In this article, we propose a method to reconstruct the total electromagnetic field in an arbitrary two-dimensional scattering environment without any prior knowledge of the incident field or the permittivities of the scatterers. However, we assume that the region between the scatterers is homogeneous and that the approximate geometry describing the environment is known. Our approach uses field measurements and a compressive sensing inspired algorithm to estimate the incident field and the tangential electric and magnetic fields on the scatterers’ surfaces. These estimates are then used to predict the field everywhere using Huygens’ principle. Further, we identify the best measurement locations in the environment, which reduces the estimation error to approximately half of the error obtained when using random locations. We show that in an indoor scenario with up to four scattering objects, the total electric field is recovered with less than 10% error when the number of measurements is just 0.3 times the number of unknowns in which the problem is formulated. The formulated problem is solved using ‘Total field - Compressive sensing based subspace optimization method’ – an algorithm that leverages the sparsity of the tangential fields in known transformation domains to obtain an optimal solution.

中文翻译：

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任意散射环境中的电磁场成像

在本文中，我们提出了一种在任意二维散射环境中重建总电磁场的方法，而无需事先了解入射场或散射体的介电常数。但是，我们假设散射体之间的区域是均匀的，并且描述环境的近似几何是已知的。我们的方法使用场测量和启发式压缩感测算法来估计入射场以及散射体表面的切向电场和磁场。然后，利用惠更斯原理将这些估计值用于预测各地的油田。此外，我们确定了环境中的最佳测量位置，这将估计误差减少到使用随机位置时获得的误差的大约一半。我们表明，在室内有最多四个散射物体的情况下，当测量次数仅为解决问题的未知数的0.3倍时，可以以不到10％的误差恢复总电场。使用“总场-基于压缩感知的子空间优化方法”解决了提出的问题，该算法利用已知转换域中切向场的稀疏性来获得最佳解。