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

Understand

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.