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学者姓名：彭济根
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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 ：
empirical Bayesian approach linear inverse problem 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 . |
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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 ：
Closed-form thresholding functions compressed sensing fraction function minimization iterative FP thresholding algorithm 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 . |
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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 . |
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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 ：
Attenuation diffusive-viscous wave 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) . |
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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 . |
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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 ：
joint sparse recovery l(2,p)-minimization multiple measurement vectors 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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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 ：
Dantzig selector l(1)-Minimization Proximity operator Sparse recovery Total-variation
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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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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 Facility location problem k-Center 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 . |
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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 Facility location problem K-center problem Unit disk graphs
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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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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 coefficients Finite difference method Matrix inverse Vandermonde matrix
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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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