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

Patrick Louis Combettes 1 Laurent Condat 2 Jean-Christophe Pesquet 3 Bang Cong Vu 4
1 UNIVERSITE PIERRE ET MARIE CURIE - PARIS
2 GIPSA-AGPIG - AGPIG
GIPSA-DIS - Département Images et Signal
3 LIGM - Laboratoire d'Informatique Gaspard-Monge
4 IIT - Istituto Italiano di Tecnologia
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.
Keywords : image recovery variational methods IndexTerms—convexoptimization duality parallel computing proximal algorithm
Type de document :
Communication dans un congrès
21st IEEE International Conference on Image Processing (ICIP 2014), Oct 2014, Paris, France. Proceedings of the IEEE International Conference on Image Processing, Paris, France, October 27-30, 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. 21st IEEE International Conference on Image Processing (ICIP 2014), Oct 2014, Paris, France. Proceedings of the IEEE International Conference on Image Processing, Paris, France, October 27-30, 2014. 〈hal-01098038〉

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