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A new nonconvex approach to low-rank matrix completion with application to image inpainting EI Scopus SCIE
期刊论文 | 2019 , 30 (1) , 145-174 | Multidimensional Systems and Signal Processing
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Abstract :

The problem of recovering a low-rank matrix from partial entries, known as low-rank matrix completion, has been extensively investigated in recent years. It can be viewed as a special case of the affine constrained rank minimization problem which is NP-hard in general and is computationally hard to solve in practice. One widely studied approach is to replace the matrix rank function by its nuclear-norm, which leads to the convex nuclear-norm minimization problem solved efficiently by many popular convex optimization algorithms. In this paper, we propose a new nonconvex approach to better approximate the rank function. The new approximation function is actually the Moreau envelope of the rank function (MER) which has an explicit expression. The new approximation problem of low-rank matrix completion based on MER can be converted to an optimization problem with two variables. We then adapt the proximal alternating minimization algorithm to solve it. The convergence (rate) of the proposed algorithm is proved and its accelerated version is also developed. Numerical experiments on completion of low-rank random matrices and standard image inpainting problems have shown that our algorithms have better performance than some state-of-art methods. © 2018 Springer Science+Business Media, LLC, part of Springer Nature

Keyword :

Alternating minimization Alternating minimization algorithms Approximation problems Convex optimization algorithms Image Inpainting Low-rank matrix completions Moreau envelope Nuclear norm minimizations

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GB/T 7714 Yu, Yongchao , Peng, Jigen , Yue, Shigang . A new nonconvex approach to low-rank matrix completion with application to image inpainting [J]. | Multidimensional Systems and Signal Processing , 2019 , 30 (1) : 145-174 .
MLA Yu, Yongchao 等. "A new nonconvex approach to low-rank matrix completion with application to image inpainting" . | Multidimensional Systems and Signal Processing 30 . 1 (2019) : 145-174 .
APA Yu, Yongchao , Peng, Jigen , Yue, Shigang . A new nonconvex approach to low-rank matrix completion with application to image inpainting . | Multidimensional Systems and Signal Processing , 2019 , 30 (1) , 145-174 .
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An improved LPTC neural model for background motion direction estimation EI Scopus
会议论文 | 2018 , 2018-January , 47-52 | 7th Joint IEEE International Conference on Development and Learning and on Epigenetic Robotics, ICDL-EpiRob 2017
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Abstract :

A class of specialized neurons, called lobula plate tangential cells (LPTCs) has been shown to respond strongly to wide-field motion. The classic model, elementary motion detector (EMD) and its improved model, two-quadrant detector (TQD) have been proposed to simulate LPTCs. Although EMD and TQD can percept background motion, their outputs are so cluttered that it is difficult to discriminate actual motion direction of the background. In this paper, we propose a max operation mechanism to model a newly-found transmedullary neuron Tm9 whose physiological properties do not map onto EMD and TQD. This proposed max operation mechanism is able to improve the detection performance of TQD in cluttered background by filtering out irrelevant motion signals. We will demonstrate the functionality of this proposed mechanism in wide-field motion perception. © 2017 IEEE.

Keyword :

Background motion Cluttered backgrounds Detection performance Elementary motion detectors Motion perception Operation mechanism Physiological properties Quadrant detectors

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GB/T 7714 Wang, Hongxin , Peng, Jigen , Yue, Shigang . An improved LPTC neural model for background motion direction estimation [C] . 2018 : 47-52 .
MLA Wang, Hongxin 等. "An improved LPTC neural model for background motion direction estimation" . (2018) : 47-52 .
APA Wang, Hongxin , Peng, Jigen , Yue, Shigang . An improved LPTC neural model for background motion direction estimation . (2018) : 47-52 .
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Sparse signals recovered by non-convex penalty in quasi-linear systems SCIE PubMed Scopus
期刊论文 | 2018 | JOURNAL OF INEQUALITIES AND APPLICATIONS
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Abstract :

The goal of compressed sensing is to reconstruct a sparse signal under a few linear measurements far less than the dimension of the ambient space of the signal. However, many real-life applications in physics and biomedical sciences carry some strongly nonlinear structures, and the linear model is no longer suitable. Compared with the compressed sensing under the linear circumstance, this nonlinear compressed sensing is much more difficult, in fact also NP-hard, combinatorial problem, because of the discrete and discontinuous nature of the L-0-norm and the nonlinearity. In order to get a convenience for sparse signal recovery, we set the nonlinear models have a smooth quasi-linear nature in this paper, and study a non-convex fraction function rho(a) in this quasi-linear compressed sensing. We propose an iterative fraction thresholding algorithm to solve the regularization problem (QP(a)(lambda)) for all a > 0. With the change of parameter a > 0, our algorithm could get a promising result, which is one of the advantages for our algorithm compared with some state-of-art algorithms. Numerical experiments show that our method performs much better than some state-of-the-art methods.

