Locating multiple multipolar acoustic sources using the direct sampling method

TL;DR

This paper introduces a direct sampling method for accurately locating multiple multipolar acoustic sources from boundary measurements, using simple integral calculations and robust indicator functions.

Contribution

The work presents novel, effective sampling schemes with rigorous justification for locating multiple multipolar sources using a single wavenumber.

Findings

Effective source localization demonstrated through numerical examples

Method is robust against noise and measurement errors

Inversion involves only simple integral calculations

Abstract

This work is concerned with the inverse source problem of locating multiple multipolar sources from boundary measurements for the Helmholtz equation. We develop simple and effective sampling schemes for location acquisition of the sources with a single wavenumber. Our algorithms are based on some novel indicator functions whose indicating behaviors could be used to locate multiple multipolar sources. The inversion schemes are totally "direct" in the sense that only simple integral calculations are involved in evaluating the indicator functions. Rigorous mathematical justifications are provided and extensive numerical examples are presented to demonstrate the effectiveness, robustness and efficiency of the proposed methods.