncation error in favor of the assumed symmetry but only to the extent that it is naturally present in the physical situation. This not only extends the range of previous algorithms and the use of new ones for these studies, but for spherical or cylindrical calculations reduces the sensitivity of the results to grid setup with equal angular zoning that has heretofore been necessary with these problems. Although this work is in two-dimensions, it does point the way to solving this problem in three-dimensions. This is particularly important for the ASCI initiative. The manner in which these results can be extended to three-dimensions will be discussed.« less

Two-Dimensional High-Lift Aerodynamic Optimization Using Neural Networks

NASA Technical Reports Server (NTRS)

Greenman, Roxana M.

1998-01-01

The high-lift performance of a multi-element airfoil was optimized by using neural-net predictions that were trained using a computational data set. The numerical data was generated using a two-dimensional, incompressible, Navier-Stokes algorithm with the Spalart-Allmaras turbulence model. Because it is difficult to predict maximum lift for high-lift systems, an empirically-based maximum lift criteria was used in this study to determine both the maximum lift and the angle at which it occurs. The 'pressure difference rule,' which states that the maximum lift condition corresponds to a certain pressure difference between the peak suction pressure and the pressure at the trailing edge of the element, was applied and verified with experimental observations for this configuration. Multiple input, single output networks were trained using the NASA Ames variation of the Levenberg-Marquardt algorithm for each of the aerodynamic coefficients (lift, drag and moment). The artificial neural networks were integrated with a gradient-based optimizer. Using independent numerical simulations and experimental data for this high-lift configuration, it was shown that this design process successfully optimized flap deflection, gap, overlap, and angle of attack to maximize lift. Once the neural nets were trained and integrated with the optimizer, minimal additional computer resources were required to perform optimization runs with different initial conditions and parameters. Applying the neural networks within the high-lift rigging optimization process reduced the amount of computational time and resources by 44% compared with traditional gradient-based optimization procedures for multiple optimization runs.

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, part 2

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noel M.

1990-01-01

It is shown how the look-ahead Lanczos process (combined with a quasi-minimal residual QMR) approach) can be used to develop a robust black box solver for large sparse non-Hermitian linear systems. Details of an implementation of the resulting QMR algorithm are presented. It is demonstrated that the QMR method is closely related to the biconjugate gradient (BCG) algorithm; however, unlike BCG, the QMR algorithm has smooth convergence curves and good numerical properties. We report numerical experiments with our implementation of the look-ahead Lanczos algorithm, both for eigenvalue problem and linear systems. Also, program listings of FORTRAN implementations of the look-ahead algorithm and the QMR method are included.

An Accurate Fire-Spread Algorithm in the Weather Research and Forecasting Model Using the Level-Set Method

NASA Astrophysics Data System (ADS)

Muñoz-Esparza, Domingo; Kosović, Branko; Jiménez, Pedro A.; Coen, Janice L.

2018-04-01

The level-set method is typically used to track and propagate the fire perimeter in wildland fire models. Herein, a high-order level-set method using fifth-order WENO scheme for the discretization of spatial derivatives and third-order explicit Runge-Kutta temporal integration is implemented within the Weather Research and Forecasting model wildland fire physics package, WRF-Fire. The algorithm includes solution of an additional partial differential equation for level-set reinitialization. The accuracy of the fire-front shape and rate of spread in uncoupled simulations is systematically analyzed. It is demonstrated that the common implementation used by level-set-based wildfire models yields to rate-of-spread errors in the range 10-35% for typical grid sizes (Δ = 12.5-100 m) and considerably underestimates fire area. Moreover, the amplitude of fire-front gradients in the presence of explicitly resolved turbulence features is systematically underestimated. In contrast, the new WRF-Fire algorithm results in rate-of-spread errors that are lower than 1% and that become nearly grid independent. Also, the underestimation of fire area at the sharp transition between the fire front and the lateral flanks is found to be reduced by a factor of ≈7. A hybrid-order level-set method with locally reduced artificial viscosity is proposed, which substantially alleviates the computational cost associated with high-order discretizations while preserving accuracy. Simulations of the Last Chance wildfire demonstrate additional benefits of high-order accurate level-set algorithms when dealing with complex fuel heterogeneities, enabling propagation across narrow fuel gaps and more accurate fire backing over the lee side of no fuel clusters.

Soft learning vector quantization and clustering algorithms based on ordered weighted aggregation operators.

PubMed

Karayiannis, N B

2000-01-01

This paper presents the development and investigates the properties of ordered weighted learning vector quantization (LVQ) and clustering algorithms. These algorithms are developed by using gradient descent to minimize reformulation functions based on aggregation operators. An axiomatic approach provides conditions for selecting aggregation operators that lead to admissible reformulation functions. Minimization of admissible reformulation functions based on ordered weighted aggregation operators produces a family of soft LVQ and clustering algorithms, which includes fuzzy LVQ and clustering algorithms as special cases. The proposed LVQ and clustering algorithms are used to perform segmentation of magnetic resonance (MR) images of the brain. The diagnostic value of the segmented MR images provides the basis for evaluating a variety of ordered weighted LVQ and clustering algorithms.

Steer-PROP: a GRASE-PROPELLER sequence with interecho steering gradient pulses.

PubMed

Srinivasan, Girish; Rangwala, Novena; Zhou, Xiaohong Joe

2018-05-01

This study demonstrates a novel PROPELLER (periodically rotated overlapping parallel lines with enhanced reconstruction) pulse sequence, termed Steer-PROP, based on gradient and spin echo (GRASE), to reduce the imaging times and address phase errors inherent to GRASE. The study also illustrates the feasibility of using Steer-PROP as an alternative to single-shot echo planar imaging (SS-EPI) to produce distortion-free diffusion images in all imaging planes. Steer-PROP uses a series of blip gradient pulses to produce N (N = 3-5) adjacent k-space blades in each repetition time, where N is the number of gradient echoes in a GRASE sequence. This sampling strategy enables a phase correction algorithm to systematically address the GRASE phase errors as well as the motion-induced phase inconsistency. Steer-PROP was evaluated on phantoms and healthy human subjects at both 1.5T and 3.0T for T 2 - and diffusion-weighted imaging. Steer-PROP produced similar image quality as conventional PROPELLER based on fast spin echo (FSE), while taking only a fraction (e.g., 1/3) of the scan time. The robustness against motion in Steer-PROP was comparable to that of FSE-based PROPELLER. Using Steer-PROP, high quality and distortion-free diffusion images were obtained from human subjects in all imaging planes, demonstrating a considerable advantage over SS-EPI. The proposed Steer-PROP sequence can substantially reduce the scan times compared with FSE-based PROPELLER while achieving adequate image quality. The novel k-space sampling strategy in Steer-PROP not only enables an integrated phase correction method that addresses various sources of phase errors, but also minimizes the echo spacing compared with alternative sampling strategies. Steer-PROP can also be a viable alternative to SS-EPI to decrease image distortion in all imaging planes. Magn Reson Med 79:2533-2541, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

A photoacoustic imaging reconstruction method based on directional total variation with adaptive directivity.

PubMed

Wang, Jin; Zhang, Chen; Wang, Yuanyuan

2017-05-30

In photoacoustic tomography (PAT), total variation (TV) based iteration algorithm is reported to have a good performance in PAT image reconstruction. However, classical TV based algorithm fails to preserve the edges and texture details of the image because it is not sensitive to the direction of the image. Therefore, it is of great significance to develop a new PAT reconstruction algorithm to effectively solve the drawback of TV. In this paper, a directional total variation with adaptive directivity (DDTV) model-based PAT image reconstruction algorithm, which weightedly sums the image gradients based on the spatially varying directivity pattern of the image is proposed to overcome the shortcomings of TV. The orientation field of the image is adaptively estimated through a gradient-based approach. The image gradients are weighted at every pixel based on both its anisotropic direction and another parameter, which evaluates the estimated orientation field reliability. An efficient algorithm is derived to solve the iteration problem associated with DDTV and possessing directivity of the image adaptively updated for each iteration step. Several texture images with various directivity patterns are chosen as the phantoms for the numerical simulations. The 180-, 90- and 30-view circular scans are conducted. Results obtained show that the DDTV-based PAT reconstructed algorithm outperforms the filtered back-projection method (FBP) and TV algorithms in the quality of reconstructed images with the peak signal-to-noise rations (PSNR) exceeding those of TV and FBP by about 10 and 18 dB, respectively, for all cases. The Shepp-Logan phantom is studied with further discussion of multimode scanning, convergence speed, robustness and universality aspects. In-vitro experiments are performed for both the sparse-view circular scanning and linear scanning. The results further prove the effectiveness of the DDTV, which shows better results than that of the TV with sharper image edges and clearer texture details. Both numerical simulation and in vitro experiments confirm that the DDTV provides a significant quality improvement of PAT reconstructed images for various directivity patterns.

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.

A Gradient Taguchi Method for Engineering Optimization

NASA Astrophysics Data System (ADS)

Hwang, Shun-Fa; Wu, Jen-Chih; He, Rong-Song

2017-10-01

To balance the robustness and the convergence speed of optimization, a novel hybrid algorithm consisting of Taguchi method and the steepest descent method is proposed in this work. Taguchi method using orthogonal arrays could quickly find the optimum combination of the levels of various factors, even when the number of level and/or factor is quite large. This algorithm is applied to the inverse determination of elastic constants of three composite plates by combining numerical method and vibration testing. For these problems, the proposed algorithm could find better elastic constants in less computation cost. Therefore, the proposed algorithm has nice robustness and fast convergence speed as compared to some hybrid genetic algorithms.