Keyword :

Iterative thresholding algorithm Non-convex fraction function Compressed sensing Quasi-linear

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GB/T 7714 Cui, Angang , Li, Haiyang , Wen, Meng et al. Sparse signals recovered by non-convex penalty in quasi-linear systems [J]. | JOURNAL OF INEQUALITIES AND APPLICATIONS , 2018 .
MLA Cui, Angang et al. "Sparse signals recovered by non-convex penalty in quasi-linear systems" . | JOURNAL OF INEQUALITIES AND APPLICATIONS (2018) .
APA Cui, Angang , Li, Haiyang , Wen, Meng , Peng, Jigen . Sparse signals recovered by non-convex penalty in quasi-linear systems . | JOURNAL OF INEQUALITIES AND APPLICATIONS , 2018 .
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Sparse signal recovery via alternating projection method EI SCIE Scopus
期刊论文 | 2018 , 143 , 161-170 | SIGNAL PROCESSING
WoS CC Cited Count: 3 SCOPUS Cited Count: 3
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Abstract :

Sparse signal recovery has attracted great attention in recent years with the development of compressive sensing. Alternating projection method is employed for this kind of recovery in this paper. The method is intuitive and can be easily implemented. The performance of the method is almost the same as that of basis pursuit (BP), while the computational cost is much lower. Restricted isometry constants and singular values of the coefficient matrix are utilized for the theoretical analyses of the method. Two sufficient conditions for the convergence and two estimates of the convergence rate are given. Numerical experiments are presented to show the performance of the method. (C) 2017 Published by Elsevier B.V.

Keyword :

Restricted isometry constant Alternating projection Compressive sensing Sparse signal recovery

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GB/T 7714 Liu, Haifeng , Peng, Jigen . Sparse signal recovery via alternating projection method [J]. | SIGNAL PROCESSING , 2018 , 143 : 161-170 .
MLA Liu, Haifeng et al. "Sparse signal recovery via alternating projection method" . | SIGNAL PROCESSING 143 (2018) : 161-170 .
APA Liu, Haifeng , Peng, Jigen . Sparse signal recovery via alternating projection method . | SIGNAL PROCESSING , 2018 , 143 , 161-170 .
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The connected disk covering problem EI SCIE Scopus
期刊论文 | 2018 , 35 (2) , 538-554 | JOURNAL OF COMBINATORIAL OPTIMIZATION
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Abstract :

Let P be a convex polygon with n vertices. We consider a variation of the K-center problem called the connected disk covering problem (CDCP), i.e., finding K congruent disks centered in P whose union covers P with the smallest possible radius, while a connected graph is generated by the centers of the K disks whose edge length can not exceed the radius. We give a 2.81-approximation algorithm in O(Kn) time.

Keyword :

Computational geometry Unit disk graphs K-center problem Facility location problem

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GB/T 7714 Xu, Yi , Peng, Jigen , Wang, Wencheng et al. The connected disk covering problem [J]. | JOURNAL OF COMBINATORIAL OPTIMIZATION , 2018 , 35 (2) : 538-554 .
MLA Xu, Yi et al. "The connected disk covering problem" . | JOURNAL OF COMBINATORIAL OPTIMIZATION 35 . 2 (2018) : 538-554 .
APA Xu, Yi , Peng, Jigen , Wang, Wencheng , Zhu, Binhai . The connected disk covering problem . | JOURNAL OF COMBINATORIAL OPTIMIZATION , 2018 , 35 (2) , 538-554 .
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Properties of seismic absorption induced reflections EI SCIE Scopus
期刊论文 | 2018 , 152 , 118-128 | JOURNAL OF APPLIED GEOPHYSICS
SCOPUS Cited Count: 1
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Abstract :

Seismic reflections at an interface are often regarded as the variation of the acoustic impedance (product of seismic velocity and density) in a medium. In fact, they can also be generated due to the difference in absorption of the seismic energy. In this paper, we investigate the properties of such reflections. Based on the diffusive-viscous wave equation and elastic diffusive-viscous wave equation, we investigate the dependency of the reflection coefficients on frequency, and their variations with incident angles. Numerical results at a boundary due to absorption contrasts are compared with those resulted from acoustic impedance variation. It is found that, the reflection coefficients resulted from absorption depend significantly on the frequency especially at lower frequencies, but vary very slowly at small incident angles. At the higher frequencies, the reflection coefficients of diffusive-viscous wave and elastic diffusive-viscous wave are close to those of acoustic and elastic cases, respectively. On the other hand, the reflections caused by acoustic impedance variation are independent of frequency but vary distinctly with incident angles before the critical angle. We also investigate the difference between the seismograms generated in the two different media. The numerical results show that the amplitudes of these reflected waves are attenuated and their phases are shifted. However, the reflections obtained by acoustic impedance contrast, show no significant amplitude attenuation and phase shift. (C) 2018 Elsevier B.V. All rights reserved.

