We present a novel method based on Huygens’ principle and compressive sensing to predict the electromagnetic (EM) fields in arbitrary scattering environments by making a few measurements of the field. In doing so, we assume a homogeneous medium between the scatterers, though we do not assume prior knowledge of the permittivities or the exact geometry of the scatterers. The major contribution of this work is a compressive sensing-based subspace optimization method (CS-SOM). Using this, we show that the EM fields in an indoor situation with up to four scattering objects can be reconstructed with approximately 12% error, when the number of measurements is only 55% of the number of variables used to formulate the problem. Our technique departs significantly from traditional ray tracing approaches. We use a surface integral formulation which captures wave-matter interactions exactly, leverage compressive sensing techniques so that field measurements at a few random locations suffice, and apply Huygens’ principle to predict the fields at any location in space.

中文翻译：

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压缩感测方法可预测散射的电磁场。

我们提出一种基于惠更斯原理和压缩感测的新颖方法，通过对场进行几次测量来预测任意散射环境中的电磁场。这样做时，我们假设散射体之间有均匀的介质，尽管我们不假设散射体的介电常数或确切几何形状具有先验知识。这项工作的主要贡献是基于压缩感知的子空间优化方法（CS-SOM）。使用此方法，我们表明在室内情况下最多包含四个散射对象的EM场可以重建，误差约为12％，而测量次数仅为用于表达问题的变量数量的55％。我们的技术与传统的光线跟踪方法大不相同。