Coupling local and nonlocal total variation flow for image despeckling

TL;DR

This paper introduces a coupled local-nonlocal total variation flow model for image despeckling, combining texture preservation with strong denoising, and provides theoretical analysis and comparisons with existing models.

Contribution

It proposes a novel coupled local-nonlocal total variation flow model for image despeckling, with proven existence, uniqueness, and convergence properties.

Findings

The model effectively preserves textures while denoising.

Weak solutions converge to classical total variation flow solutions.

Coupling improves over purely local or nonlocal approaches.

Abstract

Nonlocal equations effectively preserve textures but exhibit weak regularization effects in image denoising, whereas local equations offer strong denoising capabilities yet fail to protect textures. To integrate the advantages of both approaches, this paper investigates a coupled local-nonlocal total variation flow for image despeckling. We establish the existence and uniqueness of the weak solution for the proposed equation. Several properties, including the equivalent forms of the weak solution and its asymptotic behavior, are derived. Furthermore, we demonstrate that the weak solutions of the proposed equation converge to the weak solution of the classical total variation flow under kernel rescaling. The importance of coupling is highlighted through comparisons with local and nonlocal models for image despeckling.