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arXiv · 1406.5439

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

Patrick L. Combettes·Laurent Condat·Jean-Christophe Pesquet·Bang Cong Vu
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Abstract

A wide array of image recovery problems can be abstracted into the problem of minimizing a sum of composite convex functions in a Hilbert space. To solve such problems, primal-dual proximal approaches have been developed which provide efficient solutions to large-scale optimization problems. The objective of this paper is to show that a number of existing algorithms can be derived from a general form of the forward-backward algorithm applied in a suitable product space. Our approach also allows us to develop useful extensions of existing algorithms by introducing a variable metric. An illustration to image restoration is provided.

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Patrick L. Combettes, Laurent Condat, Jean-Christophe Pesquet, Bang Cong Vu. 2014-06-20. A forward-backward view of some primal-dual optimization methods in image recovery. https://arxiv.org/abs/1406.5439

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