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

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.