A new nonlocal nonlinear diffusion equation for image denoising and data analysis

TL;DR

This paper introduces a novel nonlocal nonlinear anisotropic diffusion model for image denoising, leveraging a new diffusivity coefficient based on local variation and oscillation patterns, with proven existence and demonstrated effectiveness.

Contribution

It presents a new nonlocal nonlinear diffusion equation with a unique diffusivity coefficient for improved feature preservation in image denoising.

Findings

Mathematical proof of solution existence for the proposed PDE

Numerical experiments showing enhanced denoising performance

Effective feature preservation in noisy images

Abstract

In this paper we introduce and study a new feature-preserving nonlinear anisotropic diffusion for denoising signals. The proposed partial differential equation is based on a novel diffusivity coefficient that uses a nonlocal automatically detected parameter related to the local bounded variation and the local oscillating pattern of the noisy input signal. We provide a mathematical analysis of the existence of the solution of our nonlinear and nonlocal diffusion equation in the two dimensional case (images processing). Finally, we propose a numerical scheme with some numerical experiments which demonstrate the effectiveness of the new method.