Volume 26, 2020
|Number of page(s)||27|
|Published online||04 September 2020|
Influence of dimension on the convergence of level-sets in total variation regularization*
Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences. Altenberger Straße 69,
4040 Linz, Austria.
2 Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.
** Corresponding author: firstname.lastname@example.org
Accepted: 30 April 2019
We extend some recent results on the Hausdorff convergence of level-sets for total variation regularized linear inverse problems. Dimensions higher than two and measurements in Banach spaces are considered. We investigate the relation between the dimension and the assumed integrability of the solution that makes such an extension possible. We also give some counterexamples of practical application scenarios where the natural choice of fidelity term makes such a convergence fail.
Mathematics Subject Classification: 49Q20 / 65J20 / 65J22 / 53A10 / 46B20
Key words: Inverse problems / total variation / Hausdorff convergence / level-sets / density estimates
© EDP Sciences, SMAI 2020
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