Vol. 14, No. 3, 2021

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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

Vol. 14 (2021), No. 3, 667–688
Abstract

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.

Keywords
time-dependent linear sampling method, inverse scattering, penetrable scatterer
Mathematical Subject Classification 2010
Primary: 35R30, 65M32
Milestones
Received: 8 July 2018
Revised: 7 May 2019
Accepted: 2 December 2019
Published: 18 May 2021
Authors
Fioralba Cakoni
Department of Mathematics
Rutgers University
New Brunswick, NJ
United States
Peter Monk
Department of Mathematical Sciences
University of Delaware
Newark, DE
United States
Virginia Selgas
Departamento de Matemáticas
Escuela Politécnica de Ingeniería de Gijón
University of Oviedo
Gijón
Spain