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< Page ，Total 22 >
POSTERIOR CONTRACTION FOR EMPIRICAL BAYESIAN APPROACH TO INVERSE PROBLEMS UNDER NON-DIAGONAL ASSUMPTION SCIE

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Abstract ：

We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a hyperparameter that quantifies regularity. By introducing two auxiliary problems, we construct an empirical Bayes method and prove that this method can automatically select the hyperparameter. In addition, we show that this adaptive Bayes procedure provides optimal contraction rates up to a slowly varying term and an arbitrarily small constant, without knowledge about the regularity index. Our method needs not the prior covariance, noise covariance and forward operator have a common basis in their singular value decomposition, enlarging the application range compared with the existing results. A simple simulation example is given that illustrates the effectiveness of the proposed method.

Keyword ：

linear inverse problem empirical Bayesian approach non-simultaneous diagonal posterior consistency

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 GB/T 7714 Jia, Junxiong , Peng, Jigen , Gao, Jinghuai . POSTERIOR CONTRACTION FOR EMPIRICAL BAYESIAN APPROACH TO INVERSE PROBLEMS UNDER NON-DIAGONAL ASSUMPTION [J]. | INVERSE PROBLEMS AND IMAGING , 2021 , 15 (2) : 201-228 . MLA Jia, Junxiong 等. "POSTERIOR CONTRACTION FOR EMPIRICAL BAYESIAN APPROACH TO INVERSE PROBLEMS UNDER NON-DIAGONAL ASSUMPTION" . | INVERSE PROBLEMS AND IMAGING 15 . 2 (2021) : 201-228 . APA Jia, Junxiong , Peng, Jigen , Gao, Jinghuai . POSTERIOR CONTRACTION FOR EMPIRICAL BAYESIAN APPROACH TO INVERSE PROBLEMS UNDER NON-DIAGONAL ASSUMPTION . | INVERSE PROBLEMS AND IMAGING , 2021 , 15 (2) , 201-228 . Export to NoteExpress RIS BibTex
Minimization of Fraction Function Penalty in Compressed Sensing EI SCIE Scopus

WoS CC Cited Count： 4 SCOPUS Cited Count： 5
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Abstract ：

In this paper, we study the minimization problem of a non-convex sparsity-promoting penalty function, i.e., fraction function, in compressed sensing. First, we discuss the equivalence of $\ell _{0}$ minimization and fraction function minimization. It is proved that the optimal solution to fraction function minimization solves $\ell _{0}$ minimization and the optimal solution to the regularization problem also solves fraction function minimization if the certain conditions are satisfied, which is similar to the regularization problem in a convex optimization theory. Second, we study the properties of the optimal solution to the regularization problem, including the first-order and second-order optimality conditions and the lower and upper bounds of the absolute value for its nonzero entries. Finally, we derive the closed-form representation of the optimal solution to the regularization problem and propose an iterative $FP$ thresholding algorithm to solve the regularization problem. We also provide a series of experiments to assess the performance of the $FP$ algorithm, and the experimental results show that the $FP$ algorithm performs well in sparse signal recovery with and without measurement noise.

Keyword ：

iterative FP thresholding algorithm fraction function minimization Closed-form thresholding functions compressed sensing non-convex optimization

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 GB/T 7714 Li, Haiyang , Zhang, Qian , Cui, Angang et al. Minimization of Fraction Function Penalty in Compressed Sensing [J]. | IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS , 2020 , 31 (5) : 1626-1637 . MLA Li, Haiyang et al. "Minimization of Fraction Function Penalty in Compressed Sensing" . | IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 31 . 5 (2020) : 1626-1637 . APA Li, Haiyang , Zhang, Qian , Cui, Angang , Peng, Jigen . Minimization of Fraction Function Penalty in Compressed Sensing . | IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS , 2020 , 31 (5) , 1626-1637 . Export to NoteExpress RIS BibTex
The discrete and mixed minimax 2-center problems EI Scopus SCIE

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Abstract ：

Letting . P be a set of . n points in the plane, the discrete minimax 2-center problem (DMM2CP) is to find two disks centered at . (p1,p2)P that minimize the maximum of two terms, namely, the Euclidean distance between two centers and the distance of any other point to the closer center. The mixed minimax 2-center problem (MMM2CP) is when one of the two centers is not in . P. We present algorithms solving the . DMM2CP and . MMM2CP. The time complexities of solving the . DMM2CP and . MMM2CP are . O(n2logn) and . O(n2log2n) respectively. Furthermore, we consider two Steiner minimum sum dipolar spanning tree problems, in which one of the two dipoles is a Steiner point and the dipoles are both Steiner points. These two problems are shown to be solvable in . O(nlogn) and . O(n) time respectively. © 2016 Elsevier B.V.

