Description
Abstract. Image denoising is a core problem in image processing which has been addressed by several authors by means of different mathematical techniques, among which variational ones have attracted particular interest.
In this talk I will focus on 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.
I will discuss regularity of the level sets and uniqueness of solutions, both for high and low values of the fidelity parameter.
I will also analyse in detail the case of binary data given by the characteristic functions of convex sets.
