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A Forward-Backward View of Some Primal-Dual Optimization Methods in Image Recovery

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Abstract

A wide array of image recovery problems can be abstracted into theproblem of minimizing a sum of composite convex functions in aHilbert space. To solve such problems, primal-dual proximalapproaches have been developed which provide efficient solutions tolarge-scale optimization problems. Theobjective of this paper is to show that a number of existingalgorithms can be derived from a general form of theforward-backward algorithm applied in a suitable product space.Our approach also allows us to develop useful extensions ofexisting algorithms by introducing a variable metric. Anillustration to image restoration is provided.
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hal-01098038 , version 1 (22-12-2014)

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Patrick Louis Combettes, Laurent Condat, Jean-Christophe Pesquet, Bang Cong Vu. A Forward-Backward View of Some Primal-Dual Optimization Methods in Image Recovery. ICIP 2014 - 21st IEEE International Conference on Image Processing, Oct 2014, Paris, France. ⟨hal-01098038⟩
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