Nonconvex models for recovering images corrupted by salt-and-pepper noise on surfaces

TL;DR

This paper introduces LpTV models on triangle meshes for denoising images corrupted by salt-and-pepper noise on surfaces, with a proven lower bound and a convergent algorithm demonstrating effective results.

Contribution

The paper develops a novel LpTV model for surface image denoising, establishes a lower bound for data fitting, and proposes a globally convergent algorithm with demonstrated effectiveness.

Findings

The proposed algorithm effectively denoises salt-and-pepper noise on surfaces.

The model's lower bound improves understanding of data fitting in surface denoising.

Numerical examples confirm the algorithm's good performance.

Abstract

Image processing on surfaces has drawn significant interest in recent years, particularly in the context of denoising. Salt-and-pepper noise is a special type of noise which randomly sets a portion of the image pixels to the minimum or maximum intensity while keeping the others unaffected. In this paper, We propose the L$_p$TV models on triangle meshes to recover images corrupted by salt-and-pepper noise on surfaces. We establish a lower bound for data fitting term of the recovered image. Motivated by the lower bound property, we propose the corresponding algorithm based on the proximal linearization method with the support shrinking strategy. The global convergence of the proposed algorithm is demonstrated. Numerical examples are given to show good performance of the algorithm.