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Reconstruction of Domains with Algebraic Boundaries from Generalized Polarization Tensors

Lookup NU author(s): Professor Mihai Putinar

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This is the final published version of an article that has been published in its final definitive form by Society for Industrial and Applied Mathematics Publications, 2019.

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Abstract

© 2019 Society for Industrial and Applied Mathematics.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.

Publication metadata

Author(s): Ammari H, Putinar M, Steenkamp A, Trikis F

Publication type: Article

Publication status: Published

Journal: SIAM Journal on Imaging Sciences

Year: 2019

Volume: 12

Issue: 4

Pages: 2097-2118

Online publication date: 17/12/2019

Acceptance date: 23/10/2019

Date deposited: 29/01/2020

ISSN (electronic): 1936-4954

Publisher: Society for Industrial and Applied Mathematics Publications

URL: https://doi.org/10.1137/19M125995X

DOI: 10.1137/19M125995X

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