A novel sampling method for time domain acoustic inverse source problems

TL;DR

This paper introduces a new, computationally efficient sampling method with a novel indicator function for reconstructing time-dependent acoustic sources in inverse scattering problems, validated through analysis and numerical experiments.

Contribution

It presents a novel sampling approach with a new indicator function for inverse acoustic source reconstruction, emphasizing simplicity and low computational cost.

Findings

The method effectively reconstructs source positions and intensities.

The indicator function's theoretical properties are analyzed.

Numerical experiments confirm the method's effectiveness.

Abstract

This paper is concerned with the inverse acoustic scattering problems of reconstructing time-dependent multiple point sources and sources on a curve $L$ of the form $\lambda(t)\tau(x)\delta_L(x)$. A direct sampling method with a novel indicator function is proposed to reconstruct the sources. The sampling method is easy to implement and low in calculation cost. Based on the sampling method, numerical algorithms are provided to get the positions and intensities of the sources. Both theoretical analysis of the indicator function and numerical experiments are provided to show the effectiveness of the proposed method.