Convergence of level sets in regularization of inverse problems

Activity: Talk or presentationInvited talk

Description

Minisymposium “Mathematical approaches to nonlinear phenomena with singularities”
We present some results bridging classical regularization theory of ill-posed inverse problems and regularity properties of almost-minimizers of the corresponding regularization energies. In the regime of vanishing noise and regularization parameter, we obtain results of convergence in Hausdorff distance of level sets of minimizers (which can be interpreted as objects to be recovered in an imaging context) and uniform $L^\infty$ bounds. These hold both for the classical total variation, and for some fractional energies.
Period24 Aug 2023
Event title10th International Congress on Industrial and Applied Mathematics, ICIAM 2023
Event typeConference
Conference number10
LocationTokyo, JapanShow on map