Application of XGBoost algorithm in hourly PM2.5 concentration prediction

NASA Astrophysics Data System (ADS)

Pan, Bingyue

2018-02-01

In view of prediction techniques of hourly PM2.5 concentration in China, this paper applied the XGBoost(Extreme Gradient Boosting) algorithm to predict hourly PM2.5 concentration. The monitoring data of air quality in Tianjin city was analyzed by using XGBoost algorithm. The prediction performance of the XGBoost method is evaluated by comparing observed and predicted PM2.5 concentration using three measures of forecast accuracy. The XGBoost method is also compared with the random forest algorithm, multiple linear regression, decision tree regression and support vector machines for regression models using computational results. The results demonstrate that the XGBoost algorithm outperforms other data mining methods.

Iterative initial condition reconstruction

NASA Astrophysics Data System (ADS)

Schmittfull, Marcel; Baldauf, Tobias; Zaldarriaga, Matias

2017-07-01

Motivated by recent developments in perturbative calculations of the nonlinear evolution of large-scale structure, we present an iterative algorithm to reconstruct the initial conditions in a given volume starting from the dark matter distribution in real space. In our algorithm, objects are first moved back iteratively along estimated potential gradients, with a progressively reduced smoothing scale, until a nearly uniform catalog is obtained. The linear initial density is then estimated as the divergence of the cumulative displacement, with an optional second-order correction. This algorithm should undo nonlinear effects up to one-loop order, including the higher-order infrared resummation piece. We test the method using dark matter simulations in real space. At redshift z =0 , we find that after eight iterations the reconstructed density is more than 95% correlated with the initial density at k ≤0.35 h Mpc-1 . The reconstruction also reduces the power in the difference between reconstructed and initial fields by more than 2 orders of magnitude at k ≤0.2 h Mpc-1 , and it extends the range of scales where the full broadband shape of the power spectrum matches linear theory by a factor of 2-3. As a specific application, we consider measurements of the baryonic acoustic oscillation (BAO) scale that can be improved by reducing the degradation effects of large-scale flows. In our idealized dark matter simulations, the method improves the BAO signal-to-noise ratio by a factor of 2.7 at z =0 and by a factor of 2.5 at z =0.6 , improving standard BAO reconstruction by 70% at z =0 and 30% at z =0.6 , and matching the optimal BAO signal and signal-to-noise ratio of the linear density in the same volume. For BAO, the iterative nature of the reconstruction is the most important aspect.

Efficient operator splitting algorithm for joint sparsity-regularized SPIRiT-based parallel MR imaging reconstruction.

PubMed

Duan, Jizhong; Liu, Yu; Jing, Peiguang

2018-02-01

Self-consistent parallel imaging (SPIRiT) is an auto-calibrating model for the reconstruction of parallel magnetic resonance imaging, which can be formulated as a regularized SPIRiT problem. The Projection Over Convex Sets (POCS) method was used to solve the formulated regularized SPIRiT problem. However, the quality of the reconstructed image still needs to be improved. Though methods such as NonLinear Conjugate Gradients (NLCG) can achieve higher spatial resolution, these methods always demand very complex computation and converge slowly. In this paper, we propose a new algorithm to solve the formulated Cartesian SPIRiT problem with the JTV and JL1 regularization terms. The proposed algorithm uses the operator splitting (OS) technique to decompose the problem into a gradient problem and a denoising problem with two regularization terms, which is solved by our proposed split Bregman based denoising algorithm, and adopts the Barzilai and Borwein method to update step size. Simulation experiments on two in vivo data sets demonstrate that the proposed algorithm is 1.3 times faster than ADMM for datasets with 8 channels. Especially, our proposal is 2 times faster than ADMM for the dataset with 32 channels. Copyright © 2017 Elsevier Inc. All rights reserved.

Improving Maritime Domain Awareness Using Neural Networks for Target of Interest Classification

DTIC Science & Technology

2015-03-01

spreading SCG scaled conjugate gradient xv THIS PAGE INTENTIONALLY LEFT BLANK xvi EXECUTIVE SUMMARY The research detailed in this thesis is a...algorithms were explored for training the neural networks: resilient backpropagation (RP) and scaled conjugate gradient backpropagation ( SCG ). The...results of the neural network training performance are presented using mean squared error convergence plots. In all implementations, the SCG learning

A landscape model for predicting potential natural vegetation of the Olympic Peninsula USA using boundary equations and newly developed environmental variables.

Treesearch

Jan A. Henderson; Robin D. Lesher; David H. Peter; Chris D. Ringo

2011-01-01

A gradient-analysis-based model and grid-based map are presented that use the potential vegetation zone as the object of the model. Several new variables are presented that describe the environmental gradients of the landscape at different scales. Boundary algorithms are conceptualized, and then defined, that describe the environmental boundaries between vegetation...

Supplemental optical specifications for imaging systems: parameters of phase gradient

NASA Astrophysics Data System (ADS)

Xuan, Bin; Li, Jun-Feng; Wang, Peng; Chen, Xiao-Ping; Song, Shu-Mei; Xie, Jing-Jiang

2009-12-01

Specifications of phase error, peak to valley (PV), and root mean square (rms) are not able to represent the properties of a wavefront reasonably because of their irresponsibility for spatial frequencies. Power spectral density is a parameter that is especially effective to indicate the frequency regime. However, it seems not convenient for opticians to implement. Parameters of phase gradient, PV gradient, and rms gradient are most correlated with a point-spread function of an imaging system, and they can provide clear instruction of manufacture. The algorithms of gradient parameters have been modified in order to represent the image quality better. In order to demonstrate the analyses, an experimental spherical mirror has been worked out. It is clear that imaging performances can be maintained while manufacture difficulties are decreased when a reasonable trade-off between specifications of phase error and phase gradient is made.

Dynamic metrology and data processing for precision freeform optics fabrication and testing

NASA Astrophysics Data System (ADS)

Aftab, Maham; Trumper, Isaac; Huang, Lei; Choi, Heejoo; Zhao, Wenchuan; Graves, Logan; Oh, Chang Jin; Kim, Dae Wook

2017-06-01

Dynamic metrology holds the key to overcoming several challenging limitations of conventional optical metrology, especially with regards to precision freeform optical elements. We present two dynamic metrology systems: 1) adaptive interferometric null testing; and 2) instantaneous phase shifting deflectometry, along with an overview of a gradient data processing and surface reconstruction technique. The adaptive null testing method, utilizing a deformable mirror, adopts a stochastic parallel gradient descent search algorithm in order to dynamically create a null testing condition for unknown freeform optics. The single-shot deflectometry system implemented on an iPhone uses a multiplexed display pattern to enable dynamic measurements of time-varying optical components or optics in vibration. Experimental data, measurement accuracy / precision, and data processing algorithms are discussed.

Numerical optimization methods for controlled systems with parameters

NASA Astrophysics Data System (ADS)

Tyatyushkin, A. I.

2017-10-01

First- and second-order numerical methods for optimizing controlled dynamical systems with parameters are discussed. In unconstrained-parameter problems, the control parameters are optimized by applying the conjugate gradient method. A more accurate numerical solution in these problems is produced by Newton's method based on a second-order functional increment formula. Next, a general optimal control problem with state constraints and parameters involved on the righthand sides of the controlled system and in the initial conditions is considered. This complicated problem is reduced to a mathematical programming one, followed by the search for optimal parameter values and control functions by applying a multimethod algorithm. The performance of the proposed technique is demonstrated by solving application problems.

Sea-surface temperature gradients across blue whale and sea turtle foraging trajectories off the Baja California Peninsula, Mexico

NASA Astrophysics Data System (ADS)

Etnoyer, Peter; Canny, David; Mate, Bruce R.; Morgan, Lance E.; Ortega-Ortiz, Joel G.; Nichols, Wallace J.

2006-02-01

Sea-surface temperature (SST) fronts are integral to pelagic ecology in the North Pacific Ocean, so it is necessary to understand their character and distribution, and the way these features influence the behavior of endangered and highly migratory species. Here, telemetry data from sixteen satellite-tagged blue whales ( Balaenoptera musculus) and sea turtles ( Caretta caretta, Chelonia mydas, and Lepidochelys olivacea) are employed to characterize 'biologically relevant' SST fronts off Baja California Sur. High residence times are used to identify presumed foraging areas, and SST gradients are calculated across advanced very high resolution radiometer (AVHRR) images of these regions. The resulting values are compared to classic definitions of SST fronts in the oceanographic literature. We find subtle changes in surface temperature (between 0.01 and 0.10 °C/km) across the foraging trajectories, near the lowest end of the oceanographic scale (between 0.03 and 0.3 °C/km), suggesting that edge-detection algorithms using gradient thresholds >0.10 °C/km may overlook pelagic habitats in tropical waters. We use this information to sensitize our edge-detection algorithm, and to identify persistent concentrations of subtle SST fronts in the Northeast Pacific Ocean between 2002 and 2004. The lower-gradient threshold increases the number of fronts detected, revealing more potential habitats in different places than we find with a higher-gradient threshold. This is the expected result, but it confirms that pelagic habitat can be overlooked, and that the temperature gradient parameter is an important one.

Reliable clarity automatic-evaluation method for optical remote sensing images

NASA Astrophysics Data System (ADS)

Qin, Bangyong; Shang, Ren; Li, Shengyang; Hei, Baoqin; Liu, Zhiwen

2015-10-01

Image clarity, which reflects the sharpness degree at the edge of objects in images, is an important quality evaluate index for optical remote sensing images. Scholars at home and abroad have done a lot of work on estimation of image clarity. At present, common clarity-estimation methods for digital images mainly include frequency-domain function methods, statistical parametric methods, gradient function methods and edge acutance methods. Frequency-domain function method is an accurate clarity-measure approach. However, its calculation process is complicate and cannot be carried out automatically. Statistical parametric methods and gradient function methods are both sensitive to clarity of images, while their results are easy to be affected by the complex degree of images. Edge acutance method is an effective approach for clarity estimate, while it needs picking out the edges manually. Due to the limits in accuracy, consistent or automation, these existing methods are not applicable to quality evaluation of optical remote sensing images. In this article, a new clarity-evaluation method, which is based on the principle of edge acutance algorithm, is proposed. In the new method, edge detection algorithm and gradient search algorithm are adopted to automatically search the object edges in images. Moreover, The calculation algorithm for edge sharpness has been improved. The new method has been tested with several groups of optical remote sensing images. Compared with the existing automatic evaluation methods, the new method perform better both in accuracy and consistency. Thus, the new method is an effective clarity evaluation method for optical remote sensing images.

