A fully polarimetric frequency-wavenumber domain algorithm for 3-D imaging using the synthetic aperture radar technique with irregular sample locations is introduced. At its core, the algorithm works with a multilevel plane-wave representation and relies on some of the concepts of the multilevel fast multipole method (MLFMM). By utilizing a recursive segmentation scheme, the presented algorithm efficiently handles irregular observation locations, which can vary along all three dimensions in space. The basic idea is to divide the observation region into subdomains of decreasing size, until the calculation of the spectral domain representation of the observation data in the individual subdomains by a discrete Fourier transform (DFT) without further acceleration is feasible. The overall uniformly sampled spectral representation of the observation data is then obtained by hierarchical aggregation of the subdomain spectra. The probe influence is fully compensated by the combined processing of several polarizations and solving small linear systems of equations related to the frequency-wavenumber samples on the coarsest level. The focused image is finally computed by fast Fourier transforms (FFTs). This approach, as opposed to conventional coherent back-projection algorithms (BPAs), allows for a fully polarimetric description of the scattering object and achieves good efficiency without loss of accuracy. To show the effectiveness of the algorithm, imaging results obtained from numerical simulations as well as from the evaluation of measured field data are presented and discussed.

中文翻译：

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用于不规则采样位置 3D 成像的全偏振多级快速谱域算法


介绍了一种使用具有不规则采样位置的合成孔径雷达技术进行 3D 成像的全偏振频波数域算法。该算法的核心是使用多级平面波表示，并依赖于多级快速多极子方法 (MLFMM) 的一些概念。通过利用递归分割方案，所提出的算法有效地处理不规则的观察位置，这些位置可以沿着空间的所有三个维度变化。其基本思想是将观测区域划分为尺寸递减的子域，直到在无需进一步加速的情况下通过离散傅里叶变换（DFT）计算各个子域中观测数据的谱域表示是可行的。然后通过子域光谱的分层聚合获得观测数据的整体均匀采样光谱表示。通过组合处理多个偏振并求解与最粗级别的频率波数样本相关的小型线性方程组，可以完全补偿探头的影响。最终通过快速傅立叶变换 (FFT) 计算聚焦图像。与传统的相干反投影算法（BPA）相反，这种方法可以对散射物体进行完全偏振的描述，并在不损失精度的情况下实现良好的效率。为了证明该算法的有效性，给出并讨论了从数值模拟以及测量现场数据评估中获得的成像结果。