Fair Primal Dual Splitting Method for Image Inverse Problems

TL;DR

This paper introduces a fair primal dual splitting method for image inverse problems, improving convergence and performance in tasks like denoising and super-resolution.

Contribution

It proposes a novel primal dual algorithmic framework that incorporates the smooth term into both primal and dual subproblems, unifying convergence analysis.

Findings

Demonstrates superior performance over state-of-the-art methods in image denoising.

Achieves established convergence rates for the proposed algorithm.

Validates effectiveness through experiments on super-resolution reconstruction.

Abstract

Image inverse problems have numerous applications, including image processing, super-resolution, and computer vision, which are important areas in image science. These application models can be seen as a three-function composite optimization problem solvable by a variety of primal dual-type methods. We propose a fair primal dual algorithmic framework that incorporates the smooth term not only into the primal subproblem but also into the dual subproblem. We unify the global convergence and establish the convergence rates of our proposed fair primal dual method. Experiments on image denoising and super-resolution reconstruction demonstrate the superiority of the proposed method over the current state-of-the-art.