Journal of Convex Analysis 17 (2010), No. 3&4, 861--883
Copyright Heldermann Verlag 2010
A New Relaxation Method for a Discrete Image Restoration Problem
Maitine Bergounioux
UFR Sciences - Mathématiques, Université d'Orléans, Route de Chartes, 45067 Orléans, France
maitine.bergounioux@univ-orleans.fr
Mounir Haddou
UFR Sciences - Mathématiques, Université d'Orléans, Route de Chartes, 45067 Orléans, France
mounir@haddou@univ-orleans.fr
The method we present in this paper has been motivated by a restoration problem in a tomography context. We are interested in blurred and noised binary images restoration. We consider the discrete version of a minimization problem settled in the space of bounded variation functions. We give a general abstract formulation of the (discrete) optimization problem with binary constraints and provide approximate and penalized formulations. Convergence results are given and we present numerical tests.
Keywords: Tomography, optimization, penalization.
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