期刊
JOURNAL OF COMPUTATIONAL MATHEMATICS
卷 28, 期 6, 页码 848-863出版社
GLOBAL SCIENCE PRESS
DOI: 10.4208/jcm.1001.m2729
关键词
Block system of equations; Matrix preconditioner; Edge-preserving; Image restoration; Half-quadratic regularization
资金
- China NSF Outstanding Young Scientist Foundation [10525102]
- National Natural Science Foundation [10471146]
- National Basic Research Program, P.R. China [2005CB321702]
- Lanzhou University, P.R. China
- Hong Kong Research Grants Council [7035/04P, 7035/05P]
- HKBU FRGs
Signal and image restoration problems are often solved by minimizing a cost function consisting of an l(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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