Since the compressed sensing (CS) theory broke through the limitation of the traditional Nyquist sampling theory, it has attracted extensive attention in the field of microwave imaging. However, in 3-D microwave sparse reconstruction application, conventional CS-based algorithms always suffer from huge computational cost. In this article, a novel 3-D microwave sparse reconstruction method based on a complex-valued sparse reconstruction network (CSR-Net) is proposed, which converts complex number operations into matrix operations for real and imaginary parts. Using the unfolding + network approximate scheme, each iteration process of CS-based iterative threshold optimization is designed as a block of CSR-Net, and a modified shrinkage term is introduced to improve the convergence performance of the approach. In addition, CSR-Net adopts a convolutional neural network module to replace a nonlinear sparse representation process, which dramatically reduces computational complexity and improves reconstruction performance over conventional CS-based iterative threshold optimization algorithms. Then, we divide the 3-D scene into a series of 2-D slices, and a phase correction scheme is adopted to ensure that the whole 3-D scene can be reconstructed with measurement matrix of a slice. Moreover, an efficient position-amplitude-random training method without additional real-measured data is employed for the proposed network, which effectively train the CSR-Net without enough real-measured data. Extensive experiment results demonstrate that CSR-Net outperforms both conventional iterative threshold optimization methods and deep network-based ISTA-NET-plus large margins. Its speed and reconstruction accuracy in 3-D imaging can achieve a state-of-the-art level.

Because of the three-dimensional (3D) imaging scene’s sparsity, compressed sensing (CS) algorithms can be used for linear array synthetic aperture radar (LASAR) 3D sparse imaging. CS algorithms usually achieve high-quality sparse imaging at the expense of computational efficiency. To solve this problem, a fast Bayesian compressed sensing algorithm via relevance vector machine (FBCS–RVM) is proposed in this paper. The proposed method calculates the maximum marginal likelihood function under the framework of the RVM to obtain the optimal hyper-parameters; the scattering units corresponding to the non-zero optimal hyper-parameters are extracted as the target-areas in the imaging scene. Then, based on the target-areas, we simplify the measurement matrix and conduct sparse imaging. In addition, under low signal to noise ratio (SNR), low sampling rate, or high sparsity, the target-areas cannot always be extracted accurately, which probably contain several elements whose scattering coefficients are too small and closer to 0 compared to other elements. Those elements probably make the diagonal matrix singular and irreversible; the scattering coefficients cannot be estimated correctly. To solve this problem, the inverse matrix of the singular matrix is replaced with the generalized inverse matrix obtained by the truncated singular value decomposition (TSVD) algorithm to estimate the scattering coefficients correctly. Based on the rank of the singular matrix, those elements with small scattering coefficients are extracted and eliminated to obtain more accurate target-areas. Both simulation and experimental results show that the proposed method can improve the computational efficiency and imaging quality of LASAR 3D imaging compared with the state-of-the-art CS-based methods.

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It is difficult for multichannel maneuvering synthetic aperture radar (SAR) to achieve ground moving target 2D velocity estimation and refocusing. In this paper, a novel method based on back projection (BP) and velocity SAR (VSAR) is proposed to cope with the issues. First, the static scene is reconstructed by BP to solve the imaging problem of multichannel maneuvering SAR. Then, the static clutter is suppressed, and the range velocity is estimated via VSAR processing. As for azimuth velocity estimation and refocusing, a velocity search method based on velocity-aided BP (VA-BP) and VSAR is proposed to accomplish them. First, each azimuth velocity in the search and the estimated range velocity are used to image the moving target in a small-sized subimage space by VA-BP, i.e., matching the range history and the Doppler phase of the moving target in the image processing. Then, multiple sets of multichannel SAR subimages corresponding to different azimuth velocities are generated, and the clutter of each set of multichannel SAR subimages is also suppressed by VSAR processing. After that, the azimuth velocity is estimated by searching the clutter-suppressed subimage of the first spatial receiving channel in each set of multichannel SAR subimages with the best refocusing quality measured by the minimum entropy. Simulation results show the proposed method can reach high accuracy in moving target 2D velocity estimation and refocusing with the absolute error of 2D velocity estimation smaller than 0.1 m/s.

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