We present an extension of the linear sampling method for solving the sound-soft inverse acoustic scattering problem with randomly distributed point sources. The theoretical justification of our sampling method is based on the Helmholtz--Kirchhoff identity, the cross-correlation between measurements, and the volume and imaginary near-field operators, which we introduce and analyze. Implementations in MATLAB using boundary elements, the SVD, Tikhonov regularization, and Morozov's discrepancy principle are also discussed. We demonstrate the robustness and accuracy of our algorithms with several numerical experiments in two dimensions.

翻译：我们提出了一种线性采样方法的扩展，用于求解含随机分布点源的声软逆声散射问题。该采样方法的理论依据基于Helmholtz-Kirchhoff恒等式、测量数据的互相关函数、以及我们引入并分析的体积算子和虚近场算子。此外，还讨论了基于边界元、奇异值分解（SVD）、Tikhonov正则化以及Morozov偏差原理的MATLAB实现方案。通过二维数值实验验证了所提算法的鲁棒性与准确性。