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