Event description
In this joint work with M. Lasica (Warsaw) we revisit old results on the localization of
the jump set of minimizer of the “Rudin-Osher-Fatemi” functional, that is, the total variation plus a
quadratic penalization. We give more natural and simpler proof of the fact that the jump set of the
solution is contained in the jump set of the data, and characterize the total-variation type
functionals, in both scalar and vectorial settings, for which the result holds true. We also consider
higher order regularizing functionals, for which some partial results hold.