BLOCK-TRIANGULAR PRECONDITIONERS FOR SYSTEMS ARISING FROM EDGE-PRESERVING IMAGE RESTORATION  

作　　者：Zhong-Zhi Bai Yu-Mei Huang Michael K. Ng 

机构地区：[1]LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China [2]School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China [3]Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

出　　处：《Journal of Computational Mathematics》2010年第6期848-863,共16页计算数学（英文）

基　　金：supported by the China NSF Outstanding Young Scientist Foundation(No.10525102);National Natural Science Foundation(No.10471146);the National Basic Research Program (No.2005CB321702)P.R.China;supported in part by the Fundamental Research Fund for Physics and Mathematics of Lanzhou University.P.R.China;supported in part by Hong Kong Research Grants Council Grant Nos.7035/04P and 7035/05P;HKBU FRGs

摘　　要：Signal and image restoration problems are often solved by minimizing a cost function consisting of an l2 data-fidelity term and a regularization term. We consider a class of convex and edge-preserving regularization functions. In specific, half-quadratic regularization as a fixed-point iteration method is usually employed to solve this problem. The main aim of this paper is to solve the above-described signal and image restoration problems with the half-quadratic regularization technique by making use of the Newton method. At each iteration of the Newton method, the Newton equation is a structured system of linear equations of a symmetric positive definite coefficient matrix, and may be efficiently solved by the preconditioned conjugate gradient method accelerated with the modified block SSOR preconditioner. Our experimental results show that the modified block-SSOR preconditioned conjugate gradient method is feasible and effective for further improving the numerical performance of the half-quadratic regularization approach.Signal and image restoration problems are often solved by minimizing a cost function consisting of an l2 data-fidelity term and a regularization term. We consider a class of convex and edge-preserving regularization functions. In specific, half-quadratic regularization as a fixed-point iteration method is usually employed to solve this problem. The main aim of this paper is to solve the above-described signal and image restoration problems with the half-quadratic regularization technique by making use of the Newton method. At each iteration of the Newton method, the Newton equation is a structured system of linear equations of a symmetric positive definite coefficient matrix, and may be efficiently solved by the preconditioned conjugate gradient method accelerated with the modified block SSOR preconditioner. Our experimental results show that the modified block-SSOR preconditioned conjugate gradient method is feasible and effective for further improving the numerical performance of the half-quadratic regularization approach.

关 键 词：Block system of equations Matrix preconditioner Edge-preserving Image restoration Half-quadratic regularization. 

分 类 号：O241.6[理学—计算数学] TP391.41[理学—数学]