Continuous Primal-Dual Methods for Image Processing

TL;DR

This paper generalizes a continuous primal-dual method for image processing, providing theoretical analysis including existence, uniqueness, convergence, and new a posteriori estimates for denoising applications.

Contribution

It extends the primal-dual method to broader image processing problems and offers rigorous mathematical analysis and convergence results.

Findings

Proved existence and uniqueness of solutions.

Established convergence for the denoising problem.

Derived new a posteriori estimates.

Abstract

In this article we study a continuous Primal-Dual method proposed by Appleton and Talbot and generalize it to other problems in image processing. We interpret it as an Arrow-Hurwicz method which leads to a better description of the system of PDEs obtained. We show existence and uniqueness of solutions and get a convergence result for the denoising problem. Our analysis also yields new a posteriori estimates.