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Influence of dimension on the convergence of level-sets in total variation regularization. (English) Zbl 1458.49030

In this paper, the authors investigate the Hausdorff convergence of level-sets for total variation regularized linear inverse problems. More precisely, a connection between the dimension and the assumed integrability of the solution is analyzed.

MSC:

49N45 Inverse problems in optimal control
49Q20 Variational problems in a geometric measure-theoretic setting
65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
65J22 Numerical solution to inverse problems in abstract spaces
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
46B20 Geometry and structure of normed linear spaces
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