Quantitative Direct Sampling for Initial Acoustic Sources

TL;DR

This paper presents a new quantitative direct sampling method for reconstructing initial acoustic sources from wave measurements, with proven uniqueness and demonstrated robustness and efficiency.

Contribution

It introduces novel indicator functions based on spacetime integrals, enabling both theoretical guarantees and practical imaging capabilities.

Findings

Indicators prove uniqueness of source reconstruction.

Numerical experiments show robustness and accuracy.

Methods are computationally efficient.

Abstract

This paper addresses the challenge of quantitatively reconstructing initial acoustic sources from time-dependent wave measurements. We introduce novel indicator functions defined through spacetime integrals of acoustic data and carefully designed auxiliary functions. These indicators are foundational for both proving the uniqueness of source reconstruction and developing a quantitative direct sampling scheme. Our comprehensive numerical experiments demonstrate the robustness, accuracy, and computational efficiency of these methods, highlighting their potential for practical acoustic imaging applications.