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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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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 等. "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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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 等. "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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Variable-Order Finite Difference Scheme for Numerical Simulation in 3-D Poroelastic Media EI SCIE Scopus
期刊论文 | 2018 , 56 (5) , 2991-3001 | IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
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Abstract :

The numerical simulation of wave fields in 3-D poroelastic media can give a better understanding of elastic properties, deformation characteristics of rocks, and interaction with pore fluids. However, the wave equations in 3-D poroelastic media include more equations, and the size of geophysical model for practical reservoir is immense. Therefore, numerical simulation is time consuming. In order to improve the efficiency, we proposed variable-order staggered-grid (SG) finite difference (FD) method to solve 3-D poroelastic wave equations. In this method, different orders of SGFD scheme can be selected for different velocities in a heterogeneous poroelastic model by restricting the dispersion parameters within a tolerable threshold. We derive the dispersion relation, numerical dispersion relation, and stability condition for 3-D poroelastic media using plane wave analysis and SGFD scheme. Based on the numerical dispersion relation of slow P-wave, S-wave, and fast P-wave, we restrict the average of dispersion parameters of the three waves within a given range; the orders of the SGFD scheme can be calculated for different velocities. Dispersion analysis shows that the variable-order SGFD method can maintain the accuracy compared with the fixed-order SGFD method. We use three numerical examples, which include laterally homogeneous model, a simplified overthrust model, and a geophysical model in a desert area in China, to demonstrate the accuracy and efficiency of the proposed method. The numerical results confirm that the variable-order SGFD method can reduce the computation time efficiently and still ensure the accuracy.

Keyword :

finite difference (FD) poroelastic media 3-D variable order dispersion relationship

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GB/T 7714 Zhang, Yijie , Gao, Jinghuai , Peng, Jigen . Variable-Order Finite Difference Scheme for Numerical Simulation in 3-D Poroelastic Media [J]. | IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING , 2018 , 56 (5) : 2991-3001 .
MLA Zhang, Yijie 等. "Variable-Order Finite Difference Scheme for Numerical Simulation in 3-D Poroelastic Media" . | IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 56 . 5 (2018) : 2991-3001 .
APA Zhang, Yijie , Gao, Jinghuai , Peng, Jigen . Variable-Order Finite Difference Scheme for Numerical Simulation in 3-D Poroelastic Media . | IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING , 2018 , 56 (5) , 2991-3001 .
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Synchronization of fractional-order linear complex networks with directed coupling topology EI SCIE Scopus
期刊论文 | 2018 , 490 , 542-553 | PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
WoS CC Cited Count: 5 SCOPUS Cited Count: 8
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Abstract :

The synchronization of fractional-order complex networks with general linear dynamics under directed connected topology is investigated. The synchronization problem is converted to an equivalent simultaneous stability problem of corresponding independent subsystems by use of a pseudo-state transformation technique and real Jordan canonical form of matrix. Sufficient conditions in terms of linear matrix inequalities for synchronization are established according to stability theory of fractional-order differential equations. In a certain range of fractional order, the effects of the fractional order on synchronization is clearly revealed. Conclusions obtained in this paper generalize the existing results. Three numerical examples are provided to illustrate the validity of proposed conclusions. (C) 2017 Elsevier B.V. All rights reserved.

Keyword :

Real Jordan canonical form Complex networks Synchronization Fractional-order derivative Linear matrix inequality

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GB/T 7714 Fang, Qingxiang , Peng, Jigen . Synchronization of fractional-order linear complex networks with directed coupling topology [J]. | PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS , 2018 , 490 : 542-553 .
MLA Fang, Qingxiang 等. "Synchronization of fractional-order linear complex networks with directed coupling topology" . | PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 490 (2018) : 542-553 .
APA Fang, Qingxiang , Peng, Jigen . Synchronization of fractional-order linear complex networks with directed coupling topology . | PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS , 2018 , 490 , 542-553 .
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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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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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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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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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Sparse recovery in probability via l(q)-minimization with Weibull random matrices for 0 < q <= 1 SCIE Scopus CSCD
期刊论文 | 2018 , 33 (1) , 1-24 | APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B
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Abstract :

Although Gaussian random matrices play an important role of measurement matrices in compressed sensing, one hopes that there exist other random matrices which can also be used to serve as the measurement matrices. Hence, Weibull random matrices induce extensive interest. In this paper, we first propose the l (2,q) robust null space property that can weaken the D-RIP, and show that Weibull random matrices satisfy the l (2,q) robust null space property with high probability. Besides, we prove that Weibull random matrices also possess the l (q) quotient property with high probability. Finally, with the combination of the above mentioned properties, we give two important approximation characteristics of the solutions to the l (q) -minimization with Weibull random matrices, one is on the stability estimate when the measurement noise e a a"e (n) needs a priori ||e||(2) ae N", the other is on the robustness estimate without needing to estimate the bound of ||e||(2). The results indicate that the performance of Weibull random matrices is similar to that of Gaussian random matrices in sparse recovery.

Keyword :

l(q)-minimization Weibull matrices quotient property compressed sensing null space property

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GB/T 7714 Gao, Yi , Peng, Ji-gen , Yue, Shi-gang . Sparse recovery in probability via l(q)-minimization with Weibull random matrices for 0 < q <= 1 [J]. | APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B , 2018 , 33 (1) : 1-24 .
MLA Gao, Yi et al. "Sparse recovery in probability via l(q)-minimization with Weibull random matrices for 0 < q <= 1" . | APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B 33 . 1 (2018) : 1-24 .
APA Gao, Yi , Peng, Ji-gen , Yue, Shi-gang . Sparse recovery in probability via l(q)-minimization with Weibull random matrices for 0 < q <= 1 . | APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B , 2018 , 33 (1) , 1-24 .
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