Fractional total variation denoising model with $L^1$ fidelity

TL;DR

This paper introduces a nonlocal fractional total variation model with $L^1$ fidelity for image denoising, analyzing solution regularity, uniqueness, and specific cases involving convex set characteristic functions.

Contribution

It extends total variation denoising to a fractional nonlocal setting and provides a detailed analysis of solution properties and special cases.

Findings

Regularity of level sets established

Uniqueness of solutions discussed for various fidelity parameters

Detailed analysis of binary data from convex sets

Abstract

We study a nonlocal version of the total variation-based model with $L^1-$fidelity for image denoising, where the regularizing term is replaced with the fractional $s$-total variation. We discuss regularity of the level sets and uniqueness of solutions, both for high and low values of the fidelity parameter. We analyse in detail the case of binary data given by the characteristic functions of convex sets.