Influence of dimension on the convergence of level-sets in total variation regularization
ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 52.

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.

DOI : 10.1051/cocv/2019035
Classification : 49Q20, 65J20, 65J22, 53A10, 46B20
Mots-clés : Inverse problems, total variation, Hausdorff convergence, level-sets, density estimates
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Iglesias, José A.; Mercier, Gwenael. Influence of dimension on the convergence of level-sets in total variation regularization. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 52. doi : 10.1051/cocv/2019035. http://www.numdam.org/articles/10.1051/cocv/2019035/

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Cité par Sources :

We would like to thank Otmar Scherzer for encouragement to work on the interplay between the space dimension and convergence of level-sets.