Passive inverse obstacle scattering problems for the Helmholtz equation

TL;DR

This paper investigates passive inverse obstacle scattering problems governed by the Helmholtz equation, establishing uniqueness results for source and obstacle identification from correlation measurements, and proposing numerical reconstruction methods.

Contribution

It introduces new uniqueness results for passive inverse problems and develops efficient numerical methods for reconstructing obstacles and sources.

Findings

Uniqueness established for source strength and obstacle shape from near-field correlations.

Effective numerical algorithms for reconstructing obstacles and sources.

Applicable to 2D and 3D Helmholtz inverse scattering scenarios.

Abstract

Passive imaging involves recording waves generated by uncontrolled, random sources and utilizing correlations of such waves to image the medium through which they propagate. In this paper, we focus on passive inverse obstacle scattering problems governed by the Helmholtz equation in $\mathbb{R}^d\;(d=2,3)$. The random source is modelled by a Gaussian random process. Uniqueness results are established for the inverse problems to determine the source strength or shape and location of an obstacle, or both of them simultaneously from near-field correlation measurements. Finally, we present efficient methods for numerical reconstructions.