A class of forward-backward diffusion equations for multiplicative noise removal

TL;DR

This paper introduces a new class of forward-backward diffusion equations with nonlinear sources for removing multiplicative noise in images, establishing mathematical existence results and demonstrating effectiveness through numerical experiments.

Contribution

It develops a novel mathematical model for multiplicative noise removal using degenerate diffusion equations and proves the existence of solutions with numerical validation.

Findings

The model effectively denoises images with multiplicative noise.

Mathematical proof of solution existence using Young measures.

Numerical results outperform some existing denoising methods.

Abstract

This paper investigates a class of degenerate forward-backward diffusion equations with a nonlinear source term, proposed as a model for removing multiplicative noise in images. Based on Rothe's method, the relaxation theorem, and Schauder's fixed-point theorem, we establish the existence of Young measure solutions for the corresponding initial boundary problem. The continuous dependence result relies on the independence property satisfied by the Young measure solution. Numerical experiments illustrate the denoising effectiveness of our model compared to other denoising models.