Proximity Operator of a Sum of Functions; Application to Depth Map Estimation

Proximal splitting algorithms for convex optimization are largely used in signal and image processing. They make possible to call the individual proximity operators of an arbitrary number of functions, whose sum is to be minimized. But the larger this number, the slower the convergence. In this letter, we show how to compute the proximity operator of a sum of two functions, for a certain type of functions operating on objects having a graph structure. The gain provided by avoiding unnecessary splitting is illustrated by an application to depth map estimation.