Recovery of interior eigenvalues from reduced near field data

TL;DR

This paper proposes an effective method to recover interior eigenvalues in inverse scattering problems using near field data measured on a boundary surface, with potential applications in obstacle detection.

Contribution

It introduces a novel procedure for recovering interior eigenvalues from reduced near field data in inverse obstacle and transmission scattering problems.

Findings

Successful recovery of interior eigenvalues demonstrated

Method effective with data from small, fixed domains

Applicable to obstacle and media inhomogeneity detection

Abstract

We consider inverse obstacle and transmission scattering problems where the source of the incident waves is located on a smooth closed surface that is a boundary of a domain located outside of the obstacle/inhomogeneity of the media. The domain can be arbitrarily small but fixed.The scattered waves are measured on the same surface. An effective procedure is suggested for recovery of interior eigenvalues by these data.