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Analysis of the
linear sampling method for imaging penetrable obstacles in
the time domain
Fioralba Cakoni, Peter Monk and Virginia Selgas |
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Vol. 14 (2021), No. 3, 667–688
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Abstract |
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We consider the problem of locating and reconstructing the geometry of a penetrable obstacle from time-domain measurements of causal waves. More precisely, we assume that we are given the scattered field due to point sources placed on a surface enclosing the obstacle and that the scattered field is measured on the same surface. From these multistatic scattering data we wish to determine the position and shape of the target. To deal with this inverse problem, we propose and analyze the time-domain linear sampling method (TDLSM) by means of localizing the interior transmission eigenvalues in the Fourier–Laplace domain. We also prove new time-domain estimates for the forward problem and the interior transmission problem, as well as analyze several time-domain operators arising in the inversion scheme. |
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Keywords
time-dependent linear sampling method, inverse scattering,
penetrable scatterer
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Mathematical Subject Classification 2010
Primary: 35R30, 65M32
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Milestones
Received: 8 July 2018
Revised: 7 May 2019
Accepted: 2 December 2019
Published: 18 May 2021
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Authors |
| Fioralba Cakoni | |
| Department of Mathematics Rutgers University New Brunswick, NJ United States |
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| Peter Monk | |
| Department of Mathematical
Sciences University of Delaware Newark, DE United States |
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| Virginia Selgas | |
| Departamento de Matemáticas Escuela Politécnica de Ingeniería de Gijón University of Oviedo Gijón Spain |
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