Two Modified Schemes for the Primal Dual Fixed Point Method (CSIAM Transactions on Applied Mathematics, 2021)
The primal dual fixed point (PDFP) proposed in [7] was designed to solveconvex composite optimization problems in imaging and data sciences. The algorithmwas shown to have some advantages for simplicity and flexibility for divers applications. In this paper we study two modified schemes in order to accelerate its performance. The first one considered is an inertial variant of PDFP, namely inertial PDFP(iPDFP) and the second one is based on a prediction correction framework proposedin [20], namely Prediction Correction PDFP (PC-PDFP). Convergence analysis on bothalgorithms is provided. Numerical experiments on sparse signal recovery and CTimage reconstruction using TV-$L_2$ model are presented to demonstrate the accelerationof the two proposed algorithms compared to the original PDFP algorithm.