论文标题
随机来源的线性抽样方法
The linear sampling method for random sources
论文作者
论文摘要
我们提出了线性采样方法的扩展，该方法用随机分布的点源解决了声音柔软的逆声散射问题。我们采样方法的理论理由是基于Helmholtz-Kirchhoff身份，测量值之间的互相关以及我们介绍和分析的体积和虚构近场操作员。还讨论了使用边界元素，SVD，Tikhonov正则化和Morozov的差异原理中的MATLAB实现。我们通过二维的几个数值实验来证明算法的鲁棒性和准确性。
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.
