  We consider an inertial primal-dual fixed point algorithm (IPDFP) to compute
the minimizations of the following Problem (1.1). This is a full splitting
approach, in the sense that the nonsmooth functions are processed individually
via their proximity operators. The convergence of the IPDFP is obtained by
reformulating the Problem (1.1) to the sum of three convex functions. This work
brings together and notably extends several classical splitting schemes, like
the primaldual method proposed by Chambolle and Pock, and the recent proximity
algorithms of Charles A. et al designed for the L1/TV image denoising model.
The iterative algorithm is used for solving nondifferentiable convex
optimization problems arising in image processing. The experimental results
indicate that the proposed IPDFP iterative algorithm performs well with respect
to state-of-the-art methods.
