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In this paper we investigate the convergence behavior of a primal-dualsplitting method for solving monotone inclusions involving mixtures ofcomposite, Lipschitzian and parallel sum type operators proposed by Combettesand Pesquet in [7]. Firstly, in the particular case of convex minimizationproblems, we derive convergence rates for the sequence of objective functionvalues by making use of conjugate duality techniques. Secondly, we propose forthe general monotone inclusion problem two new schemes which accelerate thesequences of primal and/or dual iterates, provided strong monotonicityassumptions for some of the involved operators are fulfilled. Finally, we applythe theoretical achievements in the context of different types of imagerestoration problems solved via total variation regularization.

Convergence analysis for a primal-dual monotone + skew splitting algorithm with applications to total variation minimization