A stable method solving the total variation dictionary model with L constraints

Liyan Ma, Lionel Moisan, Jian Yu, Tieyong Zeng

Research output: Contribution to journalJournal articlepeer-review

4 Citations (Scopus)


Image restoration plays an important role in image processing, and numerous approaches have been proposed to tackle this problem. This paper presents a modified model for image restoration, that is based on a combination of Total Variation and Dictionary approaches. Since the well-known TV regularization is non-differentiable, the proposed method utilizes its dual formulation instead of its approximation in order to exactly preserve its properties. The data-fidelity term combines the one commonly used in image restoration and a wavelet thresholding based term. Then, the resulting optimization problem is solved via a first-order primal-dual algorithm. Numerical experiments demonstrate the good performance of the proposed model. In a last variant, we replace the classical TV by the nonlocal TV regularization, which results in a much higher quality of restoration.

Original languageEnglish
Pages (from-to)507-535
Number of pages29
JournalInverse Problems and Imaging
Issue number2
Publication statusPublished - May 2014

Scopus Subject Areas

  • Analysis
  • Modelling and Simulation
  • Discrete Mathematics and Combinatorics
  • Control and Optimization

User-Defined Keywords

  • Image restoration
  • Nonlocal total variation
  • Proximal gradient method
  • Total variation
  • Wavelet packet decomposition


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