An inverse obstacle scattering problem with passive data in the time domain

TL;DR

This paper introduces a novel time domain linear sampling method for passive acoustic obstacle imaging, reconstructing object support directly from passive measurements using Laplace transform techniques.

Contribution

It develops a new approach linking passive time domain data to an approximate dataset via subtraction of scattered waves, enabling direct support reconstruction.

Findings

Effective reconstruction of obstacle support demonstrated in numerical examples.

The method successfully relates Laplace domain operators to time domain measurements.

Proposes a new imaging functional based on the linear sampling method for passive data.

Abstract

This work considers a time domain inverse acoustic obstacle scattering problem due to passive data. Motivated by the Helmholtz-Kirchhoff identity in the frequency domain, we propose to relate the time domain measurement data in passive imaging to an approximate data set given by the subtraction of two scattered wave fields. We propose a time domain linear sampling method for the approximate data set and show how to tackle the measurement data in passive imaging. An imaging functional is built based on the linear sampling method, which reconstructs the support of the unknown scattering object using directly the time domain measurements. The functional framework is based on the Laplace transform, which relates the mapping properties of Laplace domain factorized operators to their counterparts in the time domain. Numerical examples are provided to illustrate the capability of the proposed method.