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

doi:10.4208/nmtma.2010.m9014

	Preconditioned Iterative Methods for Algebraic Systems from Multiplicative Half-Quadratic Regularization Image Restorations
	Bai, Zhong-Zhi1 ; Huang, Yu-Mei 2; Ng, Michael K.3; Yang, Xi 1
	2010-11-01
发表期刊	NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
ISSN	1004-8979
卷号	3 期号:4 页码:461-474
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.
关键词	Edge-preserving image restoration multiplicative half-quadratic regularization Newton method preconditioned conjugate gradient method constraint preconditioner eigenvalue bounds
DOI	10.4208/nmtma.2010.m9014
语种	英语
资助项目	National Basic Research Program[2005CB321702] ; National Outstanding Young Scientist Foundation[10525102] ; Specialized Research Grant for High Educational Doctoral Program[20090211120011] ; Specialized Research Grant for High Educational Doctoral Program[LZULL200909] ; Hong Kong RGC ; HKBU FRGs
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000284725400005
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/10869
专题	计算数学与科学工程计算研究所
通讯作者	Bai, Zhong-Zhi
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China 2.Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China 3.Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi,Huang, Yu-Mei,Ng, Michael K.,et al. Preconditioned Iterative Methods for Algebraic Systems from Multiplicative Half-Quadratic Regularization Image Restorations[J]. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,2010,3(4):461-474.
APA	Bai, Zhong-Zhi,Huang, Yu-Mei,Ng, Michael K.,&Yang, Xi.(2010).Preconditioned Iterative Methods for Algebraic Systems from Multiplicative Half-Quadratic Regularization Image Restorations.NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,3(4),461-474.
MLA	Bai, Zhong-Zhi,et al."Preconditioned Iterative Methods for Algebraic Systems from Multiplicative Half-Quadratic Regularization Image Restorations".NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS 3.4(2010):461-474.