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An efficient proximity point algorithm for total-variation-based image restoration. (English) Zbl 1320.94017

Summary: In this paper, we propose a fast proximity point algorithm and apply it to total variation (TV) based image restoration. The novel method is derived from the idea of establishing a general proximity point operator framework based on which new first-order schemes for total variation (TV) based image restoration have been proposed. Many current algorithms for TV-based image restoration, such as Chambolle’s projection algorithm, the split Bregman algorithm, the Bermudez-Moreno algorithm, the Jia-Zhao denoising algorithm, and the fixed point algorithm, can be viewed as special cases of the new first-order schemes. Moreover, the convergence of the new algorithm has been analyzed at length. Finally, we make comparisons with the split Bregman algorithm which is one of the best algorithms for solving TV-based image restoration at present. Numerical experiments illustrate the efficiency of the proposed algorithms.

MSC:

94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
65F22 Ill-posedness and regularization problems in numerical linear algebra
65K10 Numerical optimization and variational techniques
68U10 Computing methodologies for image processing

Software:

ParNes; RecPF; NESTA; TFOCS
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