LRSR-ADMM-Net: A Joint Low-Rank and Sparse Recovery Network for SAR Imaging

Synthetic aperture radar (SAR) imaging with sub-Nyquist sampled echo is a challenging task. Compressed sensing (CS) has been widely applied in this case to reconstruct the unambiguous image. The CS-based methods need to set the iterative parameters manually, but the appropriate parameters are usually difficult to obtain. Besides, such methods require a large number of iterations to obtain satisfactory results, which seriously restricts their practical applications. Moreover, the observation scene of SAR is not sparse in some cases. In this article, we aim at proposing an efficient and effective imaging method for nonsparse observation scenes with reduced data. First, considering the characteristics of nonsparse observation scenes in SAR imaging, we model the SAR imaging problem as a joint low-rank and sparse matrices recovery problem. After that, the iterative alternating direction method of multipliers (ADMMs) to solve the above problem is unrolled into a layer-fixed deep neural network with trainable parameters, in which the learnable parameters are layer-varied. The threshold parameters, as well as the weight parameter between the sparse part and low-rank part of each layer, are learned adaptively instead of manually tuned. Experiments prove that the proposed low-rank and sparse recovery LRSR-ADMM-Net is capable of reconstructing the nonsparse observed scene with high efficiency and precision. Particularly, the proposed LRSR-ADMM-Net yields better reconstruction performance while maintaining high computational efficiency compared with the state-of-the-art iterative recovery methods and the trainable sparse-based network methods.