Geosynchronous Spaceborne-Airborne Bistatic SAR Imaging Based on Fast Low-Rank and Sparse Matrices Recovery

Geosynchronous spaceborne-airborne bistatic synthetic aperture radar (GEO-SA-BiSAR) consists of a GEO transmitter and airborne receiver, which has extensive application prospects in both civilian and military fields for its ability to generate high-resolution images of the ground target with frequent coverage and abundant scattering information. However, the Doppler bandwidth in this configuration exceeds the transmitted pulse repetition frequency (PRF), which leads to sub-Nyquist sampling. To solve this problem, a multireceiving technique has been applied to the receiver to increase the equivalent sampling rate and reconstruct an unambiguous image. In this article, we take a different approach to recover the unambiguous image for GEO-SA-BiSAR with fewer receiving channels. First, the accurate echo model is established based on the "non-stop-and-go" propagation delay model to lay the foundation of accurate imaging. After that, the GEO-SA-BiSAR imaging problem is modeled as a problem of joint sparse and low-rank matrices' recovery. To reduce the computing time of the traditional recovery method, a modified alternating direction method of multipliers (M-ADMM) is proposed, where the computation and storage of the computational expensive observation matrix are avoided. Furthermore, an M-ADMM method with multiple receiving channels, which combines the recovery theory and multireceiving information, is also proposed to handle the severe sub-Nyquist sampling echo of GEO-SA-BiSAR. Simulation results reveal that the proposed method can recover the original image scene with high computational efficiency. Meanwhile, the number of receiving channels can be reduced compared with the multireceiving technique.