单站配置下直接采样法的分析与改进
Analysis and improvement of direct sampling method in the mono-static configuration
AI总结：
本文分析了单站配置下直接采样法的局限性，并提出改进方法以提升成像效果。
摘要：
最近引入的非迭代成像方法，称为直接采样法（DSM），以其在多站配置下的快速、稳健和有效性而著称，但在单站配置下却失效。通过二维标量配置的渐近性和远场假设框架，获得了DSM指示函数的解析表达式，该表达式以零阶贝塞尔函数、不均匀体的尺寸、形状和介电常数为参数，并揭示了限制性的理论原因。随后提出改进的DSM版本以提升成像方法。理论结果通过合成数据的数值结果得到支持。
英文摘要：
The recently introduced non-iterative imaging method entitled \enquote{direct sampling method} (DSM) is known to be fast, robust, and effective for inverse scattering problems in the multi-static configuration but fails when applied to the mono-static one. To the best of our knowledge no explanation of this failure has been provided yet. Thanks to the framework of the asymptotic and the far-field hypothesis in the 2D scalar configuration an analytical expression of the DSM indicator function in terms of the Bessel function of order zero and sizes, shapes and permittivities of the inhomogeneities is obtained and the theoretical reason of the limitation identified. A modified version of DSM is then proposed in order to improve the imaging method. The theoretical results are supported by numerical results using synthetic data.
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