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< Page ,Total 22 >
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
WoS CC Cited Count: 1 SCOPUS Cited Count: 1
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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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The mixed center location problem EI SCIE Scopus
期刊论文 | 2018 , 36 (4) , 1128-1144 | JOURNAL OF COMBINATORIAL OPTIMIZATION
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Abstract :

This paper studies a new version of the location problem called the mixed center location problem. Let P be a set of n points in the plane. We first consider the mixed 2-center problem, where one of the centers must be in P, and we solve it in time. Second, we consider the mixed k-center problem, where m of the centers are in P, and we solve it in time. Motivated by two practical constraints, we propose two variations of the problem. Third, we present a 2-approximation algorithm and three heuristics solving the mixed k-center problem (k > 2).

Keyword :

Computational geometry k-Center problem Facility location problem Voronoi diagram

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GB/T 7714 Xu, Yi , Peng, Jigen , Xu, Yinfeng . The mixed center location problem [J]. | JOURNAL OF COMBINATORIAL OPTIMIZATION , 2018 , 36 (4) : 1128-1144 .
MLA Xu, Yi 等. "The mixed center location problem" . | JOURNAL OF COMBINATORIAL OPTIMIZATION 36 . 4 (2018) : 1128-1144 .
APA Xu, Yi , Peng, Jigen , Xu, Yinfeng . The mixed center location problem . | JOURNAL OF COMBINATORIAL OPTIMIZATION , 2018 , 36 (4) , 1128-1144 .
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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 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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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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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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Preconditioning for Orthogonal Matching Pursuit with Noisy and Random Measurements: The Gaussian Case EI SCIE Scopus
期刊论文 | 2018 , 37 (9) , 4109-4127 | CIRCUITS SYSTEMS AND SIGNAL PROCESSING
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Abstract :

The success of orthogonal matching pursuit (OMP) in the sparse signal recovery heavily depends on its ability for correct support recovery. Based on a support recovery guarantee for OMP expressed in terms of the mutual coherence, and a result about the concentration of the extreme singular values of a Gaussian random matrix, this paper proposes a preconditioning method for increasing the recovery rate of OMP from random and noisy measurements. Compared to several existing preconditionings, the proposed method can reduce the mutual coherence with a proven high probability. Simultaneously, the proposed preconditioning can also succeed with a high probability in providing slight signal-to-noise ratio reduction, which is empirically shown to be less severe than that caused by a recently suggested technique for the noisy case. The simulations show the advantages of the proposed preconditioning over other currently relevant ones in terms of both the performance improvement for OMP, and computation time.

Keyword :

Gaussian random matrices Orthogonal matching pursuit Noise Mutual coherence Preconditioning

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GB/T 7714 Chen, Yingtong , Peng, Jigen , Yue, Shigang . Preconditioning for Orthogonal Matching Pursuit with Noisy and Random Measurements: The Gaussian Case [J]. | CIRCUITS SYSTEMS AND SIGNAL PROCESSING , 2018 , 37 (9) : 4109-4127 .
MLA Chen, Yingtong et al. "Preconditioning for Orthogonal Matching Pursuit with Noisy and Random Measurements: The Gaussian Case" . | CIRCUITS SYSTEMS AND SIGNAL PROCESSING 37 . 9 (2018) : 4109-4127 .
APA Chen, Yingtong , Peng, Jigen , Yue, Shigang . Preconditioning for Orthogonal Matching Pursuit with Noisy and Random Measurements: The Gaussian Case . | CIRCUITS SYSTEMS AND SIGNAL PROCESSING , 2018 , 37 (9) , 4109-4127 .
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Frequency-dependent reflections in elastic diffusive-viscous media SCIE Scopus
期刊论文 | 2018 , 15 (5) , 1900-1916 | JOURNAL OF GEOPHYSICS AND ENGINEERING
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Abstract :