An Improved 3D Joint Inversion Method of Potential Field Data Using Cross-Gradient Constraint and LSQR Method

NASA Astrophysics Data System (ADS)

Joulidehsar, Farshad; Moradzadeh, Ali; Doulati Ardejani, Faramarz

2018-06-01

The joint interpretation of two sets of geophysical data related to the same source is an appropriate method for decreasing non-uniqueness of the resulting models during inversion process. Among the available methods, a method based on using cross-gradient constraint combines two datasets is an efficient approach. This method, however, is time-consuming for 3D inversion and cannot provide an exact assessment of situation and extension of anomaly of interest. In this paper, the first attempt is to speed up the required calculation by substituting singular value decomposition by least-squares QR method to solve the large-scale kernel matrix of 3D inversion, more rapidly. Furthermore, to improve the accuracy of resulting models, a combination of depth-weighing matrix and compacted constraint, as automatic selection covariance of initial parameters, is used in the proposed inversion algorithm. This algorithm was developed in Matlab environment and first implemented on synthetic data. The 3D joint inversion of synthetic gravity and magnetic data shows a noticeable improvement in the results and increases the efficiency of algorithm for large-scale problems. Additionally, a real gravity and magnetic dataset of Jalalabad mine, in southeast of Iran was tested. The obtained results by the improved joint 3D inversion of cross-gradient along with compacted constraint showed a mineralised zone in depth interval of about 110-300 m which is in good agreement with the available drilling data. This is also a further confirmation on the accuracy and progress of the improved inversion algorithm.

Missing value imputation in DNA microarrays based on conjugate gradient method.

PubMed

Dorri, Fatemeh; Azmi, Paeiz; Dorri, Faezeh

2012-02-01

Analysis of gene expression profiles needs a complete matrix of gene array values; consequently, imputation methods have been suggested. In this paper, an algorithm that is based on conjugate gradient (CG) method is proposed to estimate missing values. k-nearest neighbors of the missed entry are first selected based on absolute values of their Pearson correlation coefficient. Then a subset of genes among the k-nearest neighbors is labeled as the best similar ones. CG algorithm with this subset as its input is then used to estimate the missing values. Our proposed CG based algorithm (CGimpute) is evaluated on different data sets. The results are compared with sequential local least squares (SLLSimpute), Bayesian principle component analysis (BPCAimpute), local least squares imputation (LLSimpute), iterated local least squares imputation (ILLSimpute) and adaptive k-nearest neighbors imputation (KNNKimpute) methods. The average of normalized root mean squares error (NRMSE) and relative NRMSE in different data sets with various missing rates shows CGimpute outperforms other methods. Copyright © 2011 Elsevier Ltd. All rights reserved.

A new modified conjugate gradient coefficient for solving system of linear equations

NASA Astrophysics Data System (ADS)

Hajar, N.; ‘Aini, N.; Shapiee, N.; Abidin, Z. Z.; Khadijah, W.; Rivaie, M.; Mamat, M.

2017-09-01

Conjugate gradient (CG) method is an evolution of computational method in solving unconstrained optimization problems. This approach is easy to implement due to its simplicity and has been proven to be effective in solving real-life application. Although this field has received copious amount of attentions in recent years, some of the new approaches of CG algorithm cannot surpass the efficiency of the previous versions. Therefore, in this paper, a new CG coefficient which retains the sufficient descent and global convergence properties of the original CG methods is proposed. This new CG is tested on a set of test functions under exact line search. Its performance is then compared to that of some of the well-known previous CG methods based on number of iterations and CPU time. The results show that the new CG algorithm has the best efficiency amongst all the methods tested. This paper also includes an application of the new CG algorithm for solving large system of linear equations

Analysis of Online Composite Mirror Descent Algorithm.

PubMed

Lei, Yunwen; Zhou, Ding-Xuan

2017-03-01

We study the convergence of the online composite mirror descent algorithm, which involves a mirror map to reflect the geometry of the data and a convex objective function consisting of a loss and a regularizer possibly inducing sparsity. Our error analysis provides convergence rates in terms of properties of the strongly convex differentiable mirror map and the objective function. For a class of objective functions with Hölder continuous gradients, the convergence rates of the excess (regularized) risk under polynomially decaying step sizes have the order [Formula: see text] after [Formula: see text] iterates. Our results improve the existing error analysis for the online composite mirror descent algorithm by avoiding averaging and removing boundedness assumptions, and they sharpen the existing convergence rates of the last iterate for online gradient descent without any boundedness assumptions. Our methodology mainly depends on a novel error decomposition in terms of an excess Bregman distance, refined analysis of self-bounding properties of the objective function, and the resulting one-step progress bounds.

Faster PET reconstruction with a stochastic primal-dual hybrid gradient method

NASA Astrophysics Data System (ADS)

Ehrhardt, Matthias J.; Markiewicz, Pawel; Chambolle, Antonin; Richtárik, Peter; Schott, Jonathan; Schönlieb, Carola-Bibiane

2017-08-01

Image reconstruction in positron emission tomography (PET) is computationally challenging due to Poisson noise, constraints and potentially non-smooth priors-let alone the sheer size of the problem. An algorithm that can cope well with the first three of the aforementioned challenges is the primal-dual hybrid gradient algorithm (PDHG) studied by Chambolle and Pock in 2011. However, PDHG updates all variables in parallel and is therefore computationally demanding on the large problem sizes encountered with modern PET scanners where the number of dual variables easily exceeds 100 million. In this work, we numerically study the usage of SPDHG-a stochastic extension of PDHG-but is still guaranteed to converge to a solution of the deterministic optimization problem with similar rates as PDHG. Numerical results on a clinical data set show that by introducing randomization into PDHG, similar results as the deterministic algorithm can be achieved using only around 10 % of operator evaluations. Thus, making significant progress towards the feasibility of sophisticated mathematical models in a clinical setting.

Interpolation algorithm for asynchronous ADC-data

NASA Astrophysics Data System (ADS)

Bramburger, Stefan; Zinke, Benny; Killat, Dirk

2017-09-01

This paper presents a modified interpolation algorithm for signals with variable data rate from asynchronous ADCs. The Adaptive weights Conjugate gradient Toeplitz matrix (ACT) algorithm is extended to operate with a continuous data stream. An additional preprocessing of data with constant and linear sections and a weighted overlap of step-by-step into spectral domain transformed signals improve the reconstruction of the asycnhronous ADC signal. The interpolation method can be used if asynchronous ADC data is fed into synchronous digital signal processing.

Statistical Relational Learning to Predict Primary Myocardial Infarction from Electronic Health Records

PubMed Central

Weiss, Jeremy C; Page, David; Peissig, Peggy L; Natarajan, Sriraam; McCarty, Catherine

2013-01-01

Electronic health records (EHRs) are an emerging relational domain with large potential to improve clinical outcomes. We apply two statistical relational learning (SRL) algorithms to the task of predicting primary myocardial infarction. We show that one SRL algorithm, relational functional gradient boosting, outperforms propositional learners particularly in the medically-relevant high recall region. We observe that both SRL algorithms predict outcomes better than their propositional analogs and suggest how our methods can augment current epidemiological practices. PMID:25360347

Boundary layer height determination from Lidar for improving air pollution episode modelling: development of new algorithm and evaluation

NASA Astrophysics Data System (ADS)

Yang, T.; Wang, Z.; Zhang, W.; Gbaguidi, A.; Sugimoto, N.; Matsui, I.; Wang, X.; Yele, S.

2017-12-01

Predicting air pollution events in low atmosphere over megacities requires thorough understanding of the tropospheric dynamic and chemical processes, involving notably, continuous and accurate determination of the boundary layer height (BLH). Through intensive observations experimented over Beijing (China), and an exhaustive evaluation existing algorithms applied to the BLH determination, persistent critical limitations are noticed, in particular over polluted episodes. Basically, under weak thermal convection with high aerosol loading, none of the retrieval algorithms is able to fully capture the diurnal cycle of the BLH due to pollutant insufficient vertical mixing in the boundary layer associated with the impact of gravity waves on the tropospheric structure. Subsequently, a new approach based on gravity wave theory (the cubic root gradient method: CRGM), is developed to overcome such weakness and accurately reproduce the fluctuations of the BLH under various atmospheric pollution conditions. Comprehensive evaluation of CRGM highlights its high performance in determining BLH from Lidar. In comparison with the existing retrieval algorithms, the CRGM potentially reduces related computational uncertainties and errors from BLH determination (strong increase of correlation coefficient from 0.44 to 0.91 and significant decreases of the root mean square error from 643 m to 142 m). Such newly developed technique is undoubtedly expected to contribute to improve the accuracy of air quality modelling and forecasting systems.

A coarse-to-fine kernel matching approach for mean-shift based visual tracking

NASA Astrophysics Data System (ADS)

Liangfu, L.; Zuren, F.; Weidong, C.; Ming, J.

2009-03-01

Mean shift is an efficient pattern match algorithm. It is widely used in visual tracking fields since it need not perform whole search in the image space. It employs gradient optimization method to reduce the time of feature matching and realize rapid object localization, and uses Bhattacharyya coefficient as the similarity measure between object template and candidate template. This thesis presents a mean shift algorithm based on coarse-to-fine search for the best kernel matching. This paper researches for object tracking with large motion area based on mean shift. To realize efficient tracking of such an object, we present a kernel matching method from coarseness to fine. If the motion areas of the object between two frames are very large and they are not overlapped in image space, then the traditional mean shift method can only obtain local optimal value by iterative computing in the old object window area, so the real tracking position cannot be obtained and the object tracking will be disabled. Our proposed algorithm can efficiently use a similarity measure function to realize the rough location of motion object, then use mean shift method to obtain the accurate local optimal value by iterative computing, which successfully realizes object tracking with large motion. Experimental results show its good performance in accuracy and speed when compared with background-weighted histogram algorithm in the literature.

