Volume 12, Issue 2
Proximal ADMM for Euler's Elastica Based Image Decomposition Model

Zhifang Liu, Samad Wali, Yuping Duan, Huibin Chang, Chunlin Wu & Xue-Cheng Tai

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 370-402.

Published online: 2018-12

Preview Purchase PDF 159 5701
Export citation
  • Abstract

This paper studies  image decomposition models which involve functional related to total variation and Euler's elastica energy. Such kind of variational models with first order and higher order derivatives have been widely used in image processing to accomplish advanced tasks. However, these non-linear partial differential equations usually take high computational cost by the gradient descent method.  In this paper, we propose a proximal alternating direction method of multipliers (ADMM) for total variation (TV) based Vese-Osher's decomposition model [L. A. Vese and S. J. Osher, J. Sci.  Comput., 19.1 (2003), pp. 553-572]  and its extension with Euler's elastica regularization. We demonstrate that efficient and effective solutions to these minimization problems can be obtained by proximal based numerical algorithms. In numerical experiments, we present numerous results on image decomposition and image denoising, which conforms significant improvement of the proposed models over standard models.

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{NMTMA-12-370, author = {}, title = {Proximal ADMM for Euler's Elastica Based Image Decomposition Model}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {12}, number = {2}, pages = {370--402}, abstract = {

This paper studies  image decomposition models which involve functional related to total variation and Euler's elastica energy. Such kind of variational models with first order and higher order derivatives have been widely used in image processing to accomplish advanced tasks. However, these non-linear partial differential equations usually take high computational cost by the gradient descent method.  In this paper, we propose a proximal alternating direction method of multipliers (ADMM) for total variation (TV) based Vese-Osher's decomposition model [L. A. Vese and S. J. Osher, J. Sci.  Comput., 19.1 (2003), pp. 553-572]  and its extension with Euler's elastica regularization. We demonstrate that efficient and effective solutions to these minimization problems can be obtained by proximal based numerical algorithms. In numerical experiments, we present numerous results on image decomposition and image denoising, which conforms significant improvement of the proposed models over standard models.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2017-0149}, url = {http://global-sci.org/intro/article_detail/nmtma/12901.html} }
TY - JOUR T1 - Proximal ADMM for Euler's Elastica Based Image Decomposition Model JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 370 EP - 402 PY - 2018 DA - 2018/12 SN - 12 DO - http://doi.org/10.4208/nmtma.OA-2017-0149 UR - https://global-sci.org/intro/article_detail/nmtma/12901.html KW - AB -

This paper studies  image decomposition models which involve functional related to total variation and Euler's elastica energy. Such kind of variational models with first order and higher order derivatives have been widely used in image processing to accomplish advanced tasks. However, these non-linear partial differential equations usually take high computational cost by the gradient descent method.  In this paper, we propose a proximal alternating direction method of multipliers (ADMM) for total variation (TV) based Vese-Osher's decomposition model [L. A. Vese and S. J. Osher, J. Sci.  Comput., 19.1 (2003), pp. 553-572]  and its extension with Euler's elastica regularization. We demonstrate that efficient and effective solutions to these minimization problems can be obtained by proximal based numerical algorithms. In numerical experiments, we present numerous results on image decomposition and image denoising, which conforms significant improvement of the proposed models over standard models.

Zhifang Liu, Samad Wali, Yuping Duan, Huibin Chang, Chunlin Wu & Xue-Cheng Tai. (2020). Proximal ADMM for Euler's Elastica Based Image Decomposition Model. Numerical Mathematics: Theory, Methods and Applications. 12 (2). 370-402. doi:10.4208/nmtma.OA-2017-0149
Copy to clipboard
The citation has been copied to your clipboard