A time domain factorization method for obstacles with impedance boundary conditions

We consider the inverse acoustic time domain scattering problem for absorbing scatterers modeled by impedance boundary conditions. We present and analyze a factorization method for reconstructing the obstacle boundary from far field measurements. The analysis is based on using the Laplace transform...

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Bibliographic Details
Published inInverse problems Vol. 36; no. 10; pp. 105011 - 105034
Main Authors Haddar, Houssem, Liu, Xiaoli
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.10.2020
Subjects
Computer Science
factorization method
impedance boundary conditions
inverse acoustic scattering
Numerical Analysis
time domain
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Summary:We consider the inverse acoustic time domain scattering problem for absorbing scatterers modeled by impedance boundary conditions. We present and analyze a factorization method for reconstructing the obstacle boundary from far field measurements. The analysis is based on using the Laplace transform and proving the coercivity of the solution operator in suitable weighted spaces in time. This leads us to consider a modified far field operator parameterized by the imaginary part of Laplace variable which is different but can be arbitrarily close to the original far field operator. As a proof of concept we also provide some preliminary numerical examples to test and discuss the effectiveness of the resulting inversion method when applied to the original far field operator.
Bibliography:IP-102706.R1
ISSN:0266-5611
1361-6420
DOI:10.1088/1361-6420/abaf3b