As compressed sensing theory was introduced into the method of moments, an underdetermined system calculation model has been recently proposed to accelerate the solution of electromagnetic (EM) scattering problems. In this method, the measurement matrix is generated by extracting several rows from the impedance matrix, and the unknown current coefficient vector can be reconstructed from a sparse transform domain. In the actual application of this method, the selection of the sparse transform is the key difficult point, which greatly determines the final efficiency. Up until now, with some commonly used sparse transform bases (e.g., Fourier basis and wavelet basis), the solution can only be applied to 2-D and 2.5-D EM scattering problems. In order to extend its application and further reduce the number of measurements, this letter employs the Krylov subspace to replace the sparse transform in the underdetermined system calculation model. Benefiting from the exploitation of the Krylov subspace, the underdetermined equations will no longer be solved as a sparse reconstruction but rather as a standard least-squares solution. Numerical results have shown that the proposed method, compared to the original method, can not only reduce the number of measurements for the EM scattering problems of 2-D and 2.5-D objects but can also be applied to 3-D objects.

中文翻译：

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用欠定方程和 Krylov 子空间求解电磁散射问题

随着压缩感知理论被引入矩量法，最近提出了一种欠定系统计算模型来加速电磁 (EM) 散射问题的求解。在该方法中，通过从阻抗矩阵中提取几行来生成测量矩阵，并且可以从稀疏变换域中重构未知电流系数向量。在该方法的实际应用中，稀疏变换的选择是关键难点，极大地决定了最终的效率。到目前为止，对于一些常用的稀疏变换基（例如傅立叶基和小波基），该解只能应用于二维和2.5 维电磁散射问题。为了扩大其应用范围，进一步减少测量次数，这封信采用 Krylov 子空间代替欠定系统计算模型中的稀疏变换。受益于 Krylov 子空间的利用，欠定方程将不再作为稀疏重建求解，而是作为标准最小二乘解。数值结果表明，与原始方法相比，所提出的方法不仅可以减少2-D和2.5-D物体的EM散射问题的测量次数，而且还可以应用于3-D物体。