Volume 6, Issue 2
An Efficient Proximity Point Algorithm for Total-Variation-Based Image Restoration

Wei Zhu, Shi Shu & Lizhi Cheng

Adv. Appl. Math. Mech., 6 (2014), pp. 145-164.

Published online: 2014-06

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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 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.

  • Keywords

Proximity point operator image restoration total variation first-order schemes

  • AMS Subject Headings

68U10 65F22 65K10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-6-145, author = {Wei Zhu, Shi Shu and Lizhi Cheng}, title = {An Efficient Proximity Point Algorithm for Total-Variation-Based Image Restoration}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2014}, volume = {6}, number = {2}, pages = {145--164}, 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 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m175}, url = {http://global-sci.org/intro/article_detail/aamm/10.html} }
TY - JOUR T1 - An Efficient Proximity Point Algorithm for Total-Variation-Based Image Restoration AU - Wei Zhu, Shi Shu & Lizhi Cheng JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 145 EP - 164 PY - 2014 DA - 2014/06 SN - 6 DO - http://doi.org/10.4208/aamm.2013.m175 UR - https://global-sci.org/intro/article_detail/aamm/10.html KW - Proximity point operator KW - image restoration KW - total variation KW - first-order schemes AB -

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.

Wei Zhu, Shi Shu & Lizhi Cheng. (1970). An Efficient Proximity Point Algorithm for Total-Variation-Based Image Restoration. Advances in Applied Mathematics and Mechanics. 6 (2). 145-164. doi:10.4208/aamm.2013.m175
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