An inertial primal-dual fixed point algorithm for composite optimization problems

TL;DR

This paper introduces an inertial primal-dual fixed point algorithm (IPDFP) for efficiently solving composite convex optimization problems, especially in image processing, by extending classical splitting schemes and demonstrating competitive performance.

Contribution

The work extends classical splitting algorithms by incorporating inertia into a primal-dual fixed point framework for full splitting of nonsmooth functions.

Findings

IPDFP converges reliably for composite convex problems.

The algorithm performs competitively with state-of-the-art methods.

Effective in image denoising applications.

Abstract

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.