A novel quantitative inverse scattering scheme using interior resonant modes

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Original languageEnglish
Article number085002
Journal / PublicationInverse Problems
Volume39
Issue number8
Online published20 Jun 2023
Publication statusPublished - Aug 2023

Abstract

This paper is devoted to a novel quantitative imaging scheme of identifying impenetrable obstacles in time-harmonic acoustic scattering from the associated far-field data. The proposed method consists of two phases. In the first phase, we determine the interior eigenvalues of the underlying unknown obstacle from the far-field data via the indicating behavior of the linear sampling method. Then we further determine the associated interior eigenfunctions by solving a constrained optimization problem, again only involving the far-field data. In the second phase, we propose a novel iteration scheme of Newton's type to identify the boundary surface of the obstacle. By using the interior eigenfunctions determined in the first phase, we can avoid computing any direct scattering problem at each Newton's iteration. The proposed method is particularly valuable for recovering a sound-hard obstacle, where the Newton's formula involves the geometric quantities of the unknown boundary surface in a natural way. We provide rigorous theoretical justifications of the proposed method. Numerical experiments in both 2D and 3D are conducted, which confirm the promising features of the proposed imaging scheme. In particular, it can produce quantitative reconstructions of high accuracy in a very efficient manner. © 2023 IOP Publishing Ltd.

Research Area(s)

  • inverse scattering problem, sound-hard obstacle, interior resonant modes, linear sampling method, Newton-type method, LINEAR SAMPLING METHOD, SOUND-HARD, POLYHEDRAL SCATTERERS, STABLE DETERMINATION, OBSTACLE SCATTERING, UNIQUENESS, PROBE

Citation Format(s)

A novel quantitative inverse scattering scheme using interior resonant modes. / He, Youzi; Liu, Hongyu; Wang, Xianchao.
In: Inverse Problems, Vol. 39, No. 8, 085002, 08.2023.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review