兰州大学机构库 >数学与统计学院
A restrictive preconditioner for the system arising in half-quadratic regularized image restoration
Zhao, Pei-Pei; Huang, YM(黄玉梅)
2021-05-01
Source PublicationApplied Mathematics Letters
ISSN08939659
Volume115
AbstractImage restoration is an ill-conditioned problem, so the regularization method is often applied to stabilize the solution. In this paper, we consider an additive half-quadratic (HQ) regularized image restoration problem and use the Newton method to solve it. At each Newton iteration step, a structured system of linear equations with symmetric positive definite coefficient matrix is needed to be solved. By taking an approximate Schur complement in the coefficient matrix, we construct a restrictive preconditioner and combine it into the conjugate gradient method in order to solve the linear system. The spectral properties of the preconditioned matrix are also analyzed. The numerical experiments demonstrate the effectiveness of the proposed method for image restoration. © 2020 Elsevier Ltd
KeywordConjugate gradient method Linear systems Matrix algebra Newton-Raphson method Numerical methods Restoration Ill conditioned problems Image restoration problem Numerical experiments Preconditioned matrix Regularization methods Spectral properties Structured systems Symmetric positive definite
PublisherElsevier Ltd
DOI10.1016/j.aml.2020.106916
Indexed ByEI
Language英语
EI Accession Number20205209682021
EI KeywordsImage reconstruction
EI Classification Number921 Mathematics - 961 Systems Science
Citation statistics
Document Type期刊论文
Identifierhttp://ir.lzu.edu.cn/handle/262010/443861
Collection数学与统计学院
Corresponding AuthorHuang, Yu-Mei
AffiliationSchool of Mathematics and Statistics, Lanzhou University, Lanzhou; 730000, China
First Author AffilicationSchool of Mathematics and Statistics
Corresponding Author AffilicationSchool of Mathematics and Statistics
Recommended Citation
GB/T 7714
Zhao, Pei-Pei,Huang, Yu-Mei. A restrictive preconditioner for the system arising in half-quadratic regularized image restoration[J]. Applied Mathematics Letters,2021,115.
APA Zhao, Pei-Pei,&Huang, Yu-Mei.(2021).A restrictive preconditioner for the system arising in half-quadratic regularized image restoration.Applied Mathematics Letters,115.
MLA Zhao, Pei-Pei,et al."A restrictive preconditioner for the system arising in half-quadratic regularized image restoration".Applied Mathematics Letters 115(2021).
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