Modulus-based iterative methods for constrained Tikhonov regularization

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:319

Article

Bai, Zhong-Zhi¹  Buccini, Alessandro²  Hayami, Ken^3,4  Reichel, Lothar⁵  Yin, Jun-Feng⁶  Zheng, Ning^3,4 

[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

关键词: Discrete ill-posed problem;    Regularization method;    Constrained minimization;   

DOI  :  10.1016/j.cam.2016.12.023

来源: Elsevier

【 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.

【 授权许可】

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