This work is concerned with an inverse scattering problem of determining unknown scatterers from time-dependent acoustic measurements. A novel time-domain direct sampling method is developed to efficiently determine both the locations and shapes of inhomogeneous media. In particular, our approach is very easy to implement since only cheap space-time integrations are involved in the evaluation of the imaging functionals. Based on the Fourier-Laplace transform, we establish an inherent connection between the time-domain and frequency-domain direct sampling method. Moreover, rigorous theoretical justifications and numerical experiments are provided to verify the validity and feasibility of the proposed method.

翻译：本文研究了一类基于时变声学测量确定未知散射体的逆散射问题。我们提出了一种新的时域直接采样方法，能高效确定非均匀介质的位置和形状。特别地，本方法易于实现，因为成像泛函的评估仅涉及廉价的空间-时间积分。基于傅里叶-拉普拉斯变换，我们建立了时域与频域直接采样方法之间的内在联系。此外，我们提供了严格的理论论证和数值实验，以验证所提方法的有效性与可行性。