Proximal ADMM for Euler's elastica based image decomposition model

Zhifang Liu, Samad Wali*, Yuping Duan, Huibin Chang, Chunlin Wu, Xue-Cheng TAI

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

14 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)370-402
Number of pages33
JournalNumerical Mathematics
Issue number2
Early online dateDec 2018
Publication statusPublished - May 2019

Scopus Subject Areas

  • Modelling and Simulation
  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Alternating direction method of multipliers
  • Euler's elastica
  • Image decomposition
  • Image denoising
  • Proximal method
  • Total variation


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