Regularization methods have been substantially applied in image restoration due to the ill-posedness of the image restoration problem.Different assumptions or priors on images are applied in the construction of image ...Regularization methods have been substantially applied in image restoration due to the ill-posedness of the image restoration problem.Different assumptions or priors on images are applied in the construction of image regularization methods.In recent years,matrix low-rank approximation has been successfully introduced in the image denoising problem and significant denoising effects have been achieved.Low-rank matrix minimization is an NP-hard problem and it is often replaced with the matrix’s weighted nuclear norm minimization(WNNM).The assumption that an image contains an extensive amount of self-similarity is the basis for the construction of the matrix low-rank approximation-based image denoising method.In this paper,we develop a model for image restoration using the sum of block matching matrices’weighted nuclear norm to be the regularization term in the cost function.An alternating iterative algorithm is designed to solve the proposed model and the convergence analyses of the algorithm are also presented.Numerical experiments show that the proposed method can recover the images much better than the existing regularization methods in terms of both recovered quantities and visual qualities.展开更多
This paper studies non-convex programming problems. It is known that, in statistical inference, many constrained estimation problems may be expressed as convex programming problems. However, in many practical problems...This paper studies non-convex programming problems. It is known that, in statistical inference, many constrained estimation problems may be expressed as convex programming problems. However, in many practical problems, the objective functions are not convex. In this paper, we give a definition of a semi-convex objective function and discuss the corresponding non-convex programming problems. A two-step iterative algorithm called the alternating iterative method is proposed for finding solutions for such problems. The method is illustrated by three examples in constrained estimation problems given in Sasabuchi et al. （Biometrika, 72, 465472 （1983））, Shi N. Z. （J. Multivariate Anal., 50, 282-293 （1994）） and El Barmi H. and Dykstra R. （Ann. Statist., 26, 1878 1893 （1998））.展开更多
This paper proposes a decentralized robust two-stage dispatch framework for multi-area integrated electric-gas systems (M-IEGSs), with the consideration of Weymouth and linepack equations of tie-pipelines. The overall...This paper proposes a decentralized robust two-stage dispatch framework for multi-area integrated electric-gas systems (M-IEGSs), with the consideration of Weymouth and linepack equations of tie-pipelines. The overall methodology includes the equivalent conversion for the robust two-stage program and the decentralized optimization for the equivalent form. To obtain a tractable and equivalent counterpart for the robust two-stage program, a quadruple-loop procedure based on the column-and-constraint generation (C&CG) and the penalty convex-concave procedure (P-CCP) algorithms is derived, resulting in a series of mixed integer second-order cone programs (MISOCPs). Then, an improved I-ADMM is proposed to realize the decentralized optimization for MISOCPs. Moreover, three acceleration methods are devised to reduce the computation burden. Simulation results validate the effectiveness of the proposed methodology and corresponding acceleration measures.展开更多
基金This work is supported by the National Natural Science Foundation of China nos.11971215 and 11571156,MOE-LCSMSchool of Mathematics and Statistics,Hunan Normal University,Changsha,Hunan 410081,China.
文摘Regularization methods have been substantially applied in image restoration due to the ill-posedness of the image restoration problem.Different assumptions or priors on images are applied in the construction of image regularization methods.In recent years,matrix low-rank approximation has been successfully introduced in the image denoising problem and significant denoising effects have been achieved.Low-rank matrix minimization is an NP-hard problem and it is often replaced with the matrix’s weighted nuclear norm minimization(WNNM).The assumption that an image contains an extensive amount of self-similarity is the basis for the construction of the matrix low-rank approximation-based image denoising method.In this paper,we develop a model for image restoration using the sum of block matching matrices’weighted nuclear norm to be the regularization term in the cost function.An alternating iterative algorithm is designed to solve the proposed model and the convergence analyses of the algorithm are also presented.Numerical experiments show that the proposed method can recover the images much better than the existing regularization methods in terms of both recovered quantities and visual qualities.
基金the National Natural Science Foundation of China (Nos.10431010,10501005)Science Foundation for Young Teachers of NENU (No.20070103)
文摘This paper studies non-convex programming problems. It is known that, in statistical inference, many constrained estimation problems may be expressed as convex programming problems. However, in many practical problems, the objective functions are not convex. In this paper, we give a definition of a semi-convex objective function and discuss the corresponding non-convex programming problems. A two-step iterative algorithm called the alternating iterative method is proposed for finding solutions for such problems. The method is illustrated by three examples in constrained estimation problems given in Sasabuchi et al. （Biometrika, 72, 465472 （1983））, Shi N. Z. （J. Multivariate Anal., 50, 282-293 （1994）） and El Barmi H. and Dykstra R. （Ann. Statist., 26, 1878 1893 （1998））.
文摘This paper proposes a decentralized robust two-stage dispatch framework for multi-area integrated electric-gas systems (M-IEGSs), with the consideration of Weymouth and linepack equations of tie-pipelines. The overall methodology includes the equivalent conversion for the robust two-stage program and the decentralized optimization for the equivalent form. To obtain a tractable and equivalent counterpart for the robust two-stage program, a quadruple-loop procedure based on the column-and-constraint generation (C&CG) and the penalty convex-concave procedure (P-CCP) algorithms is derived, resulting in a series of mixed integer second-order cone programs (MISOCPs). Then, an improved I-ADMM is proposed to realize the decentralized optimization for MISOCPs. Moreover, three acceleration methods are devised to reduce the computation burden. Simulation results validate the effectiveness of the proposed methodology and corresponding acceleration measures.
