Compressed Sensing Radar Imaging With Magnitude Sparse Representation

Compressed sensing (CS) is a sparsity-driven and regularization-based approach. The CS theory has led to superior imaging methods, offering a number of benefits, including increased image quality and robustness to the limitations in data quantity. In such imaging methods, if the targets are not originally sparse (not sparse in the canonical basis), sparse representation is required. However, in synthetic aperture radar (SAR) imaging scenarios, owing to the potentially random phase of the scene, it is very difficult to find bases to sparsify a complex-valued and extended scene. In this paper, an improved framework to handle the magnitude and phase of the scene separately is proposed. Although the phase of the scene is potentially random, the magnitude can usually be sparsely represented. In the proposed framework, besides the sparsity, the real-valued information of the magnitude and the coefficient distribution of the sparse representation are also utilized. In the reconstruction process, the magnitude of the scene is constrained to be real-valued, and the coefficients of the sparse representation are limited in the low-frequency area. A novel gradient-based optimization algorithm is developed to solve the proposed framework effectively. Since more a priori knowledge is utilized in the proposed algorithm, it can reduce the computational complexity and improve the reconstruction precision. The simulation results and real data results from an airborne SAR system are presented to show the superiority of the proposed algorithm.