Structured Low-Rank and Sparse Method for ISAR Imaging With 2-D Compressive Sampling

With the development of modern advanced radar, there are high demands to perform inverse synthetic aperture radar (ISAR) imaging from sparse frequency band (SFB) and sparse aperture (SA) data, respectively. The compressed sensing (CS)-based methods are commonly applied to deal with the sparse sampling data, nevertheless, suffering from the inherent problem of basis mismatch on the discrete dictionary. Alternatively, the matrix completion (MC) approaches using the low-rank property are also employed to avoid the discrete error by directly reconstructing the missing data, belonging to the group of grid-free technology. However, this class method can hardly provide satisfactory performance on the type of block sparse sampling data. In this article, a novel structured low-rank and sparse (SLR + S) algorithm is proposed for high-resolution ISAR imaging with 2-D compressive sampling, which can effectively deal with various types of sparse sampling patterns. In the scheme, the ISAR signal model with 2-D compressive sampling is established to integrate three commonly used waveforms, including linear frequency modulation (LFM), sparse stepped LFM, and random frequency division modulation. Then, a novel algorithm is proposed for complete sampling data recovery using joint low-rank and sparse constraints. In particular, a structured Hankel formulation is utilized to effectively exploit the latent information of data structure with the enhanced low-rank property. As follows, a fast alternating direction method of multipliers (ADMMs) is applied for high-efficiency and high-precision image reconstruction. Compared with traditional CS and MC methods, the proposed algorithm has the capability of dealing with different patterns of 2-D compressive sampling. Finally, the experiments using both simulated and measured data are performed to confirm the effectiveness of the proposal.