On a class of forward-backward reaction-diffusion systems with local and nonlocal coupling for image restoration

TL;DR

This paper introduces a new class of nonlinear reaction-diffusion systems with fractional diffusion for image restoration, effectively preserving contours and textures, and demonstrates their theoretical existence and practical effectiveness.

Contribution

It proposes a novel reaction-diffusion model with fractional diffusion for image restoration, establishing existence and uniqueness of solutions, and validating performance through numerical experiments.

Findings

Effective preservation of contours and textures in images

Successful denoising and deblurring results

Theoretical validation of model solutions

Abstract

This paper investigates a class of novel nonlinear reaction-diffusion systems that couple forward-backward with fractional diffusion for image restoration, offering the advantage of preserving both contour features and textures. The existence of Young measure solutions to the proposed model is established using the regularization technique, Rothe's method, relaxation theorem, and Moser's iteration. Uniqueness follows from the independence property satisfied by the solution. Numerical experiments illustrate the effectiveness of our model in image denoising and deblurring, in comparison with existing methods.