Sparse recovery for inverse potential problems in divergence form

Laurent Baratchart (1) , Cristóbal Villalobos Guillén (2) , Douglas Hardin , Juliette Leblond (1)

1 FACTAS - Analyse fonctionnelle pour la conception et l'analyse de systèmes
2 DeFI - Shape reconstruction and identification

We discuss recent results on sparse recovery for inverse potential problem with source term in divergence form. The notion of sparsity which is set forth is measure-theoretic, namely pure 1-unrectifiability of the support. The theory applies when a superset of the support is known to be slender, meaning it has measure zero and all connected components of its complement has infinite measure in R^3. We also discuss open issues in the non-slender case.

Domaines: Mathématiques [math]

Laurent Baratchart, Cristóbal Villalobos Guillén, Douglas Hardin, Juliette Leblond. Sparse recovery for inverse potential problems in divergence form. 9th International Conference on New Computational Methods for Inverse Problems, NCMIP 2019 24 May 2019, Cachan, France, 1476, IOP Publishing, pp.012009, 2020, Journal of Physics: Conference Series, ⟨10.1088/1742-6596/1476/1/012009⟩. ⟨hal-03434756⟩