Reconstruction of domains with algebraic boundaries from generalized polarization tensors

Habib Ammari (1) , Mihai Putinar (2) , Andries Steenkamp (1) , Faouzi Triki (3)

1 ETH-SAM - Seminar for Applied Mathematics
2 UC Santa Barbara - University of California [Santa Barbara]
3 EDP - Equations aux Dérivées Partielles

This paper aims at showing the stability of the recovery of a smooth planar domain with a real algebraic boundary from a finite number of its generalized polarization tensors. It is a follow-up of the work [H. Ammari et al., Math. Annalen, 2018], where it is proved that the minimal polynomial with real coefficients vanishing on the boundary can be identified as the generator of a one dimensional kernel of a matrix whose entries are obtained from a finite number of generalized polarization tensors. The recovery procedure is implemented without any assumption on the regularity of the domain to be reconstructed and its performance and limitations are illustrated.

Domaines: Equations aux dérivées partielles [math.AP]

Habib Ammari, Mihai Putinar, Andries Steenkamp, Faouzi Triki. Reconstruction of domains with algebraic boundaries from generalized polarization tensors. SIAM Journal on Imaging Sciences, 2019, 12 (4), pp.2097-2118. ⟨10.1137/19M125995X⟩. ⟨hal-02139978⟩