Efficient primal-dual fixed point algorithm with dynamic stepsize for convex problems with applications to imaging restoration

TL;DR

This paper introduces a new primal-dual fixed point algorithm with dynamic stepsize for convex optimization problems, leveraging proximity operators and fixed point theory to improve convergence in imaging restoration tasks.

Contribution

The paper proposes a novel primal-dual fixed point algorithm with a dynamic stepsize, providing a closed-form iteration scheme and convergence guarantees for convex problems.

Findings

Convergence of the proposed algorithm is established.

The algorithm has a closed-form solution per iteration.

Applications demonstrated in imaging restoration.

Abstract

We consider the problem of finding the minimization of the sum of a convex function and the composition of another convex function with a continuous linear operator from the view of fixed point algorithms based on proximity operators. We design a primal-dual fixed point algorithm with dynamic stepsize based on the proximity operator and obtain a scheme with a closed form solution for each iteration. Based on Modified Mann iteration and the firmly nonexpansive properties of the proximity operator, we achieve the convergence of the proposed algorithm.