Year: 2010
Journal of Computational Mathematics, Vol. 28 (2010), Iss. 6 : pp. 848–863
Abstract
Signal and image restoration problems are often solved by minimizing a cost function consisting of an $\ell_2$ data-fidelity term and a regularization term. We consider a class of convex and edge-preserving regularization functions. In specific, half-quadratic regularization as a fixed-point iteration method is usually employed to solve this problem. The main aim of this paper is to solve the above-described signal and image restoration problems with the half-quadratic regularization technique by making use of the Newton method. At each iteration of the Newton method, the Newton equation is a structured system of linear equations of a symmetric positive definite coefficient matrix, and may be efficiently solved by the preconditioned conjugate gradient method accelerated with the modified block SSOR preconditioner. Our experimental results show that the modified block-SSOR preconditioned conjugate gradient method is feasible and effective for further improving the numerical performance of the half-quadratic regularization approach.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1001.m2729
Journal of Computational Mathematics, Vol. 28 (2010), Iss. 6 : pp. 848–863
Published online: 2010-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Block system of equations Matrix preconditioner Edge-preserving Image restoration Half-quadratic regularization.
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