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Reconstruction of domains with algebraic boundaries from generalized polarization tensors

by H. Ammari and M. Putinar and A. Steenkamp and F. Triki

(Report number 2019-25)

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 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.

Keywords: inverse problems, generalized polarization tensors, algebraic domains, shape classification

@Techreport{APST19_829,
  author = {H. Ammari and M. Putinar and A. Steenkamp and F. Triki},
  title = { Reconstruction of domains with algebraic boundaries from generalized polarization tensors},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2019-25},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2019/2019-25.pdf },
  year = {2019}
}

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