Keyword :

Absorption Numerical modeling Frequency-dependent Seismic reflections Acoustic impedance

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GB/T 7714 Zhao, Haixia , Gao, Jinghuai , Peng, Jigen . Properties of seismic absorption induced reflections [J]. | JOURNAL OF APPLIED GEOPHYSICS , 2018 , 152 : 118-128 .
MLA Zhao, Haixia et al. "Properties of seismic absorption induced reflections" . | JOURNAL OF APPLIED GEOPHYSICS 152 (2018) : 118-128 .
APA Zhao, Haixia , Gao, Jinghuai , Peng, Jigen . Properties of seismic absorption induced reflections . | JOURNAL OF APPLIED GEOPHYSICS , 2018 , 152 , 118-128 .
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A robust method of computing finite difference coefficients based on Vandermonde matrix EI SCIE Scopus
期刊论文 | 2018 , 152 , 110-117 | JOURNAL OF APPLIED GEOPHYSICS
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Abstract :

When the finite difference (FD) method is employed to simulate the wave propagation, high-order FD method is preferred in order to achieve better accuracy. However, if the order of FD scheme is high enough, the coefficient matrix of the formula for calculating finite difference coefficients is close to be singular. In this case, when the FD coefficients are computed by matrix inverse operator of MATLAB, inaccuracy can be produced. In order to overcome this problem, we have suggested an algorithm based on Vandermonde matrix in this paper. After specified mathematical transformation, the coefficient matrix is transformed into a Vandermonde matrix. Then the FD coefficients of high-order FD method can be computed by the algorithm of Vandermonde matrix, which prevents the inverse of the singular matrix. The dispersion analysis and numerical results of a homogeneous elastic model and a geophysical model of oil and gas reservoir demonstrate that the algorithm based on Vandermonde matrix has better accuracy compared with matrix inverse operator of MATLAB. (C) 2017 Elsevier B.V. All rights reserved.

Keyword :

Finite difference method Vandermonde matrix Finite difference coefficients Matrix inverse

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GB/T 7714 Zhang, Yijie , Gao, Jinghuai , Peng, Jigen et al. A robust method of computing finite difference coefficients based on Vandermonde matrix [J]. | JOURNAL OF APPLIED GEOPHYSICS , 2018 , 152 : 110-117 .
MLA Zhang, Yijie et al. "A robust method of computing finite difference coefficients based on Vandermonde matrix" . | JOURNAL OF APPLIED GEOPHYSICS 152 (2018) : 110-117 .
APA Zhang, Yijie , Gao, Jinghuai , Peng, Jigen , Han, Weimin . A robust method of computing finite difference coefficients based on Vandermonde matrix . | JOURNAL OF APPLIED GEOPHYSICS , 2018 , 152 , 110-117 .
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Exact recovery of sparse multiple measurement vectors by l(2,p)-minimization SCIE PubMed Scopus
期刊论文 | 2018 | JOURNAL OF INEQUALITIES AND APPLICATIONS
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Abstract :

The joint sparse recovery problem is a generalization of the single measurement vector problem widely studied in compressed sensing. It aims to recover a set of jointly sparse vectors, i.e., those that have nonzero entries concentrated at a common location. Meanwhile l(p)-minimization subject to matrixes is widely used in a large number of algorithms designed for this problem, i.e., l(2,p)-minimization min(X is an element of Rnxr) parallel to X parallel to(2,p) s.t. AX = B. Therefore the main contribution in this paper is two theoretical results about this technique. The first one is proving that in every multiple system of linear equations there exists a constant p* such that the original unique sparse solution also can be recovered from a minimization in l(p) quasi-norm subject to matrixes whenever 0 < p < p*. The other one is showing an analytic expression of such p*. Finally, we display the results of one example to confirm the validity of our conclusions, and we use some numerical experiments to show that we increase the efficiency of these algorithms designed for l(2,p)-minimization by using our results.

