Image denoising is a core problem in image processing, consisting in finding a regular approximation of a given degraded image. In this seminar we will first survey the deeply investigated class of total-variation based denoising models highlighting their main features. We will then focus our attention on denoising models whose regularizing term is a nonlocal total variation induced by a singular kernel. Specifically, we will study the fidelity of the solutions of these models to the initial data as well as their smoothness. Finally, we will discuss the relationship between the jump sets of the regularized images and the ones of the initial data.

Part of the results that we will present was obtained in collaboration with Giorgio Stefani (University of Padova) and part is based on an ongoing project with Antonin Chambolle (CEREMADE, CNRS & Université Paris-Dauphine).