High‐dimensional sparse recovery using modified generalised SL0 and its application in 3D ISAR imaging

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.