The Factorization Method for a Cavity in an Inhomogeneous Medium - Inria - Institut national de recherche en sciences et technologies du numérique
Article Dans Une Revue Inverse Problems Année : 2014

The Factorization Method for a Cavity in an Inhomogeneous Medium

Shixu Meng
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Houssem Haddar
Fioralba Cakoni
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Résumé

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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Dates et versions

hal-00936557 , version 1 (26-01-2014)

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Shixu Meng, Houssem Haddar, Fioralba Cakoni. The Factorization Method for a Cavity in an Inhomogeneous Medium. Inverse Problems, 2014, 30 (045008), ⟨10.1088/0266-5611/30/4/045008⟩. ⟨hal-00936557⟩
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