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

TL;DR

A novel nonlinear coupled nonlocal reaction-diffusion system proposed for image restoration, characterized by the advantages of preserving low gray level features and textures is proposed, addressing the lack of theoretical analysis in those existing similar types of models.

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.

Figures (87)

• Figure 1: Original
• Figure 2: Blurred
• Figure 3: $\lambda=5$
• Figure 4: $\lambda=15$
• Figure 5: $\lambda=50$

Theorems & Definitions (21)

• Theorem 2.1
• Definition 2.2
• Theorem 2.3
• Definition 3.1
• Remark 3.2
• proof : Proof of Theorem \ref{['thm:well-posedness-weak']}
• Remark 3.3
• Proposition 3.4
• proof
• Proposition 3.5