A novel coupled <i>p</i> ( <i>x</i> ) and fractional PDE denoising model with theoretical results

Abstract

In this paper, we formulate a new coupled PDE-based configuration for image denoising. We elaborate a new class of coupled PDE that involves a p(x)-Laplace and a controlled fractional-type operator, which takes into account the texture and smooth components during the recovering process. We give some essential theoretical results and we establish the well-posedness of the suggested coupled equation based on Galerkin approximation. Finally, we perform a fully discretization part of the system and illustrate some various numerical realizations to ensure the efficiency of our coupled PDE by conducting some comparison experiments against state of art PDE denoising models.