ORTP: A Video SAR Imaging Algorithm Based on Low-Tubal-Rank Tensor Recovery

Video synthetic aperture radar (SAR) is attracting more and more attention because of its continuous imaging capability for ground scene of interest under any weather conditions and any time of the day. To reduce the sampling amount of video SAR, the imaging processing can be formulated into a low-tubal-rank tensor recovery problem. In this paper, we proposed an Orthogonal Rank-one Tensor Pursuit (ORTP) algorithm to solve the low-tubal-rank tensor recovery problem in video SAR imaging. The proposed ORTP algorithm is an extension of orthogonal rank-1 matrix pursuit algorithm in matrix sensing problem from the matrix case to the tensor case under tubal-rank model. It is capable of reconstructing target tensor efficiently without requiring any prior information about pre-specified or pre-estimated tensor tubal-rank value. To achieve this, rank-one basis tensors and weight tensors of the target tensor are estimated iteratively, and residual error between the observed tensor and the estimated tensor through linear mapping is utilized as the stop condition. We theoretically prove the convergence and correctness of the proposed ORTP method. The methodology was tested on synthetic data, real video data and video SAR data. These tests show that the proposed approach outperforms other video SAR imaging algorithms and low-rank tensor recovery algorithms.