Efficient methods for overlapping group lasso.

PubMed

Yuan, Lei; Liu, Jun; Ye, Jieping

2013-09-01

The group Lasso is an extension of the Lasso for feature selection on (predefined) nonoverlapping groups of features. The nonoverlapping group structure limits its applicability in practice. There have been several recent attempts to study a more general formulation where groups of features are given, potentially with overlaps between the groups. The resulting optimization is, however, much more challenging to solve due to the group overlaps. In this paper, we consider the efficient optimization of the overlapping group Lasso penalized problem. We reveal several key properties of the proximal operator associated with the overlapping group Lasso, and compute the proximal operator by solving the smooth and convex dual problem, which allows the use of the gradient descent type of algorithms for the optimization. Our methods and theoretical results are then generalized to tackle the general overlapping group Lasso formulation based on the l(q) norm. We further extend our algorithm to solve a nonconvex overlapping group Lasso formulation based on the capped norm regularization, which reduces the estimation bias introduced by the convex penalty. We have performed empirical evaluations using both a synthetic and the breast cancer gene expression dataset, which consists of 8,141 genes organized into (overlapping) gene sets. Experimental results show that the proposed algorithm is more efficient than existing state-of-the-art algorithms. Results also demonstrate the effectiveness of the nonconvex formulation for overlapping group Lasso.

Gradient design for liquid chromatography using multi-scale optimization.

PubMed

López-Ureña, S; Torres-Lapasió, J R; Donat, R; García-Alvarez-Coque, M C

2018-01-26

In reversed phase-liquid chromatography, the usual solution to the "general elution problem" is the application of gradient elution with programmed changes of organic solvent (or other properties). A correct quantification of chromatographic peaks in liquid chromatography requires well resolved signals in a proper analysis time. When the complexity of the sample is high, the gradient program should be accommodated to the local resolution needs of each analyte. This makes the optimization of such situations rather troublesome, since enhancing the resolution for a given analyte may imply a collateral worsening of the resolution of other analytes. The aim of this work is to design multi-linear gradients that maximize the resolution, while fulfilling some restrictions: all peaks should be eluted before a given maximal time, the gradient should be flat or increasing, and sudden changes close to eluting peaks are penalized. Consequently, an equilibrated baseline resolution for all compounds is sought. This goal is achieved by splitting the optimization problem in a multi-scale framework. In each scale κ, an optimization problem is solved with N κ  ≈ 2 κ variables that are used to build the gradients. The N κ variables define cubic splines written in terms of a B-spline basis. This allows expressing gradients as polygonals of M points approximating the splines. The cubic splines are built using subdivision schemes, a technique of fast generation of smooth curves, compatible with the multi-scale framework. Owing to the nature of the problem and the presence of multiple local maxima, the algorithm used in the optimization problem of each scale κ should be "global", such as the pattern-search algorithm. The multi-scale optimization approach is successfully applied to find the best multi-linear gradient for resolving a mixture of amino acid derivatives. Copyright © 2017 Elsevier B.V. All rights reserved.

On-line object feature extraction for multispectral scene representation

NASA Technical Reports Server (NTRS)

Ghassemian, Hassan; Landgrebe, David

1988-01-01

A new on-line unsupervised object-feature extraction method is presented that reduces the complexity and costs associated with the analysis of the multispectral image data and data transmission, storage, archival and distribution. The ambiguity in the object detection process can be reduced if the spatial dependencies, which exist among the adjacent pixels, are intelligently incorporated into the decision making process. The unity relation was defined that must exist among the pixels of an object. Automatic Multispectral Image Compaction Algorithm (AMICA) uses the within object pixel-feature gradient vector as a valuable contextual information to construct the object's features, which preserve the class separability information within the data. For on-line object extraction the path-hypothesis and the basic mathematical tools for its realization are introduced in terms of a specific similarity measure and adjacency relation. AMICA is applied to several sets of real image data, and the performance and reliability of features is evaluated.

NMR diffusion simulation based on conditional random walk.

PubMed

Gudbjartsson, H; Patz, S

1995-01-01

The authors introduce here a new, very fast, simulation method for free diffusion in a linear magnetic field gradient, which is an extension of the conventional Monte Carlo (MC) method or the convolution method described by Wong et al. (in 12th SMRM, New York, 1993, p.10). In earlier NMR-diffusion simulation methods, such as the finite difference method (FD), the Monte Carlo method, and the deterministic convolution method, the outcome of the calculations depends on the simulation time step. In the authors' method, however, the results are independent of the time step, although, in the convolution method the step size has to be adequate for spins to diffuse to adjacent grid points. By always selecting the largest possible time step the computation time can therefore be reduced. Finally the authors point out that in simple geometric configurations their simulation algorithm can be used to reduce computation time in the simulation of restricted diffusion.

Using adaptive grid in modeling rocket nozzle flow

NASA Technical Reports Server (NTRS)

Chow, Alan S.; Jin, Kang-Ren

1992-01-01

The mechanical behavior of a rocket motor internal flow field results in a system of nonlinear partial differential equations which cannot be solved analytically. However, this system of equations called the Navier-Stokes equations can be solved numerically. The accuracy and the convergence of the solution of the system of equations will depend largely on how precisely the sharp gradients in the domain of interest can be resolved. With the advances in computer technology, more sophisticated algorithms are available to improve the accuracy and convergence of the solutions. An adaptive grid generation is one of the schemes which can be incorporated into the algorithm to enhance the capability of numerical modeling. It is equivalent to putting intelligence into the algorithm to optimize the use of computer memory. With this scheme, the finite difference domain of the flow field called the grid does neither have to be very fine nor strategically placed at the location of sharp gradients. The grid is self adapting as the solution evolves. This scheme significantly improves the methodology of solving flow problems in rocket nozzles by taking the refinement part of grid generation out of the hands of computational fluid dynamics (CFD) specialists and place it into the computer algorithm itself.

Airfoil optimization for unsteady flows with application to high-lift noise reduction

NASA Astrophysics Data System (ADS)

Rumpfkeil, Markus Peer

The use of steady-state aerodynamic optimization methods in the computational fluid dynamic (CFD) community is fairly well established. In particular, the use of adjoint methods has proven to be very beneficial because their cost is independent of the number of design variables. The application of numerical optimization to airframe-generated noise, however, has not received as much attention, but with the significant quieting of modern engines, airframe noise now competes with engine noise. Optimal control techniques for unsteady flows are needed in order to be able to reduce airframe-generated noise. In this thesis, a general framework is formulated to calculate the gradient of a cost function in a nonlinear unsteady flow environment via the discrete adjoint method. The unsteady optimization algorithm developed in this work utilizes a Newton-Krylov approach since the gradient-based optimizer uses the quasi-Newton method BFGS, Newton's method is applied to the nonlinear flow problem, GMRES is used to solve the resulting linear problem inexactly, and last but not least the linear adjoint problem is solved using Bi-CGSTAB. The flow is governed by the unsteady two-dimensional compressible Navier-Stokes equations in conjunction with a one-equation turbulence model, which are discretized using structured grids and a finite difference approach. The effectiveness of the unsteady optimization algorithm is demonstrated by applying it to several problems of interest including shocktubes, pulses in converging-diverging nozzles, rotating cylinders, transonic buffeting, and an unsteady trailing-edge flow. In order to address radiated far-field noise, an acoustic wave propagation program based on the Ffowcs Williams and Hawkings (FW-H) formulation is implemented and validated. The general framework is then used to derive the adjoint equations for a novel hybrid URANS/FW-H optimization algorithm in order to be able to optimize the shape of airfoils based on their calculated far-field pressure fluctuations. Validation and application results for this novel hybrid URANS/FW-H optimization algorithm show that it is possible to optimize the shape of an airfoil in an unsteady flow environment to minimize its radiated far-field noise while maintaining good aerodynamic performance.

Iterative solution of the inverse Cauchy problem for an elliptic equation by the conjugate gradient method

NASA Astrophysics Data System (ADS)

Vasil'ev, V. I.; Kardashevsky, A. M.; Popov, V. V.; Prokopev, G. A.

2017-10-01

This article presents results of computational experiment carried out using a finite-difference method for solving the inverse Cauchy problem for a two-dimensional elliptic equation. The computational algorithm involves an iterative determination of the missing boundary condition from the override condition using the conjugate gradient method. The results of calculations are carried out on the examples with exact solutions as well as at specifying an additional condition with random errors are presented. Results showed a high efficiency of the iterative method of conjugate gradients for numerical solution

Ionospheric-thermospheric UV tomography: 1. Image space reconstruction algorithms

NASA Astrophysics Data System (ADS)

Dymond, K. F.; Budzien, S. A.; Hei, M. A.

2017-03-01

We present and discuss two algorithms of the class known as Image Space Reconstruction Algorithms (ISRAs) that we are applying to the solution of large-scale ionospheric tomography problems. ISRAs have several desirable features that make them useful for ionospheric tomography. In addition to producing nonnegative solutions, ISRAs are amenable to sparse-matrix formulations and are fast, stable, and robust. We present the results of our studies of two types of ISRA: the Least Squares Positive Definite and the Richardson-Lucy algorithms. We compare their performance to the Multiplicative Algebraic Reconstruction and Conjugate Gradient Least Squares algorithms. We then discuss the use of regularization in these algorithms and present our new approach based on regularization to a partial differential equation.

The Modified HZ Conjugate Gradient Algorithm for Large-Scale Nonsmooth Optimization.

PubMed

Yuan, Gonglin; Sheng, Zhou; Liu, Wenjie

2016-01-01

In this paper, the Hager and Zhang (HZ) conjugate gradient (CG) method and the modified HZ (MHZ) CG method are presented for large-scale nonsmooth convex minimization. Under some mild conditions, convergent results of the proposed methods are established. Numerical results show that the presented methods can be better efficiency for large-scale nonsmooth problems, and several problems are tested (with the maximum dimensions to 100,000 variables).

