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，用于解决具有随机分布点源的声学反演散射问题。我们的采样方法的理论验证基于Helmholtz-Kirchhoff恒等式，测量之间的互相关性以及引入和分析的体积和虚数近场算子。我们还讨论了MATLAB的实现，包括边界元素、SVD、Tikhonov正则化和Morozov的差异原则。我们通过在二维中进行数值实验展示了算法的稳健性和精度。