SIAM Journal on Scientific Computing, Volume 42, Issue 3, Page B722-B737, January 2020.
This paper is concerned with the electromagnetic inverse scattering problem that aims to determine the location and shape of anisotropic scatterers from far field data (at a fixed frequency). We study the orthogonality sampling method, which is a simple, fast, and robust imaging method for solving the inverse scattering problem. We provide a theoretical analysis as well as a stability estimate for the sampling method. An equivalent relation between the orthogonality sampling method and the direct sampling method is also established. The analysis uses the Factorization method for the far field operator, and it plays an important role in the justifications along with the Funk--Hecke integral identity. Finally, we present some numerical examples to validate the performance of the sampling methods for anisotropic scatterers in three dimensions.

中文翻译：

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电磁逆散射问题的正交采样方法

SIAM科学计算杂志，第42卷，第3期，第B722-B737页，2020年1月。
本文涉及电磁逆散射问题，该问题旨在根据远场数据（以固定频率）确定各向异性散射体的位置和形状。我们研究正交采样方法，这是一种解决逆散射问题的简单，快速且鲁棒的成像方法。我们提供了抽样方法的理论分析和稳定性估计。还建立了正交采样方法和直接采样方法之间的等效关系。该分析对远场算子使用了因子分解方法，它与Funk-Hecke积分恒等式在证明中起着重要作用。最后，我们提供了一些数值示例，以验证三维三维各向异性散射体采样方法的性能。