Tensor RPCA for Downward-Looking 3-D SAR Imaging with Sparse Linear Array

Downward-looking 3-D SAR with a sparse linear array alleviates the storage and transmission burden with the sacrifice of the imaging performance. Although many sparse reconstruction methods can improve the quality of 3-D image results, the vectorizing or matrixing of 3-D data makes unacceptable computation load. In this paper, a novel 3-D imaging algorithm based on tensor space is proposed. The 3-D echo data is represented as a 3-mode tensor. Then, the missing data can be recovered by tensor robust principal component analysis on the assumption that the echo tensor is essentially low rank. Finally, the resulting 3-D images can be well focused by any Fourier transform-based 3-D imaging algorithms with the recovered full-sampled data tensor. The proposed algorithm achieves not only high resolution and low-level side-lobes but also the ideal computational cost and memory consumption. The effectiveness of the proposed algorithm has been verified by several numerical simulations and multiple comparative studies.