| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 52 | |
| Number of page(s) | 27 | |
| DOI | https://doi.org/10.1051/cocv/2019035 | |
| Published online | 04 September 2020 | |
Influence of dimension on the convergence of level-sets in total variation regularization*
1
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: jose.iglesias@ricam.oeaw.ac.at
Received:
29
November
2018
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.