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An Efficient Proximity Point Algorithm for Total-Variation-Based Image Restoration

Published online by Cambridge University Press:  03 June 2015

Wei Zhu ,
Shi Shu  and
Lizhi Cheng
Wei Zhu*
Affiliation:
School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, China
Shi Shu*
Affiliation:
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, Hunan, China
Lizhi Cheng*
Affiliation:
Department of Mathematics and Computational Science, College of Science, National University of Defense Technology, Changsha 410073, Hunan, China
*
Email: zw_1012@163.com
Corresponding author. Email: shushi@xtu.edu.cn
Email: clzcheng@vip.sina.com
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Abstract

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 Bermúdez-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.

Keywords

68U1065F2265K10Proximity point operatorimage restorationtotal variationfirst-order schemes
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 2 , April 2014 , pp. 145 - 164
Copyright
Copyright © Global-Science Press 2014

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