Improved Perona-Malik Model with a Leray-Lions Operator for Image Denoising

Abstract

In the current paper, we introduce an extended framework for image denoising.
The formulated diffusion model integrates both the Perona-Malik and a Leray-Lions’s
type operator, aiming to achieve both effective noise suppression and preservation
of important image features. We first explore the proposed model mathematically,
determining whether solutions exist and are unique. Then, we demonstrate the model’s
applicability for image noise reduction, by providing various numerical simulations.