Influence of dimension on the convergence of level-sets in total variation regularization
Optimization and Control
2021-06-09 v3
Abstract
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.
Keywords
Cite
@article{arxiv.1811.12243,
title = {Influence of dimension on the convergence of level-sets in total variation regularization},
author = {José A. Iglesias and Gwenael Mercier},
journal= {arXiv preprint arXiv:1811.12243},
year = {2021}
}
Comments
26 pages, 1 figure. Final accepted version. The original publication is available at www.esaim-cocv.org