Modulus-based iterative methods for constrained Tikhonov regularization

doi:10.1016/j.cam.2016.12.023

	Modulus-based iterative methods for constrained Tikhonov regularization
	Bai, Zhong-Zhi1 ; Buccini, Alessandro 2; Hayami, Ken 3,4; Reichel, Lothar 5; Yin, Jun-Feng 6; Zheng, Ning 3,4
	2017-08-01
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	319 页码:1-13
摘要	Tikhonov regularization is one of the most popular methods for the solution of linear discrete ill-posed problems. In many applications the desired solution is known to lie in the nonnegative cone. It is then natural to require that the approXimate solution determined by Tikhonov regularization also lies in this cone. The present paper describes two iterative methods, that employ modulus-based iterative methods, to compute approximate solutions in the nonnegative cone of large-scale Tikhonov regularization problems. The first method considered consists of two steps: first the given linear discrete ill-posed problem is reduced to a small problem by a Krylov subspace method, and then the reduced Tikhonov regularization problems so obtained is solved. The second method described explores the structure of certain image restoration problems. Computed examples illustrate the performances of these methods. (C) 2016 Elsevier B.V. All rights reserved.
关键词	Discrete ill-posed problem Regularization method Constrained minimization
DOI	10.1016/j.cam.2016.12.023
语种	英语
资助项目	National Natural Science Foundation, P.R. China[11671393] ; MIUR-PRIN[2012MTE38N] ; GNCS of INdAM Project : New aspects of imaging regularization
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000397362900001
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/25207
专题	计算数学与科学工程计算研究所
通讯作者	Buccini, Alessandro
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, POB 2719, Beijing 100190, Peoples R China 2.Univ Insubria, Dipartimento Sci & Alta Tecnol, I-22100 Como, Italy 3.Grad Univ Adv Studies, SOKENDAI, Sch Multidisciplinary Sci, Natl Inst Informat,Chiyoda Ku, 2-1-2 Hitotsubashi, Tokyo 1018430, Japan 4.Grad Univ Adv Studies, SOKENDAI, Sch Multidisciplinary Sci, Dept Informat,Chiyoda Ku, 2-1-2 Hitotsubashi, Tokyo 1018430, Japan 5.Kent State Univ, Dept Math Sci, Kent, OH 44242 USA 6.Tongji Univ, Dept Math, 1239 Siping Rd, Shanghai 200092, Peoples R China
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi,Buccini, Alessandro,Hayami, Ken,et al. Modulus-based iterative methods for constrained Tikhonov regularization[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2017,319:1-13.
APA	Bai, Zhong-Zhi,Buccini, Alessandro,Hayami, Ken,Reichel, Lothar,Yin, Jun-Feng,&Zheng, Ning.(2017).Modulus-based iterative methods for constrained Tikhonov regularization.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,319,1-13.
MLA	Bai, Zhong-Zhi,et al."Modulus-based iterative methods for constrained Tikhonov regularization".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 319(2017):1-13.