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A wide array of image recovery problems can be abstracted into the problem ofminimizing a sum of composite convex functions in a Hilbert space. To solvesuch problems, primal-dual proximal approaches have been developed whichprovide efficient solutions to large-scale optimization problems. The objectiveof this paper is to show that a number of existing algorithms can be derivedfrom a general form of the forward-backward algorithm applied in a suitableproduct space. Our approach also allows us to develop useful extensions ofexisting algorithms by introducing a variable metric. An illustration to imagerestoration is provided.

A forward-backward view of some primal-dual optimization methods in image recovery