Direct and Inverse Acoustic Scattering by a Combined Scatterer

Abstract

This paper is concerned with the scattering problem of time-harmonic acoustic plane waves by a union of a crack and a penetrable inhomogeneous medium with compact support. The well-posedness of the direct problem is established by the variational method. An uniqueness result for the inverse problem is proved, that is, both the crack and the inhomogeneous medium can be uniquely determined by a knowledge of the far-field pattern for incident plane waves. The linear sampling method is employed to recover the location and shape of the combined scatterer. It is worth noting that we make the first step on reconstructing a mixed-type scatterer of a crack and an inhomogeneous medium by the linear sampling method.

Solving Inverse Scattering Problem with a Crack in Inhomogeneous Medium Based on a Convolutional Neural Network

“…For the inverse scattering problem of the crack in an inhomogeneous medium, the far-field data are generated by coupling the inhomogeneous medium and the crack, which clearly makes the settlement of the inverse problem more challenging. Jin et al determined the uniqueness result of the inverse scattering problem with a crack, and also theoretically proved that the linear sampling method can reconstruct the crack [21].…”