The U.S. Geological Survey Modular Ground-Water Model - PCGN: A Preconditioned Conjugate Gradient Solver with Improved Nonlinear Control

USGS Publications Warehouse

Naff, Richard L.; Banta, Edward R.

2008-01-01

The preconditioned conjugate gradient with improved nonlinear control (PCGN) package provides addi-tional means by which the solution of nonlinear ground-water flow problems can be controlled as compared to existing solver packages for MODFLOW. Picard iteration is used to solve nonlinear ground-water flow equations by iteratively solving a linear approximation of the nonlinear equations. The linear solution is provided by means of the preconditioned conjugate gradient algorithm where preconditioning is provided by the modi-fied incomplete Cholesky algorithm. The incomplete Cholesky scheme incorporates two levels of fill, 0 and 1, in which the pivots can be modified so that the row sums of the preconditioning matrix and the original matrix are approximately equal. A relaxation factor is used to implement the modified pivots, which determines the degree of modification allowed. The effects of fill level and degree of pivot modification are briefly explored by means of a synthetic, heterogeneous finite-difference matrix; results are reported in the final section of this report. The preconditioned conjugate gradient method is coupled with Picard iteration so as to efficiently solve the nonlinear equations associated with many ground-water flow problems. The description of this coupling of the linear solver with Picard iteration is a primary concern of this document.

Predicting the survival of diabetes using neural network

NASA Astrophysics Data System (ADS)

Mamuda, Mamman; Sathasivam, Saratha

2017-08-01

Data mining techniques at the present time are used in predicting diseases of health care industries. Neural Network is one among the prevailing method in data mining techniques of an intelligent field for predicting diseases in health care industries. This paper presents a study on the prediction of the survival of diabetes diseases using different learning algorithms from the supervised learning algorithms of neural network. Three learning algorithms are considered in this study: (i) The levenberg-marquardt learning algorithm (ii) The Bayesian regulation learning algorithm and (iii) The scaled conjugate gradient learning algorithm. The network is trained using the Pima Indian Diabetes Dataset with the help of MATLAB R2014(a) software. The performance of each algorithm is further discussed through regression analysis. The prediction accuracy of the best algorithm is further computed to validate the accurate prediction

Particle Swarm Optimization of Low-Thrust, Geocentric-to-Halo-Orbit Transfers

NASA Astrophysics Data System (ADS)

Abraham, Andrew J.

Missions to Lagrange points are becoming increasingly popular amongst spacecraft mission planners. Lagrange points are locations in space where the gravity force from two bodies, and the centrifugal force acting on a third body, cancel. To date, all spacecraft that have visited a Lagrange point have done so using high-thrust, chemical propulsion. Due to the increasing availability of low-thrust (high efficiency) propulsive devices, and their increasing capability in terms of fuel efficiency and instantaneous thrust, it has now become possible for a spacecraft to reach a Lagrange point orbit without the aid of chemical propellant. While at any given time there are many paths for a low-thrust trajectory to take, only one is optimal. The traditional approach to spacecraft trajectory optimization utilizes some form of gradient-based algorithm. While these algorithms offer numerous advantages, they also have a few significant shortcomings. The three most significant shortcomings are: (1) the fact that an initial guess solution is required to initialize the algorithm, (2) the radius of convergence can be quite small and can allow the algorithm to become trapped in local minima, and (3) gradient information is not always assessable nor always trustworthy for a given problem. To avoid these problems, this dissertation is focused on optimizing a low-thrust transfer trajectory from a geocentric orbit to an Earth-Moon, L1, Lagrange point orbit using the method of Particle Swarm Optimization (PSO). The PSO method is an evolutionary heuristic that was originally written to model birds swarming to locate hidden food sources. This PSO method will enable the exploration of the invariant stable manifold of the target Lagrange point orbit in an effort to optimize the spacecraft's low-thrust trajectory. Examples of these optimized trajectories are presented and contrasted with those found using traditional, gradient-based approaches. In summary, the results of this dissertation find that the PSO method does, indeed, successfully optimize the low-thrust trajectory transfer problem without the need for initial guessing. Furthermore, a two-degree-of-freedom PSO problem formulation significantly outperformed a one-degree-of-freedom formulation by at least an order of magnitude, in terms of CPU time. Finally, the PSO method is also used to solve a traditional, two-burn, impulsive transfer to a Lagrange point orbit using a hybrid optimization algorithm that incorporates a gradient-based shooting algorithm as a pre-optimizer. Surprisingly, the results of this study show that "fast" transfers outperform "slow" transfers in terms of both Deltav and time of flight.

Three-dimensional full waveform inversion of short-period teleseismic wavefields based upon the SEM-DSM hybrid method

NASA Astrophysics Data System (ADS)

Monteiller, Vadim; Chevrot, Sébastien; Komatitsch, Dimitri; Wang, Yi

2015-08-01

We present a method for high-resolution imaging of lithospheric structures based on full waveform inversion of teleseismic waveforms. We model the propagation of seismic waves using our recently developed direct solution method/spectral-element method hybrid technique, which allows us to simulate the propagation of short-period teleseismic waves through a regional 3-D model. We implement an iterative quasi-Newton method based upon the L-BFGS algorithm, where the gradient of the misfit function is computed using the adjoint-state method. Compared to gradient or conjugate-gradient methods, the L-BFGS algorithm has a much faster convergence rate. We illustrate the potential of this method on a synthetic test case that consists of a crustal model with a crustal discontinuity at 25 km depth and a sharp Moho jump. This model contains short- and long-wavelength heterogeneities along the lateral and vertical directions. The iterative inversion starts from a smooth 1-D model derived from the IASP91 reference Earth model. We invert both radial and vertical component waveforms, starting from long-period signals filtered at 10 s and gradually decreasing the cut-off period down to 1.25 s. This multiscale algorithm quickly converges towards a model that is very close to the true model, in contrast to inversions involving short-period waveforms only, which always get trapped into a local minimum of the cost function.

Hybrid intelligent optimization methods for engineering problems

NASA Astrophysics Data System (ADS)

Pehlivanoglu, Yasin Volkan

The purpose of optimization is to obtain the best solution under certain conditions. There are numerous optimization methods because different problems need different solution methodologies; therefore, it is difficult to construct patterns. Also mathematical modeling of a natural phenomenon is almost based on differentials. Differential equations are constructed with relative increments among the factors related to yield. Therefore, the gradients of these increments are essential to search the yield space. However, the landscape of yield is not a simple one and mostly multi-modal. Another issue is differentiability. Engineering design problems are usually nonlinear and they sometimes exhibit discontinuous derivatives for the objective and constraint functions. Due to these difficulties, non-gradient-based algorithms have become more popular in recent decades. Genetic algorithms (GA) and particle swarm optimization (PSO) algorithms are popular, non-gradient based algorithms. Both are population-based search algorithms and have multiple points for initiation. A significant difference from a gradient-based method is the nature of the search methodologies. For example, randomness is essential for the search in GA or PSO. Hence, they are also called stochastic optimization methods. These algorithms are simple, robust, and have high fidelity. However, they suffer from similar defects, such as, premature convergence, less accuracy, or large computational time. The premature convergence is sometimes inevitable due to the lack of diversity. As the generations of particles or individuals in the population evolve, they may lose their diversity and become similar to each other. To overcome this issue, we studied the diversity concept in GA and PSO algorithms. Diversity is essential for a healthy search, and mutations are the basic operators to provide the necessary variety within a population. After having a close scrutiny of the diversity concept based on qualification and quantification studies, we improved new mutation strategies and operators to provide beneficial diversity within the population. We called this new approach as multi-frequency vibrational GA or PSO. They were applied to different aeronautical engineering problems in order to study the efficiency of these new approaches. These implementations were: applications to selected benchmark test functions, inverse design of two-dimensional (2D) airfoil in subsonic flow, optimization of 2D airfoil in transonic flow, path planning problems of autonomous unmanned aerial vehicle (UAV) over a 3D terrain environment, 3D radar cross section minimization problem for a 3D air vehicle, and active flow control over a 2D airfoil. As demonstrated by these test cases, we observed that new algorithms outperform the current popular algorithms. The principal role of this multi-frequency approach was to determine which individuals or particles should be mutated, when they should be mutated, and which ones should be merged into the population. The new mutation operators, when combined with a mutation strategy and an artificial intelligent method, such as, neural networks or fuzzy logic process, they provided local and global diversities during the reproduction phases of the generations. Additionally, the new approach also introduced random and controlled diversity. Due to still being population-based techniques, these methods were as robust as the plain GA or PSO algorithms. Based on the results obtained, it was concluded that the variants of the present multi-frequency vibrational GA and PSO were efficient algorithms, since they successfully avoided all local optima within relatively short optimization cycles.

A blind deconvolution method based on L1/L2 regularization prior in the gradient space

NASA Astrophysics Data System (ADS)

Cai, Ying; Shi, Yu; Hua, Xia

2018-02-01

In the process of image restoration, the result of image restoration is very different from the real image because of the existence of noise, in order to solve the ill posed problem in image restoration, a blind deconvolution method based on L1/L2 regularization prior to gradient domain is proposed. The method presented in this paper first adds a function to the prior knowledge, which is the ratio of the L1 norm to the L2 norm, and takes the function as the penalty term in the high frequency domain of the image. Then, the function is iteratively updated, and the iterative shrinkage threshold algorithm is applied to solve the high frequency image. In this paper, it is considered that the information in the gradient domain is better for the estimation of blur kernel, so the blur kernel is estimated in the gradient domain. This problem can be quickly implemented in the frequency domain by fast Fast Fourier Transform. In addition, in order to improve the effectiveness of the algorithm, we have added a multi-scale iterative optimization method. This paper proposes the blind deconvolution method based on L1/L2 regularization priors in the gradient space can obtain the unique and stable solution in the process of image restoration, which not only keeps the edges and details of the image, but also ensures the accuracy of the results.