Keyword :

multiple measurement vectors l(2,p)-minimization sparse recovery joint sparse recovery

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GB/T 7714 Wang, Changlong , Peng, Jigen . Exact recovery of sparse multiple measurement vectors by l(2,p)-minimization [J]. | JOURNAL OF INEQUALITIES AND APPLICATIONS , 2018 .
MLA Wang, Changlong et al. "Exact recovery of sparse multiple measurement vectors by l(2,p)-minimization" . | JOURNAL OF INEQUALITIES AND APPLICATIONS (2018) .
APA Wang, Changlong , Peng, Jigen . Exact recovery of sparse multiple measurement vectors by l(2,p)-minimization . | JOURNAL OF INEQUALITIES AND APPLICATIONS , 2018 .
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The matrix splitting based proximal fixed-point algorithms for quadratically constrained l(1) minimization and Dantzig selector EI SCIE Scopus
期刊论文 | 2018 , 125 , 23-50 | APPLIED NUMERICAL MATHEMATICS
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Abstract :

This paper studies algorithms for solving quadratically constrained l(1) minimization and Dantzig selector which have recently been widely used to tackle sparse recovery problems in compressive sensing. The two optimization models can be reformulated via two indicator functions as special cases of a general convex composite model which minimizes the sum of two convex functions with one composed with a matrix operator. The general model can be transformed into a fixed-point problem for a nonlinear operator which is composed of a proximity operator and an expansive matrix operator, and then a new iterative scheme based on the expansive matrix splitting is proposed to find fixed-points of the nonlinear operator. We also give some mild conditions to guarantee that the iterative sequence generated by the scheme converges to a fixed-point of the nonlinear operator. Further, two specific proximal fixed-point algorithms based on the scheme are developed and then applied to quadratically constrained l(1) minimization and Dantzig selector. Numerical results have demonstrated that the proposed algorithms are comparable to the state-of-the-art algorithms for recovering sparse signals with different sizes and dynamic ranges in terms of both accuracy and speed. In addition, we also extend the proposed algorithms to solve two harder constrained total-variation minimization problems. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.

Keyword :

l(1)-Minimization Sparse recovery Proximity operator Total-variation Dantzig selector

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GB/T 7714 Yu, Yongchao , Peng, Jigen . The matrix splitting based proximal fixed-point algorithms for quadratically constrained l(1) minimization and Dantzig selector [J]. | APPLIED NUMERICAL MATHEMATICS , 2018 , 125 : 23-50 .
MLA Yu, Yongchao et al. "The matrix splitting based proximal fixed-point algorithms for quadratically constrained l(1) minimization and Dantzig selector" . | APPLIED NUMERICAL MATHEMATICS 125 (2018) : 23-50 .
APA Yu, Yongchao , Peng, Jigen . The matrix splitting based proximal fixed-point algorithms for quadratically constrained l(1) minimization and Dantzig selector . | APPLIED NUMERICAL MATHEMATICS , 2018 , 125 , 23-50 .
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Manifold Preserving: An Intrinsic Approach for Semisupervised Distance Metric Learning EI SCIE Scopus
期刊论文 | 2018 , 29 (7) , 2731-2742 | IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
WoS CC Cited Count: 6 SCOPUS Cited Count: 8
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Abstract :

In this paper, we address the semisupervised distance metric learning problem and its applications in classification and image retrieval. First, we formulate a semisupervised distance metric learning model by considering the metric information of inner classes and interclasses. In this model, an adaptive parameter is designed to balance the inner metrics and intermetrics by using data structure. Second, we convert the model to a minimization problem whose variable is symmetric positive-definite matrix. Third, in implementation, we deduce an intrinsic steepest descent method, which assures that the metric matrix is strictly symmetric positive-definite at each iteration, with the manifold structure of the symmetric positive-definite matrix manifold. Finally, we test the proposed algorithm on conventional data sets, and compare it with other four representative methods. The numerical results validate that the proposed method significantly improves the classification with the same computational efficiency.

Keyword :

semisupervised learning matrix manifold intrinsic algorithm Classification distance metric learning

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GB/T 7714 Ying, Shihui , Wen, Zhijie , Shi, Jun et al. Manifold Preserving: An Intrinsic Approach for Semisupervised Distance Metric Learning [J]. | IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS , 2018 , 29 (7) : 2731-2742 .
MLA Ying, Shihui et al. "Manifold Preserving: An Intrinsic Approach for Semisupervised Distance Metric Learning" . | IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 29 . 7 (2018) : 2731-2742 .
APA Ying, Shihui , Wen, Zhijie , Shi, Jun , Peng, Yaxin , Peng, Jigen , Qiao, Hong . Manifold Preserving: An Intrinsic Approach for Semisupervised Distance Metric Learning . | IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS , 2018 , 29 (7) , 2731-2742 .
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