Compressive SAR Imaging Based on Modified Low-Rank and Sparse Decomposition

In this paper, we propose a novel imaging method for synthetic aperture radar (SAR) systems with compressive sensing (CS) by modifying the existing low-rank and sparse decomposition (LRSD) scheme. The proposed CS-based modified LRSD (CS-MLRSD) method uses 2D random sampling for SAR raw data compression and then employs the dual-tree complex wavelet transform (DCWT) instead of singular value decomposition to more accurately reconstruct directional information in the low-rank background image. For the CS-MLRSD scheme, an iterative thresholding algorithm is derived to separately reconstruct the low-rank and sparse components. A bivariate shrinkage function is employed to threshold the wavelet coefficients for sparse representation of the low-rank part, while soft thresholding is used to sparsely represent the dominant objects in the image space. The proposed CS-MLRSD scheme is applicable to arbitrary SAR geometries in which the SAR imaging and inverse SAR imaging functions are defined. Numerical simulations using SAR modeling data validate the convergence of the proposed method and compare its computational complexity with baseline CS-SAR imaging schemes. Moreover, using both SAR modeling data and real SAR measurement data, the proposed scheme demonstrates significant improvements in reconstructed image quality compared to existing CS-SAR techniques.