On a coupled PDE model for image restoration

TL;DR

This paper introduces a novel coupled PDE model for image restoration that simultaneously considers image and edge variables, establishing the existence of global solutions and setting the stage for future modeling and numerical analysis.

Contribution

It proposes a new coupled PDE framework for image restoration, proving the existence of global dissipative solutions and outlining future modeling and numerical experiments.

Findings

Existence of global in time dissipative solutions.

Coupled PDE model incorporates image and edge variables.

Framework sets foundation for future numerical methods.

Abstract

In this paper, we consider a new coupled PDE model for image restoration. Both the image and the edge variables are incorporated by coupling them into two different PDEs. It is shown that the initial-boundary value problem has global in time dissipative solutions (in a sense going back to P.-L. Lions), and several properties of these solutions are established. This is a rough draft, and the final version of the paper will contain a modelling part and numerical experiments.