We present an extension of the linear sampling method for solving the sound-soft inverse scattering problem in two dimensions with data generated by randomly distributed small scatterers. The theoretical justification of our novel sampling method is based on a rigorous asymptotic model, a modified Helmholtz--Kirchhoff identity, and our previous work on the linear sampling method for random sources. Our numerical implementation incorporates boundary elements, Singular Value Decomposition, Tikhonov regularization, and Morozov's discrepancy principle. We showcase the robustness and accuracy of our algorithms with a series of numerical experiments.

翻译：本文提出了一种线性采样方法的扩展，用于求解由随机分布的小散射体生成的二维声软反散射问题。我们提出的新型采样方法的理论依据基于严格的渐近模型、修正的Helmholtz-Kirchhoff恒等式，以及我们先前关于随机源线性采样方法的研究工作。数值实现结合了边界元法、奇异值分解、Tikhonov正则化和Morozov偏差原理。通过一系列数值实验，我们展示了该算法的鲁棒性与准确性。