Journal of Mathematical Imaging and Vision

, Volume 26, Issue 3, pp 261–276 | Cite as

Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization

  • Jérôme DarbonEmail author
  • Marc Sigelle


This paper deals with the total variation minimization problem in image restoration for convex data fidelity functionals. We propose a new and fast algorithm which computes an exact solution in the discrete framework. Our method relies on the decomposition of an image into its level sets. It maps the original problems into independent binary Markov Random Field optimization problems at each level. Exact solutions of these binary problems are found thanks to minimum cost cut techniques in graphs. These binary solutions are proved to be monotone increasing with levels and yield thus an exact solution of the discrete original problem. Furthermore we show that minimization of total variation under L 1 data fidelity term yields a self-dual contrast invariant filter. Finally we present some results.


restoration total variation level sets Markov random fields graph cuts 


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Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.EPITA Research and Development Laboratory (LRDE)Le Kremlin-BicêtreFrance
  2. 2.École Nationale Supérieure des Télécommunications (ENST)ParisFrance
  3. 3.École Nationale Supérieure des Télécommunications (ENST) / LTCI CNRS UMR 5141ParisFrance

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