Amplitude variation with offset/angle of incidence (AVO/AVA) analysis is essential for hydrocarbon detection and reservoir characterization. Frequency-dependent AVO analysis plays an important role in seismic interpretation especially for the low-frequency seismic anomalies related to hydrocarbon reservoir. The diffusive-viscous model is used to explain these anomalies, but it does not consider the shear effects of rocks. In this work, we firstly extend the diffusiveviscous model to elastic case based on the mechanisms in a macroscopic porous medium. The elastic diffusive-viscous model describes attenuation of compressional and shear waves in a fluid-saturated medium and it reduces to the classic elastic wave equation in a special case. Then, we investigate the properties of reflection/transmission coefficients at an interface between two different elastic diffusive-viscous media. The reflection/transmission coefficients not only relate to the parameters of the media but also depend on the frequency. Two examples are given to analyze the dependence of the reflection/transmission coefficients on the frequency and incident angle at interfaces between gas-saturated sandstone and brine-saturated shale and between brinesaturated shale and oil-saturated sandstone. The results show that the magnitudes and phase angles of the reflection/transmission coefficients are significantly dependent on the frequency at lower frequency (<20 Hz). Finally, we apply the frequency-dependent reflection/transmission coefficients to the extended reflectivity method to model the propagation of the elastic diffusiveviscous wave in a layered medium. The modeling results show that the diffusive-viscous wave has strong amplitude attenuation and phase shift compared with those of elastic wave when the wave propagates across fluid-saturated layers.

Keyword :

attenuation wave propagation reflection/transmission coefficient frequency-dependent

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GB/T 7714 Zhao, Haixia , Gao, Jinghuai , Peng, Jigen . Frequency-dependent reflections in elastic diffusive-viscous media [J]. | JOURNAL OF GEOPHYSICS AND ENGINEERING , 2018 , 15 (5) : 1900-1916 .
MLA Zhao, Haixia et al. "Frequency-dependent reflections in elastic diffusive-viscous media" . | JOURNAL OF GEOPHYSICS AND ENGINEERING 15 . 5 (2018) : 1900-1916 .
APA Zhao, Haixia , Gao, Jinghuai , Peng, Jigen . Frequency-dependent reflections in elastic diffusive-viscous media . | JOURNAL OF GEOPHYSICS AND ENGINEERING , 2018 , 15 (5) , 1900-1916 .
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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
WoS CC Cited Count: 1 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 modified primal-dual method with applications to some sparse recovery problems EI SCIE Scopus
期刊论文 | 2018 , 333 , 76-94 | APPLIED MATHEMATICS AND COMPUTATION
WoS CC Cited Count: 1 SCOPUS Cited Count: 1
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Abstract :

In this paper, we first present a modified Chambolle-Pock primal-dual method (MCPPDM) to solve a convex composite optimization problem which minimizes the sum of two convex functions with one composed by a linear operator. It is well known that the Chambolle-Pock primal-dual method (CPPDM) with the combination parameter being 1 is an application of the proximal point algorithm and thus is convergent, however, when the combination parameter is not 1, the method may be not convergent. To choose flexibly the combination parameter, we develop a slightly modified version with little additional computation cost. In CPPDM, one variable is updated twice but another variable is updated only once at each iteration. However, in the modified version, two variables are respectively updated twice at each iteration. Another main task of this paper is that we reformulate some well-known sparse recovery problems as special cases of the convex composite optimization problem and then apply MCPPDM to address these sparse recovery problems. A large number of numerical experiments have demonstrated that the efficiency of the proposed method is generally comparable or superior to that of existing well-known methods such as the linearized alternating direction method of multipliers and the graph projection splitting algorithm in terms of solution quality and run time. (C) 2018 Elsevier Inc. All rights reserved.

Keyword :

Proximity operator Sparse recovery problems Primal-dual method

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GB/T 7714 Yu, Yongchao , Peng, Jigen . A modified primal-dual method with applications to some sparse recovery problems [J]. | APPLIED MATHEMATICS AND COMPUTATION , 2018 , 333 : 76-94 .
MLA Yu, Yongchao et al. "A modified primal-dual method with applications to some sparse recovery problems" . | APPLIED MATHEMATICS AND COMPUTATION 333 (2018) : 76-94 .
APA Yu, Yongchao , Peng, Jigen . A modified primal-dual method with applications to some sparse recovery problems . | APPLIED MATHEMATICS AND COMPUTATION , 2018 , 333 , 76-94 .
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