Structural optimization with approximate sensitivities

NASA Technical Reports Server (NTRS)

Patnaik, S. N.; Hopkins, D. A.; Coroneos, R.

1994-01-01

Computational efficiency in structural optimization can be enhanced if the intensive computations associated with the calculation of the sensitivities, that is, gradients of the behavior constraints, are reduced. Approximation to gradients of the behavior constraints that can be generated with small amount of numerical calculations is proposed. Structural optimization with these approximate sensitivities produced correct optimum solution. Approximate gradients performed well for different nonlinear programming methods, such as the sequence of unconstrained minimization technique, method of feasible directions, sequence of quadratic programming, and sequence of linear programming. Structural optimization with approximate gradients can reduce by one third the CPU time that would otherwise be required to solve the problem with explicit closed-form gradients. The proposed gradient approximation shows potential to reduce intensive computation that has been associated with traditional structural optimization.

Development of gradient descent adaptive algorithms to remove common mode artifact for improvement of cardiovascular signal quality.

PubMed

Ciaccio, Edward J; Micheli-Tzanakou, Evangelia

2007-07-01

Common-mode noise degrades cardiovascular signal quality and diminishes measurement accuracy. Filtering to remove noise components in the frequency domain often distorts the signal. Two adaptive noise canceling (ANC) algorithms were tested to adjust weighted reference signals for optimal subtraction from a primary signal. Update of weight w was based upon the gradient term of the steepest descent equation: [see text], where the error epsilon is the difference between primary and weighted reference signals. nabla was estimated from Deltaepsilon(2) and Deltaw without using a variable Deltaw in the denominator which can cause instability. The Parallel Comparison (PC) algorithm computed Deltaepsilon(2) using fixed finite differences +/- Deltaw in parallel during each discrete time k. The ALOPEX algorithm computed Deltaepsilon(2)x Deltaw from time k to k + 1 to estimate nabla, with a random number added to account for Deltaepsilon(2) . Deltaw--> 0 near the optimal weighting. Using simulated data, both algorithms stably converged to the optimal weighting within 50-2000 discrete sample points k even with a SNR = 1:8 and weights which were initialized far from the optimal. Using a sharply pulsatile cardiac electrogram signal with added noise so that the SNR = 1:5, both algorithms exhibited stable convergence within 100 ms (100 sample points). Fourier spectral analysis revealed minimal distortion when comparing the signal without added noise to the ANC restored signal. ANC algorithms based upon difference calculations can rapidly and stably converge to the optimal weighting in simulated and real cardiovascular data. Signal quality is restored with minimal distortion, increasing the accuracy of biophysical measurement.

Distributed convex optimisation with event-triggered communication in networked systems

NASA Astrophysics Data System (ADS)

Liu, Jiayun; Chen, Weisheng

2016-12-01

This paper studies the distributed convex optimisation problem over directed networks. Motivated by practical considerations, we propose a novel distributed zero-gradient-sum optimisation algorithm with event-triggered communication. Therefore, communication and control updates just occur at discrete instants when some predefined condition satisfies. Thus, compared with the time-driven distributed optimisation algorithms, the proposed algorithm has the advantages of less energy consumption and less communication cost. Based on Lyapunov approaches, we show that the proposed algorithm makes the system states asymptotically converge to the solution of the problem exponentially fast and the Zeno behaviour is excluded. Finally, simulation example is given to illustrate the effectiveness of the proposed algorithm.

Phase gradient algorithm based on co-axis two-step phase-shifting interferometry and its application

NASA Astrophysics Data System (ADS)

Wang, Yawei; Zhu, Qiong; Xu, Yuanyuan; Xin, Zhiduo; Liu, Jingye

2017-12-01

A phase gradient method based on co-axis two-step phase-shifting interferometry, is used to reveal the detailed information of a specimen. In this method, the phase gradient distribution can only be obtained by calculating both the first-order derivative and the radial Hilbert transformation of the intensity difference between two phase-shifted interferograms. The feasibility and accuracy of this method were fully verified by the simulation results for a polystyrene sphere and a red blood cell. The empirical results demonstrated that phase gradient is sensitive to changes in the refractive index and morphology. Because phase retrieval and tedious phase unwrapping are not required, the calculation speed is faster. In addition, co-axis interferometry has high spatial resolution.

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.

An empirical method to correct for temperature-dependent variations in the overlap function of CHM15k ceilometers

NASA Astrophysics Data System (ADS)

Hervo, Maxime; Poltera, Yann; Haefele, Alexander

2016-07-01

Imperfections in a lidar's overlap function lead to artefacts in the background, range and overlap-corrected lidar signals. These artefacts can erroneously be interpreted as an aerosol gradient or, in extreme cases, as a cloud base leading to false cloud detection. A correct specification of the overlap function is hence crucial in the use of automatic elastic lidars (ceilometers) for the detection of the planetary boundary layer or of low cloud. In this study, an algorithm is presented to correct such artefacts. It is based on the assumption of a homogeneous boundary layer and a correct specification of the overlap function down to a minimum range, which must be situated within the boundary layer. The strength of the algorithm lies in a sophisticated quality-check scheme which allows the reliable identification of favourable atmospheric conditions. The algorithm was applied to 2 years of data from a CHM15k ceilometer from the company Lufft. Backscatter signals corrected for background, range and overlap were compared using the overlap function provided by the manufacturer and the one corrected with the presented algorithm. Differences between corrected and uncorrected signals reached up to 45 % in the first 300 m above ground. The amplitude of the correction turned out to be temperature dependent and was larger for higher temperatures. A linear model of the correction as a function of the instrument's internal temperature was derived from the experimental data. Case studies and a statistical analysis of the strongest gradient derived from corrected signals reveal that the temperature model is capable of a high-quality correction of overlap artefacts, in particular those due to diurnal variations. The presented correction method has the potential to significantly improve the detection of the boundary layer with gradient-based methods because it removes false candidates and hence simplifies the attribution of the detected gradients to the planetary boundary layer. A particularly significant benefit can be expected for the detection of shallow stable layers typical of night-time situations. The algorithm is completely automatic and does not require any on-site intervention but requires the definition of an adequate instrument-specific configuration. It is therefore suited for use in large ceilometer networks.

Role of spatial averaging in multicellular gradient sensing.

PubMed

Smith, Tyler; Fancher, Sean; Levchenko, Andre; Nemenman, Ilya; Mugler, Andrew

2016-05-20

Gradient sensing underlies important biological processes including morphogenesis, polarization, and cell migration. The precision of gradient sensing increases with the length of a detector (a cell or group of cells) in the gradient direction, since a longer detector spans a larger range of concentration values. Intuition from studies of concentration sensing suggests that precision should also increase with detector length in the direction transverse to the gradient, since then spatial averaging should reduce the noise. However, here we show that, unlike for concentration sensing, the precision of gradient sensing decreases with transverse length for the simplest gradient sensing model, local excitation-global inhibition. The reason is that gradient sensing ultimately relies on a subtraction of measured concentration values. While spatial averaging indeed reduces the noise in these measurements, which increases precision, it also reduces the covariance between the measurements, which results in the net decrease in precision. We demonstrate how a recently introduced gradient sensing mechanism, regional excitation-global inhibition (REGI), overcomes this effect and recovers the benefit of transverse averaging. Using a REGI-based model, we compute the optimal two- and three-dimensional detector shapes, and argue that they are consistent with the shapes of naturally occurring gradient-sensing cell populations.

Role of spatial averaging in multicellular gradient sensing

NASA Astrophysics Data System (ADS)

Smith, Tyler; Fancher, Sean; Levchenko, Andre; Nemenman, Ilya; Mugler, Andrew

2016-06-01

Gradient sensing underlies important biological processes including morphogenesis, polarization, and cell migration. The precision of gradient sensing increases with the length of a detector (a cell or group of cells) in the gradient direction, since a longer detector spans a larger range of concentration values. Intuition from studies of concentration sensing suggests that precision should also increase with detector length in the direction transverse to the gradient, since then spatial averaging should reduce the noise. However, here we show that, unlike for concentration sensing, the precision of gradient sensing decreases with transverse length for the simplest gradient sensing model, local excitation-global inhibition. The reason is that gradient sensing ultimately relies on a subtraction of measured concentration values. While spatial averaging indeed reduces the noise in these measurements, which increases precision, it also reduces the covariance between the measurements, which results in the net decrease in precision. We demonstrate how a recently introduced gradient sensing mechanism, regional excitation-global inhibition (REGI), overcomes this effect and recovers the benefit of transverse averaging. Using a REGI-based model, we compute the optimal two- and three-dimensional detector shapes, and argue that they are consistent with the shapes of naturally occurring gradient-sensing cell populations.

