Abstract

Imaging the reflectivity of targets in random media, in remote sensing regimes

Liliana Borcea
Rice University

Collaborators: George Papanicolaou and Chrysoula Tsogka

We consider the inverse problem of imaging the reflectivity of a target
buried in a random medium, in a remote sensing regime. Data is collected
by sending pulses in the medium and recording the scattered responses.
The excitation and recording is done via one or multiple arrays
of transducers. The size of the target is R and it is much smaller than
L, the distance of its center to the surface of measurements (remote
sensing regime). Moreover, R is larger than the carrier wavelength of the
probing pulse, which is comparable with l, the size of the inhomogeneities
in the medium. The problem is to image the reflectivity of the target.
Based on recent results on time reversal and imaging in random media, we
develop a model for imaging the unknown reflectivity. The analysis is
based on the Born approximation (single scattering by the target). We
derive a simple model which shows explicitly the resolution limits of
the images that one can obtain. Moreover, it shows how to use to our
advantage, a large physical aperture, when imaging in random media.
A brief comparison with known, high frequency, deterministic imaging
methods (the Beylkin determinant) will be presented, as well.