The factorization method for a cavity in an inhomogeneous medium

Shixu Meng, Houssem Haddar, Fioralba Cakoni

Research output: Contribution to journalArticle

21 Citations (Scopus)

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

Fingerprint

Anisotropic media
Factorization Method
Inhomogeneous Media
Factorization
Cavity
Scattering
Anisotropic Media
Inverse Scattering Problem
Compact Support
Viability
Internal
Numerical Examples
Curve
Operator
Range of data

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

Cite this

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The factorization method for a cavity in an inhomogeneous medium. / Meng, Shixu; Haddar, Houssem; Cakoni, Fioralba.

In: Inverse Problems, Vol. 30, No. 4, 045008, 01.01.2014.

Research output: Contribution to journalArticle

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AU - Haddar, Houssem

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AB - 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.

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