Preconditioned Iterative Methods for Algebraic Systems from Multiplicative Half-Quadratic Regularization Image Restorations  

作　　者：Michael K.Ng 

机构地区：[1]Department of Mathematics,Hong Kong Baptist University,Kowloon Tong,Hong Kong

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2010年第4期461-474,共14页高等学校计算数学学报（英文版）

基　　金：supported by the National Basic Research Program (No.2005CB321702);the National Outstanding Young Scientist Foundation(No. 10525102);the Specialized Research Grant for High Educational Doctoral Program(Nos. 20090211120011 and LZULL200909),Hong Kong RGC grants and HKBU FRGs

摘　　要：Image restoration is often solved by minimizing an energy function consisting of a data-fidelity term and a regularization term.A regularized convex term can usually preserve the image edges well in the restored image.In this paper,we consider a class of convex and edge-preserving regularization functions,i.e.,multiplicative half-quadratic regularizations,and we use the Newton method to solve the correspondingly reduced systems of nonlinear equations.At each Newton iterate,the preconditioned conjugate gradient method,incorporated with a constraint preconditioner,is employed to solve the structured Newton equation that has a symmetric positive definite coefficient matrix. The eigenvalue bounds of the preconditioned matrix are deliberately derived,which can be used to estimate the convergence speed of the preconditioned conjugate gradient method.We use experimental results to demonstrate that this new approach is efficient, and the effect of image restoration is reasonably well.Image restoration is often solved by minimizing an energy function consisting of a data-fidelity term and a regularization term. A regularized convex term can usually preserve the image edges well in the restored image. In this paper, we consider a class of convex and edge-preserving regularization functions, I.e., multiplicative half-quadratic regularizations, and we use the Newton method to solve the correspondingly reduced systems of nonlinear equations. At each Newton iterate, the preconditioned conjugate gradient method, incorporated with a constraint preconditioner, is employed to solve the structured Newton equation that has a symmetric positive definite coefficient matrix.The igenvalue bounds of the preconditioned matrix are deliberately derived, which can be used to estimate the convergence speed of the preconditioned conjugate gradient method. We use experimental results to demonstrate that this new approach is efficient,and the effect of image restoration is r0easonably well.

关 键 词：Edge-preserving     image restoration     multiplicative half-quadratic regularization     Newton method     preconditioned conjugate gradient method     constraint preconditioner     eigenvalue bounds 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]