一种用于定位逆散射中微小不均匀体的多频MUSIC算法
A multifrequency MUSIC algorithm for locating small inhomogeneities in inverse scattering
AI总结：
本文提出一种多频MUSIC算法，用于从不同频率的远场数据中定位嵌入在均匀介质中的微小穿透体，通过渐近展开公式设计分析该方法，并建立频率和接收方向的下限。
摘要：
我们考虑时间谐波声学或电磁波的逆散射问题。目标是从平面波入射场的远场模式观测中定位多个嵌入在均匀背景介质中的微小穿透体。利用散体相对于波长的微小性，我们利用远场模式的渐近表示公式来设计和分析该设置的MUSIC型重建方法。我们建立了恢复给定配置中散体数量和位置所需的频率和接收方向的下限。此外，我们还将该方法应用于多频后向散射数据的实际情况。数值例子用于说明该方法的潜力和限制。
英文摘要：
We consider an inverse scattering problem for time-harmonic acoustic or electromagnetic waves. The goal is to localize several small penetrable objects embedded inside an otherwise homogeneous background medium from observations of far field patterns of scattered fields corresponding to plane wave incident fields with one fixed incident direction but several different frequencies. Taking advantage of the smallness of the scatterers with respect to wave length we utilize an asymptotic representation formula for the far field pattern to design and analyze a MUSIC-type reconstruction method for this setup. We establish lower bounds on the number of frequencies and receiver directions required to recover the number and the positions of the scatterers for a given configuration by the reconstruction algorithm. Furthermore we apply the method to the practically interesting case of multifrequency backscattering data. Numerical examples are presented to document the potentials and limitations of this approach.
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