Sparse representation can be extended to high dimensions and can be used in many applications, including three-dimensional (3D) Inverse synthetic aperture radar (ISAR) imaging. In this study, the high-dimensional sparse representation problem and a recovery method called high-dimensional smoothed least zero-norm (HDSL0) are formulated. In this method, the theory and computation of tensors and approximating L0 norm using Gaussian functions are used for sparse recovery of high-dimensional data. To enhance the performance of HDSL0, modified regularised high-dimensional SL0 (MRe-HDSL0) algorithm, which benefits from the regularised form of SL0 and an additional hard thresholding step, is proposed. According to the numerical simulations, the recovery signal to noise ratio for MRe-HDSL0 compared to HDSL0, under the same experimental conditions, is 10, 9, and 8 dB higher in 1D, 2D, and 3D cases, respectively. The proposed algorithm also maintains the benefits of high speed and low computational cost of SL0. Besides, the formulation of compressed sensing-based 3D ISAR imaging is expressed. Finally, the proposed algorithm is applied to reconstruct 3D ISAR images of two synthetic targets, which are created based on the scattering point model. Based on the achieved results, the quality of reconstructed images using MRe-HDSL0 is better than other simulated methods.

中文翻译：

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使用改进的广义SL0进行高维稀疏恢复及其在3D ISAR成像中的应用

稀疏表示可以扩展到高维度，并且可以在许多应用中使用，包括三维（3D）逆合成孔径雷达（ISAR）成像。在这项研究中，制定了高维稀疏表示问题和一种称为高维平滑最小零范数（HDSL0）的恢复方法。在这种方法中，张量的理论和计算以及使用高斯函数逼近L0范数用于稀疏恢复高维数据。为了提高HDSL0的性能，提出了改进的正则化高维SL0（MRe-HDSL0）算法，该算法得益于SL0的正则形式和附加的硬阈值步骤。根据数值模拟，在相同的实验条件下，MRe-HDSL0与HDSL0的恢复信噪比分别为10、9，在1D，2D和3D情况下分别提高了8 dB和8 dB。所提出的算法还保持了SL0的高速和低计算成本的优点。此外，表达了基于压缩感测的3D ISAR成像的公式。最后，将所提出的算法应用于基于散射点模型创建的两个合成目标的3D ISAR图像的重建。基于获得的结果，使用MRe-HDSL0重建图像的质量优于其他模拟方法。它们是基于散射点模型创建的。基于获得的结果，使用MRe-HDSL0重建图像的质量优于其他模拟方法。它们是基于散射点模型创建的。基于获得的结果，使用MRe-HDSL0重建图像的质量优于其他模拟方法。