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

This paper deals with the total variation minimization problem in image restoration for convex data fidelityfunctionals.Weproposeanewandfastalgorithmwhichcomputesanexactsolutioninthediscreteframework. Our method relies on the decomposition of an image into its level sets. It maps the original problems into independent binaryMarkovRandomFieldoptimizationproblemsateachlevel.Exactsolutionsofthesebinaryproblemsarefound 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 L1 data fidelity term yields a self-dual contrast invariant filter. Finally we present some results.

• Type: Journal
• Year: 2006
• Where: JMIV
• Authors: Jérôme Darbon, Marc Sigelle
• Keywords: JMIV 2006, Original Problem, Total Variation, Total Variation Minimization