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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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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
SCOPUS Cited Count: 1
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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 et al. "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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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
WoS CC Cited Count: 2 SCOPUS Cited Count: 2
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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 et al. "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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