  In this paper we investigate the convergence behavior of a primal-dual
splitting method for solving monotone inclusions involving mixtures of
composite, Lipschitzian and parallel sum type operators proposed by Combettes
and Pesquet in [7]. Firstly, in the particular case of convex minimization
problems, we derive convergence rates for the sequence of objective function
values by making use of conjugate duality techniques. Secondly, we propose for
the general monotone inclusion problem two new schemes which accelerate the
sequences of primal and/or dual iterates, provided strong monotonicity
assumptions for some of the involved operators are fulfilled. Finally, we apply
the theoretical achievements in the context of different types of image
restoration problems solved via total variation regularization.
