Dual constrained TV-based regularization on graphs

Camille Couprie 1 Leo Grady 2 Laurent Najman 3 Jean-Christophe Pesquet 3 Hugues Talbot 3
1 Direction Technologie, Informatique et Mathématiques appliquées
2 Research & Development [Redwood City]
3 LIGM - Laboratoire d'Informatique Gaspard-Monge
Abstract : Algorithms based on Total Variation (TV) minimization are prevalent in image processing. They play a key role in a variety of applications such as image denoising, compressive sensing and inverse problems in general. In this work, we extend the TV dual framework that includes Chambolle's and Gilboa-Osher's projection algorithms for TV minimization. We use a flexible graph data representation that allows us to generalize the constraint on the projection variable. We show how this new formulation of the TV problem may be solved by means of fast parallel proximal algorithms. On denoising and deblurring examples, the proposed approach is shown not only to perform better than recent TV-based approaches, but also to perform well on arbitrary graphs instead of regular grids. The proposed method consequently applies to a variety of other inverse problems including image fusion and mesh filtering.
Keywords : Proximal methods inverse problem image denoising convex optimization parallel algorithms image restoration bounded variation mesh smoothing discrete calculus
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Journal articles
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https://hal-upec-upem.archives-ouvertes.fr/hal-00743968
Contributor : Laurent Najman <>
Submitted on : Saturday, April 20, 2013 - 6:24:30 PM
Last modification on : Friday, April 19, 2019 - 1:28:12 PM
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Camille Couprie, Leo Grady, Laurent Najman, Jean-Christophe Pesquet, Hugues Talbot. Dual constrained TV-based regularization on graphs. SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2013, 6 (3), pp.246-1273. ⟨10.1137/120895068⟩. ⟨hal-00743968v2⟩

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