The factorization method for a cavity in an inhomogeneous medium

Shixu Meng, Houssem Haddar, Fioralba Cakoni

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27 Scopus citations

Abstract

We consider the inverse scattering problem for a cavity that is bounded by a penetrable anisotropic inhomogeneous medium of compact support and seek to determine the shape of the cavity from internal measurements on a curve or surface inside the cavity. We derive a factorization method which provides a rigorous characterization of the support of the cavity in terms of the range of an operator which is computable from the measured data. The support of the cavity is determined without a priori knowledge of the constitutive parameters of the surrounding anisotropic medium provided they satisfy appropriate physical as well as mathematical assumptions imposed by our analysis. Numerical examples are given showing the viability of our method.

Original languageEnglish (US)
Article number045008
JournalInverse Problems
Volume30
Issue number4
DOIs
StatePublished - Jan 1 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics

Keywords

  • anisotropic medium
  • exterior transmission eigenvalues
  • factorization method
  • interior scattering problem
  • inverse scattering

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