On theoretical result of a controlled $ p(x) $-reaction diffusion equation for Poisson noise reduction

Abstract

Image denoising is an active field in image processing. This paper proposes a new reaction diffusion equation with a variable $ p(x) $-exponent with a combination with a Weickert-type term to control the singular part caused by the Poisson noise. Since the introduced PDE is complicated, a theoretical study is involved. We construct in fact a Galerkin approximation for the studied equation to ensure the existence of a weak solution for the problem. Finally, representative experiments and comparisons to other denoising models are done to ensure the proposed reaction diffusion choice.