On a nonlinear nonlocal reaction-diffusion system applied to image restoration

TL;DR

This paper introduces a novel nonlinear nonlocal reaction-diffusion model for image restoration that effectively preserves textures and low gray level features, with theoretical analysis and successful numerical experiments on noisy, blurred images.

Contribution

The paper proposes a new reaction-diffusion system with a porous media regularization for image restoration, providing theoretical analysis and demonstrating improved denoising and deblurring performance.

Findings

Effective preservation of textures and low gray levels.

Successful application to noisy and blurred images.

Theoretical validation of model properties.

Abstract

This paper deals with a novel nonlinear coupled nonlocal reaction-diffusion system proposed for image restoration, characterized by the advantages of preserving low gray level features and textures.The gray level indicator in the proposed model is regularized using a new method based on porous media type equations, which is suitable for recovering noisy blurred images. The well-posedness, regularity, and other properties of the model are investigated, addressing the lack of theoretical analysis in those existing similar types of models. Numerical experiments conducted on texture and satellite images demonstrate the effectiveness of the proposed model in denoising and deblurring tasks.