  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,
however applied in different underlying Hilbert spaces. Most importantly, the
algorithms allow 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 performances of the primal-dual algorithms are emphasized via
some numerical experiments on location and image deblurring problems.
