Recovery of an embedded obstacle and its surrounding medium by formally-determined scattering data

TL;DR

This paper demonstrates that unique recovery of an embedded obstacle and surrounding medium is possible using far-field scattering data, and proposes a practical sampling method for reconstruction.

Contribution

It introduces a theoretical framework for uniquely identifying both obstacle and medium from limited data and develops a robust sampling algorithm for practical reconstruction.

Findings

Unique identification of obstacle and medium from fixed incident data

Recovery of obstacle shape and location using the proposed sampling method

Theoretical proof of medium recoverability within an admissible class

Abstract

We consider an inverse acoustic scattering problem in simultaneously recovering an embedded obstacle and its surrounding inhomogeneous medium by formally determined far-field data. It is shown that the knowledge of the scattering amplitude with a fixed incident direction and all observation angles along with frequencies from an open interval can be used to uniquely identify the embedded obstacle, sound-soft or sound-hard disregarding the surrounding medium. Furthermore, if the surrounding inhomogeneous medium is from an admissible class (still general), then the medium can be recovered as well. Our argument is based on deriving certain integral identities involving the unknowns and then inverting them by certain harmonic analysis techniques. Finally, based on our theoretical study, a fast and robust sampling method is proposed to reconstruct the shape and location of the buried targets and the support of the surrounding inhomogeneities.