Feedback-Based Projected-Gradient Method for Real-Time Optimization of Aggregations of Energy Resources

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

Dall-Anese, Emiliano; Bernstein, Andrey; Simonetto, Andrea

This paper develops an online optimization method to maximize operational objectives of distribution-level distributed energy resources (DERs), while adjusting the aggregate power generated (or consumed) in response to services requested by grid operators. The design of the online algorithm is based on a projected-gradient method, suitably modified to accommodate appropriate measurements from the distribution network and the DERs. By virtue of this approach, the resultant algorithm can cope with inaccuracies in the representation of the AC power flows, it avoids pervasive metering to gather the state of noncontrollable resources, and it naturally lends itself to a distributed implementation. Optimality claimsmore » are established in terms of tracking of the solution of a well-posed time-varying convex optimization problem.« less

Feedback-Based Projected-Gradient Method For Real-Time Optimization of Aggregations of Energy Resources: Preprint

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

Dall-Anese, Emiliano; Bernstein, Andrey; Simonetto, Andrea

This paper develops an online optimization method to maximize the operational objectives of distribution-level distributed energy resources (DERs) while adjusting the aggregate power generated (or consumed) in response to services requested by grid operators. The design of the online algorithm is based on a projected-gradient method, suitably modified to accommodate appropriate measurements from the distribution network and the DERs. By virtue of this approach, the resultant algorithm can cope with inaccuracies in the representation of the AC power, it avoids pervasive metering to gather the state of noncontrollable resources, and it naturally lends itself to a distributed implementation. Optimality claimsmore » are established in terms of tracking of the solution of a well-posed time-varying optimization problem.« less

Ionosphere Threat Model Investigations by Using Turkish National Permanent GPS Network

NASA Astrophysics Data System (ADS)

Köroǧlu, Meltem; Arikan, Feza; Koroglu, Ozan

2016-07-01

Global Positioning System (GPS) signal realibity may decrease significantly due to the variable electron density structure of ionosphere. In the literature, ionospheric disturbance is modeled as a linear semi-definite wave which has width, gradient and a constant velocity. To provide precise positioning, Ground Based Augmentation Systems (GBAS) are used. GBAS collects all measurements from GPS network receivers and computes an integrity level for the measurement by comparing the network GPS receivers measurements with the threat models of ionosphere. Threat models are computed according to ionosphere gradient characteristics. Gradient is defined as the difference of slant delays between the receivers. Slant delays are estimated from the STEC (Slant Total Electron Content) values of the ionosphere that is given by the line integral of the electron density between the receiver and GPS satellite. STEC can be estimated over Global Navigation Satellite System (GNSS) signals by using IONOLAB-STEC and IONOLAB-BIAS algorithms. Since most of the ionospheric disturbance observed locally, threat models for the GBAS systems must be extracted as locally. In this study, an automated ionosphere gradient estimation algorithm was developed by using Turkish National Permanent GPS Network (TNPGN-Active) data for year 2011. The GPS receivers are grouped within 150 km radius. For each region, for each day and for each satellite all STEC values are estimated by using IONOLAB-STEC and IONOLAB-BIAS softwares (www.ionolab.org). In the gradient estimation, station-pair method is used. Statistical properties of the valid gradients are extracted as tables for each region, day and satellite. By observing the histograms of the maximum gradients and standard deviations of the gradients with respect to the elevation angle for each day, the anomalies and disturbances of the ionosphere can be detected. It is observed that, maximum gradient estimates are less than 40 mm/km and maximum standard deviation of the gradients are observed as 5 mm/km. In the stormy days, the level of gradients and the standard deviation values becomes larger than those of quiet days. These observations may also form a basis for the estimationof velocity and width of the traveling ionospheric disturbances. The study is supported by TUBITAK 115E915 and Joint TUBITAK 114E092 and AS CR14/001 projects.

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

Yang, Y. M., E-mail: ymingy@gmail.com; Bednarz, B.; Svatos, M.

Purpose: The future of radiation therapy will require advanced inverse planning solutions to support single-arc, multiple-arc, and “4π” delivery modes, which present unique challenges in finding an optimal treatment plan over a vast search space, while still preserving dosimetric accuracy. The successful clinical implementation of such methods would benefit from Monte Carlo (MC) based dose calculation methods, which can offer improvements in dosimetric accuracy when compared to deterministic methods. The standard method for MC based treatment planning optimization leverages the accuracy of the MC dose calculation and efficiency of well-developed optimization methods, by precalculating the fluence to dose relationship withinmore » a patient with MC methods and subsequently optimizing the fluence weights. However, the sequential nature of this implementation is computationally time consuming and memory intensive. Methods to reduce the overhead of the MC precalculation have been explored in the past, demonstrating promising reductions of computational time overhead, but with limited impact on the memory overhead due to the sequential nature of the dose calculation and fluence optimization. The authors propose an entirely new form of “concurrent” Monte Carlo treat plan optimization: a platform which optimizes the fluence during the dose calculation, reduces wasted computation time being spent on beamlets that weakly contribute to the final dose distribution, and requires only a low memory footprint to function. In this initial investigation, the authors explore the key theoretical and practical considerations of optimizing fluence in such a manner. Methods: The authors present a novel derivation and implementation of a gradient descent algorithm that allows for optimization during MC particle transport, based on highly stochastic information generated through particle transport of very few histories. A gradient rescaling and renormalization algorithm, and the concept of momentum from stochastic gradient descent were used to address obstacles unique to performing gradient descent fluence optimization during MC particle transport. The authors have applied their method to two simple geometrical phantoms, and one clinical patient geometry to examine the capability of this platform to generate conformal plans as well as assess its computational scaling and efficiency, respectively. Results: The authors obtain a reduction of at least 50% in total histories transported in their investigation compared to a theoretical unweighted beamlet calculation and subsequent fluence optimization method, and observe a roughly fixed optimization time overhead consisting of ∼10% of the total computation time in all cases. Finally, the authors demonstrate a negligible increase in memory overhead of ∼7–8 MB to allow for optimization of a clinical patient geometry surrounded by 36 beams using their platform. Conclusions: This study demonstrates a fluence optimization approach, which could significantly improve the development of next generation radiation therapy solutions while incurring minimal additional computational overhead.« less

Concurrent Monte Carlo transport and fluence optimization with fluence adjusting scalable transport Monte Carlo

PubMed Central

Svatos, M.; Zankowski, C.; Bednarz, B.

2016-01-01

Purpose: The future of radiation therapy will require advanced inverse planning solutions to support single-arc, multiple-arc, and “4π” delivery modes, which present unique challenges in finding an optimal treatment plan over a vast search space, while still preserving dosimetric accuracy. The successful clinical implementation of such methods would benefit from Monte Carlo (MC) based dose calculation methods, which can offer improvements in dosimetric accuracy when compared to deterministic methods. The standard method for MC based treatment planning optimization leverages the accuracy of the MC dose calculation and efficiency of well-developed optimization methods, by precalculating the fluence to dose relationship within a patient with MC methods and subsequently optimizing the fluence weights. However, the sequential nature of this implementation is computationally time consuming and memory intensive. Methods to reduce the overhead of the MC precalculation have been explored in the past, demonstrating promising reductions of computational time overhead, but with limited impact on the memory overhead due to the sequential nature of the dose calculation and fluence optimization. The authors propose an entirely new form of “concurrent” Monte Carlo treat plan optimization: a platform which optimizes the fluence during the dose calculation, reduces wasted computation time being spent on beamlets that weakly contribute to the final dose distribution, and requires only a low memory footprint to function. In this initial investigation, the authors explore the key theoretical and practical considerations of optimizing fluence in such a manner. Methods: The authors present a novel derivation and implementation of a gradient descent algorithm that allows for optimization during MC particle transport, based on highly stochastic information generated through particle transport of very few histories. A gradient rescaling and renormalization algorithm, and the concept of momentum from stochastic gradient descent were used to address obstacles unique to performing gradient descent fluence optimization during MC particle transport. The authors have applied their method to two simple geometrical phantoms, and one clinical patient geometry to examine the capability of this platform to generate conformal plans as well as assess its computational scaling and efficiency, respectively. Results: The authors obtain a reduction of at least 50% in total histories transported in their investigation compared to a theoretical unweighted beamlet calculation and subsequent fluence optimization method, and observe a roughly fixed optimization time overhead consisting of ∼10% of the total computation time in all cases. Finally, the authors demonstrate a negligible increase in memory overhead of ∼7–8 MB to allow for optimization of a clinical patient geometry surrounded by 36 beams using their platform. Conclusions: This study demonstrates a fluence optimization approach, which could significantly improve the development of next generation radiation therapy solutions while incurring minimal additional computational overhead. PMID:27277051

The crack detection algorithm of pavement image based on edge information

NASA Astrophysics Data System (ADS)

Yang, Chunde; Geng, Mingyue

2018-05-01

As the images of pavement cracks are affected by a large amount of complicated noises, such as uneven illumination and water stains, the detected cracks are discontinuous and the main body information at the edge of the cracks is easily lost. In order to solve the problem, a crack detection algorithm in pavement image based on edge information is proposed. Firstly, the image is pre-processed by the nonlinear gray-scale transform function and reconstruction filter to enhance the linear characteristic of the crack. At the same time, an adaptive thresholding method is designed to coarsely extract the cracks edge according to the gray-scale gradient feature and obtain the crack gradient information map. Secondly, the candidate edge points are obtained according to the gradient information, and the edge is detected based on the single pixel percolation processing, which is improved by using the local difference between pixels in the fixed region. Finally, complete crack is obtained by filling the crack edge. Experimental results show that the proposed method can accurately detect pavement cracks and preserve edge information.

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.

A gradient-based approach for automated crest-line detection and analysis of sand dune patterns on planetary surfaces

NASA Astrophysics Data System (ADS)

Lancaster, N.; LeBlanc, D.; Bebis, G.; Nicolescu, M.

2015-12-01

Dune-field patterns are believed to behave as self-organizing systems, but what causes the patterns to form is still poorly understood. The most obvious (and in many cases the most significant) aspect of a dune system is the pattern of dune crest lines. Extracting meaningful features such as crest length, orientation, spacing, bifurcations, and merging of crests from image data can reveal important information about the specific dune-field morphological properties, development, and response to changes in boundary conditions, but manual methods are labor-intensive and time-consuming. We are developing the capability to recognize and characterize patterns of sand dunes on planetary surfaces. Our goal is to develop a robust methodology and the necessary algorithms for automated or semi-automated extraction of dune morphometric information from image data. Our main approach uses image processing methods to extract gradient information from satellite images of dune fields. Typically, the gradients have a dominant magnitude and orientation. In many cases, the images have two major dominant gradient orientations, for the sunny and shaded side of the dunes. A histogram of the gradient orientations is used to determine the dominant orientation. A threshold is applied to the image based on gradient orientations which agree with the dominant orientation. The contours of the binary image can then be used to determine the dune crest-lines, based on pixel intensity values. Once the crest-lines have been extracted, the morphological properties can be computed. We have tested our approach on a variety of images of linear and crescentic (transverse) dunes and compared dune detection algorithms with manually-digitized dune crest lines, achieving true positive values of 0.57-0.99; and false positives values of 0.30-0.67, indicating that out approach is generally robust.

