  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.
