SIAM Journal on Mathematical Analysis, Volume 52, Issue 5, Page 5213-5231, January 2020.
This paper concerns time-harmonic inverse source problems with a single far-field pattern in two dimensions, where the source term is compactly supported in an a priori given inhomogeneous background medium. For convex-polygonal source terms, we prove that the source support together with the zeroth and first-order derivatives of the source function at corner points can be uniquely determined. Further, we prove that an admissible set of source functions (including harmonic functions) having a convex-polygonal support can be uniquely identified by a single far-field pattern. A class of radiating sources is characterized, and the extension of the radiated field across a corner point is proven impossible. Finally, the corner scattering theory motivates us to design a data-driven inversion scheme for imaging a convex polygonal source support.

中文翻译：

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具有单个远场模式的非均匀介质中的逆源问题

SIAM数学分析杂志，第52卷，第5期，第5213-5231页，2020年1月。
本文涉及二维的单个远场模式的时谐逆源问题，其中源项在给定的不均匀背景介质的先验条件下得到了紧密支持。对于凸多边形源项，我们证明可以唯一确定源支持以及源函数在角点处的零阶和一阶导数。此外，我们证明了具有凸多边形支持的一组源函数（包括谐波函数）的允许集合可以通过单个远场模式唯一地标识。表征了一类辐射源，并且证明了辐射场在拐角处的扩展是不可能的。最后，角散射理论激励我们设计一种数据驱动的反演方案来成像凸多边形源支架。