A comparison of hydrographically and optically derived mixed layer depths

USGS Publications Warehouse

Zawada, D.G.; Zaneveld, J.R.V.; Boss, E.; Gardner, W.D.; Richardson, M.J.; Mishonov, A.V.

2005-01-01

Efforts to understand and model the dynamics of the upper ocean would be significantly advanced given the ability to rapidly determine mixed layer depths (MLDs) over large regions. Remote sensing technologies are an ideal choice for achieving this goal. This study addresses the feasibility of estimating MLDs from optical properties. These properties are strongly influenced by suspended particle concentrations, which generally reach a maximum at pycnoclines. The premise therefore is to use a gradient in beam attenuation at 660 nm (c660) as a proxy for the depth of a particle-scattering layer. Using a global data set collected during World Ocean Circulation Experiment cruises from 1988-1997, six algorithms were employed to compute MLDs from either density or temperature profiles. Given the absence of published optically based MLD algorithms, two new methods were developed that use c660 profiles to estimate the MLD. Intercomparison of the six hydrographically based algorithms revealed some significant disparities among the resulting MLD values. Comparisons between the hydrographical and optical approaches indicated a first-order agreement between the MLDs based on the depths of gradient maxima for density and c660. When comparing various hydrographically based algorithms, other investigators reported that inherent fluctuations of the mixed layer depth limit the accuracy of its determination to 20 m. Using this benchmark, we found a ???70% agreement between the best hydrographical-optical algorithm pairings. Copyright 2005 by the American Geophysical Union.

A simple acquisition strategy to avoid off-resonance blurring in spiral imaging with redundant spiral-in/out k-space trajectories

PubMed Central

Fielden, Samuel W.; Meyer, Craig H.

2014-01-01

Purpose The major hurdle to widespread adoption of spiral trajectories has been their poor off-resonance performance. Here we present a self-correcting spiral k-space trajectory that avoids much of the well-known spiral blurring during data acquisition. Theory and Methods In comparison with a traditional spiral-out trajectory, the spiral-in/out trajectory has improved off-resonance performance. By combining two spiral-in/out acquisitions, one rotated 180° in k-space compared to the other, multi-shot spiral-in/out artifacts are eliminated. A phantom was scanned with the center frequency manually tuned 20, 40, 80, and 160 Hz off-resonance with both a spiral-out gradient echo sequence and the redundant spiral-in/out sequence. The phantom was also imaged in an oblique orientation in order to demonstrate improved concomitant gradient field performance of the sequence, and was additionally incorporated into a spiral turbo spin echo sequence for brain imaging. Results Phantom studies with manually-tuned off-resonance agree well with theoretical calculations, showing that moderate off-resonance is well-corrected by this acquisition scheme. Blur due to concomitant fields is reduced, and good results are obtained in vivo. Conclusion The redundant spiral-in/out trajectory results in less image blur for a given readout length than a traditional spiral-out scan, reducing the need for complex off-resonance correction algorithms. PMID:24604539

A simple acquisition strategy to avoid off-resonance blurring in spiral imaging with redundant spiral-in/out k-space trajectories.

PubMed

Fielden, Samuel W; Meyer, Craig H

2015-02-01

The major hurdle to widespread adoption of spiral trajectories has been their poor off-resonance performance. Here we present a self-correcting spiral k-space trajectory that avoids much of the well-known spiral blurring during data acquisition. In comparison with a traditional spiral-out trajectory, the spiral-in/out trajectory has improved off-resonance performance. By combining two spiral-in/out acquisitions, one rotated 180° in k-space compared with the other, multishot spiral-in/out artifacts are eliminated. A phantom was scanned with the center frequency manually tuned 20, 40, 80, and 160 Hz off-resonance with both a spiral-out gradient echo sequence and the redundant spiral-in/out sequence. The phantom was also imaged in an oblique orientation in order to demonstrate improved concomitant gradient field performance of the sequence. Additionally, the trajectory was incorporated into a spiral turbo spin echo sequence for brain imaging. Phantom studies with manually tuned off-resonance agree well with theoretical calculations, showing that moderate off-resonance is well-corrected by this acquisition scheme. Blur due to concomitant fields is reduced, and good results are obtained in vivo. The redundant spiral-in/out trajectory results in less image blur for a given readout length than a traditional spiral-out scan, reducing the need for complex off-resonance correction algorithms. © 2014 Wiley Periodicals, Inc.

A Fast Deep Learning System Using GPU

DTIC Science & Technology

2014-06-01

hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and...widely used in data modeling until three decades later when efficient training algorithm for RBM is invented by Hinton [3] and the computing power is...be trained using most of optimization algorithms , such as BP, conjugate gradient descent (CGD) or Levenberg-Marquardt (LM). The advantage of this

SU-E-J-252: A Motion Algorithm to Extract Physical and Motion Parameters of a Mobile Target in Cone-Beam Computed Tomographic Imaging Retrospective to Image Reconstruction

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

Ali, I; Ahmad, S; Alsbou, N

Purpose: A motion algorithm was developed to extract actual length, CT-numbers and motion amplitude of a mobile target imaged with cone-beam-CT (CBCT) retrospective to image-reconstruction. Methods: The motion model considered a mobile target moving with a sinusoidal motion and employed three measurable parameters: apparent length, CT number level and gradient of a mobile target obtained from CBCT images to extract information about the actual length and CT number value of the stationary target and motion amplitude. The algorithm was verified experimentally with a mobile phantom setup that has three targets with different sizes manufactured from homogenous tissue-equivalent gel material embeddedmore » into a thorax phantom. The phantom moved sinusoidal in one-direction using eight amplitudes (0–20mm) and a frequency of 15-cycles-per-minute. The model required imaging parameters such as slice thickness, imaging time. Results: This motion algorithm extracted three unknown parameters: length of the target, CT-number-level, motion amplitude for a mobile target retrospective to CBCT image reconstruction. The algorithm relates three unknown parameters to measurable apparent length, CT-number-level and gradient for well-defined mobile targets obtained from CBCT images. The motion model agreed with measured apparent lengths which were dependent on actual length of the target and motion amplitude. The cumulative CT-number for a mobile target was dependent on CT-number-level of the stationary target and motion amplitude. The gradient of the CT-distribution of mobile target is dependent on the stationary CT-number-level, actual target length along the direction of motion, and motion amplitude. Motion frequency and phase did not affect the elongation and CT-number distributions of mobile targets when imaging time included several motion cycles. Conclusion: The motion algorithm developed in this study has potential applications in diagnostic CT imaging and radiotherapy to extract actual length, size and CT-numbers distorted by motion in CBCT imaging. The model provides further information about motion of the target.« less

Perimeter Security and Intruder Detection Using Gravity Gradiometry: A Feasibility Study

DTIC Science & Technology

2011-03-24

design, build, and operate, and it is usually not feasible to integrate new technology into an already existing system. So far, however, the...gravitational gradients is not a new concept and has been applied across a variety of industries. The first device for gravity gradient measurement was the...which generates a new simulated GGI reading. The program loops for a set number of iterations, and then ends by calculating algorithm performance

Towards Seismic Tomography Based Upon Adjoint Methods

NASA Astrophysics Data System (ADS)

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

2006-12-01

We outline the theory behind tomographic inversions based on 3D reference models, fully numerical 3D wave propagation, and adjoint methods. Our approach involves computing the Fréchet derivatives for tomographic inversions via the interaction between a forward wavefield, propagating from the source to the receivers, and an `adjoint' wavefield, propagating from the receivers back to the source. The forward wavefield is computed using a spectral-element method (SEM) and a heterogeneous wave-speed model, and stored as synthetic seismograms at particular receivers for which there is data. We specify an objective or misfit function that defines a measure of misfit between data and synthetics. For a given receiver, the differences between the data and the synthetics are time reversed and used as the source of the adjoint wavefield. For each earthquake, the interaction between the regular and adjoint wavefields is used to construct finite-frequency sensitivity kernels, which we call event kernel. These kernels may be thought of as weighted sums of measurement-specific banana-donut kernels, with weights determined by the measurements. The overall sensitivity is simply the sum of event kernels, which defines the misfit kernel. The misfit kernel is multiplied by convenient orthonormal basis functions that are embedded in the SEM code, resulting in the gradient of the misfit function, i.e., the Fréchet derivatives. The misfit kernel is multiplied by convenient orthonormal basis functions that are embedded in the SEM code, resulting in the gradient of the misfit function, i.e., the Fréchet derivatives. A conjugate gradient algorithm is used to iteratively improve the model while reducing the misfit function. Using 2D examples for Rayleigh wave phase-speed maps of southern California, we illustrate the construction of the gradient and the minimization algorithm, and consider various tomographic experiments, including source inversions, structural inversions, and joint source-structure inversions. We also illustrate the characteristics of these 3D finite-frequency kernels based upon adjoint simulations for a variety of global arrivals, e.g., Pdiff, P'P', and SKS, and we illustrate how the approach may be used to investigate body- and surface-wave anisotropy. In adjoint tomography any time segment in which the data and synthetics match reasonably well is suitable for measurement, and this implies a much greater number of phases per seismogram can be used compared to classical tomography in which the sensitivity of the measurements is determined analytically for specific arrivals, e.g., P. We use an automated picking algorithm based upon short-term/long-term averages and strict phase and amplitude anomaly criteria to determine arrivals and time windows suitable for measurement. For shallow global events the algorithm typically identifies of the order of 1000~windows suitable for measurement, whereas for a deep event the number can reach 4000. For southern California earthquakes the number of phases is of the order of 100 for a magnitude 4.0 event and up to 450 for a magnitude 5.0 event. We will show examples of event kernels for both global and regional earthquakes. These event kernels form the basis of adjoint tomography.