A variable p[u] exponent reaction-diffusion PDE for image denoising

Abstract

The paper presents a unique reaction-diffusion coupled system with p(u(t,x))-growth, employing the decomposition approach of H−1 norm. This method is designed to address image denoising by considering both texture and smooth components during the recovery process. The existence and uniqueness of weak solutions for the coupled system are established using Galerkin's method within a suitable space framework. Experimental analysis demonstrates the model's effectiveness in image restoration, and it is compared with other competitive models to showcase its performance.