Journal of Mathematical Imaging and Vision

, Volume 41, Issue 1–2, pp 3–22 | Cite as

Proximal Algorithms for Multicomponent Image Recovery Problems

  • L. M. Briceño-Arias
  • P. L. Combettes
  • J.-C. Pesquet
  • N. Pustelnik
Article

Abstract

In recent years, proximal splitting algorithms have been applied to various monocomponent signal and image recovery problems. In this paper, we address the case of multicomponent problems. We first provide closed form expressions for several important multicomponent proximity operators and then derive extensions of existing proximal algorithms to the multicomponent setting. These results are applied to stereoscopic image recovery, multispectral image denoising, and image decomposition into texture and geometry components.

Keywords

Convex minimization Image recovery Inverse problems Multicomponent images Multichannel images Multispectral images Proximal algorithm Sparsity Stereoscopy Wavelets 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • L. M. Briceño-Arias
    • 1
    • 2
  • P. L. Combettes
    • 1
  • J.-C. Pesquet
    • 3
  • N. Pustelnik
    • 3
  1. 1.Laboratoire Jacques-Louis Lions—CNRS UMR 7598UPMC Université Paris 06ParisFrance
  2. 2.Équipe Combinatoire et Optimisation—CNRS FRE 3232UPMC Université Paris 06ParisFrance
  3. 3.Laboratoire d’Informatique Gaspard Monge—CNRS UMR 8049Université Paris-EstMarne la Vallée Cedex 2France

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