Quantitative Direct Sampling for Initial Acoustic Sources
Mathematical Physics
2026-04-23 v1 Numerical Analysis
math.MP
Numerical Analysis
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.
Cite
@article{arxiv.2604.20187,
title = {Quantitative Direct Sampling for Initial Acoustic Sources},
author = {Xiaodong Liu and Xianchao Wang},
journal= {arXiv preprint arXiv:2604.20187},
year = {2026}
}