Image Restoration Using a Novel Model Combining the Perona-Malik Equation and the Heat Equation

Abstract

This article is devoted to the mathematical study of a new proposed model based on a Perona-Malik equation combined with a heat equation. This study shows how system of partial differential equations can be used to restore a digital image. By using compactness method and the monotonicity arguments, with suitable assumptions on the nonlinearities, we prove the existence of the weak solution for the proposed model which its consistency is given in our work.