Keyword ：

2-center problem Euclidean distance Facility location problem Spanning tree problems Steiner Steiner points Time complexity Voronoi diagrams

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 GB/T 7714 Xu, Yi , Peng, Jigen , Xu, Yinfeng et al. The discrete and mixed minimax 2-center problems [J]. | Theoretical Computer Science , 2019 , 774 : 95-102 . MLA Xu, Yi et al. "The discrete and mixed minimax 2-center problems" . | Theoretical Computer Science 774 (2019) : 95-102 . APA Xu, Yi , Peng, Jigen , Xu, Yinfeng , Zhu, Binhai . The discrete and mixed minimax 2-center problems . | Theoretical Computer Science , 2019 , 774 , 95-102 . Export to NoteExpress RIS BibTex
Modeling Attenuation of Diffusive-Viscous Wave Using Reflectivity Method SCIE Scopus

WoS CC Cited Count： 1 SCOPUS Cited Count： 1
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Abstract ：

Seismic waves in earth materials are subject to attenuation and dispersion in a broad range of frequencies. The commonly accepted mechanism of intrinsic attenuation and dispersion is the presence of fluids in the pore space of rocks. The diffusive-viscous model was proposed to explain low-frequency seismic anomalies related to hydrocarbon reservoirs. But, the model is only a description of compressional wave. In this work, we firstly discuss the extended elastic diffusive-viscous model. Then, we extend reflectivity method to the diffusive-viscous medium. Finally, we present two numerical models to simulate the attenuation of diffusive-viscous wave in horizontal and dip multi-layered media compared with the results of viscoelastic wave. The modeling results show that the diffusive-viscous wave has strong amplitude attenuation and phase shift when it propagates across absorptive layers.

Keyword ：

diffusive-viscous wave Attenuation reflectivity method

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 GB/T 7714 Zhao, Haixia , Gao, Jinghuai , Peng, Jigen et al. Modeling Attenuation of Diffusive-Viscous Wave Using Reflectivity Method [J]. | JOURNAL OF THEORETICAL AND COMPUTATIONAL ACOUSTICS , 2019 , 27 (3) . MLA Zhao, Haixia et al. "Modeling Attenuation of Diffusive-Viscous Wave Using Reflectivity Method" . | JOURNAL OF THEORETICAL AND COMPUTATIONAL ACOUSTICS 27 . 3 (2019) . APA Zhao, Haixia , Gao, Jinghuai , Peng, Jigen , Zhang, Gulan . Modeling Attenuation of Diffusive-Viscous Wave Using Reflectivity Method . | JOURNAL OF THEORETICAL AND COMPUTATIONAL ACOUSTICS , 2019 , 27 (3) . Export to NoteExpress RIS BibTex
A new nonconvex approach to low-rank matrix completion with application to image inpainting EI Scopus SCIE

WoS CC Cited Count： 3 SCOPUS Cited Count： 2
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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 et al. "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 . Export to NoteExpress RIS BibTex
Sparse signals recovered by non-convex penalty in quasi-linear systems SCIE PubMed Scopus

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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 . Export to NoteExpress RIS BibTex
The mixed center location problem EI SCIE Scopus

WoS CC Cited Count： 2
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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 et al. "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 . Export to NoteExpress RIS BibTex
An improved LPTC neural model for background motion direction estimation EI Scopus

SCOPUS Cited Count： 4
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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 . Export to NoteExpress RIS BibTex
The matrix splitting based proximal fixed-point algorithms for quadratically constrained l(1) minimization and Dantzig selector EI SCIE Scopus

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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 . Export to NoteExpress RIS BibTex
Exact recovery of sparse multiple measurement vectors by l(2,p)-minimization SCIE PubMed Scopus

WoS CC Cited Count： 1 SCOPUS Cited Count： 2
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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 . Export to NoteExpress RIS BibTex
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