Solving constrained total-variation image restoration and reconstruction problems via alternating direction methods

Kwok Po NG, Pierre Weiss, Xiaoming YUAN

Research output: Contribution to journalArticlepeer-review

177 Citations (Scopus)

Abstract

In this paper, we study alternating direction methods for solving constrained totalvariation image restoration and reconstruction problems. Alternating direction methods can be implementable variants of the classical augmented Lagrangian method for optimization problems with separable structures and linear constraints. The proposed framework allows us to solve problems of image restoration, impulse noise removal, inpainting, and image cartoon+texture decomposition. As the constrained model is employed, we need only to input the noise level, and the estimation of the regularization parameter is not required in these imaging problems. Experimental results for such imaging problems are presented to illustrate the effectiveness of the proposed method. We show that the alternating direction method is very efficient for solving image restoration and reconstruction problems.

Original languageEnglish
Pages (from-to)2710-2736
Number of pages27
JournalSIAM Journal of Scientific Computing
Volume32
Issue number5
DOIs
Publication statusPublished - 2010

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Alternating direction method
  • Augmented Lagrangian
  • Image reconstruction
  • Image restoration
  • Total-variation

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