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

International audienceA 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