101. A proximity algorithm accelerated by Gauss-Seidel iterations for L1/TV denoising models.
- Author
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Qia Li, Micchelli, Charles A, Lixin Shen, and Yuesheng Xu
- Subjects
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ITERATIVE methods (Mathematics) , *ALGORITHMS , *MATHEMATICAL models , *FIXED point theory , *STOCHASTIC convergence , *NUMERICAL analysis - Abstract
Our goal in this paper is to improve the computational performance of the proximity algorithms for the L1/TV denoising model. This leads us to a new characterization of all solutions to the L1/TV model via fixed-point equations expressed in terms of the proximity operators. Based upon this observation we develop an algorithm for solving the model and establish its convergence. Furthermore, we demonstrate that the proposed algorithm can be accelerated through the use of the componentwise Gauss-Seidel iteration so that the CPU time consumed is significantly reduced. Numerical experiments using the proposed algorithm for impulsive noise removal are included, with a comparison to three recently developed algorithms. The numerical results show that while the proposed algorithm enjoys a high quality of the restored images, as the other three known algorithms do, it performs significantly better in terms of computational efficiency measured in the CPU time consumed. [ABSTRACT FROM AUTHOR]
- Published
- 2012
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