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：我们提出了用随机分布点源解决声软反声波散射问题的线性取样方法的延伸,我们的取样方法的理论依据是基于赫尔姆霍尔茨-基尔希夫特征、测量结果之间的交叉关系、以及我们介绍和分析的量和想象的近地操作者。还讨论了MATLAB使用边界要素、SVD、Tikhonov正规化和Morozov差异原则的执行情况。我们用两个层面的若干数字实验来证明我们的算法的稳健性和准确性。