Reaction–diffusion systems with p(x)p(x)-growth for image denoising

A new anisotropic diffusion model is proposed for image denoising, which is based on reaction–diffusion systems with p(x)p(x)-growth. By Galerkin’s method, we establish the existence and uniqueness of weak solutions of the system for Neumann boundary conditions. Experimental results illustrate the effectiveness of the model in image restoration.