A DOUGLAS-RACHFORD TYPE PRIMAL-DUAL METHOD FOR SOLVING INCLUSIONS WITH MIXTURES OF COMPOSITE AND PARALLEL-SUM TYPE MONOTONE OPERATORS

In this paper we propose two different primal-dual splitting algorithms for solving inclusions involving mixtures of composite and parallel-sum type monotone operators which rely on an inexact Douglas-Rachford splitting method, but applied in different underlying Hilbert spaces. Most importantly, the algorithms allow one to process the bounded linear operators and the set-valued operators occurring in the formulation of the monotone inclusion problem separately at each iteration, the latter being individually accessed via their resolvents. The performance of the primal-dual algorithms is emphasized via some numerical experiments on location and image denoising problems.