Reconstruction of Domains with Algebraic Boundaries from Generalized Polarization Tensors

Abstract

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, M. Putinar, A. Steenkamp, and F. Triki, Math. Ann., 375 (2019), pp. 1337-1354], 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. © 2019 Society for Industrial and Applied Mathematics.