Nonlocal Cahn-Hilliard type model for image inpainting

Abstract

This paper proposes a Cahn-Hilliard type inpainting model equipped with a nonlocal diffusion operator. A rigorous analysis of the well-posedness of the stationary solution is established using Schauder's fixed point theory. We construct a time stepping scheme based on the convex splitting method with the nonlocal term treated implicitly and the fidelity term treated explicitly. We prove the consistency, stability and convergence of the semidiscrete-in-time scheme. To the best of our knowledge, this is the first study to present such an analysis for semidiscrete-in-time problems of this model, which provides valuable guidance for parameter selection. Numerical experiments validate the effectiveness of the proposed nonlocal model, which shows superior performance compared to both local and classical total variation models in preserving fine textures and recovering image edges.