Fair Primal Dual Splitting Method for Image Inverse Problems
Yunfei Qu, Deren Han
TL;DR
This paper tackles image inverse problems by formulating them as a three-function composite optimization and introducing a fair primal dual framework that distributes the data-fidelity term into both primal and dual subproblems. By splitting the smooth term and balancing updates, the method achieves global convergence with an $O(1/N)$ ergodic rate, and an inexact variant (IFPD) enables practical computation through approximate dual subproblem solves. The approach is validated on non-negative Lasso, LRTV-based super-resolution, and constrained TV inpainting, showing faster convergence and superior reconstruction quality compared to traditional primal-dual schemes. The work offers a robust, balance-oriented alternative for large-scale image inverse problems with potential for accelerated variants in the future.
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.