A Motion Compensation Scheme for Compressed Sensing SAR Image Restoration Using Measured Antenna Phase Center Data

Compressed sensing (CS) synthetic aperture radar (SAR) can recover images from undersampled SAR data based on accurate observation models. However, motion errors often cause inaccuracies in observation data and result in defocusing of the reconstructed SAR images. Existing methods can restore and compensate the motion error from data by iterative optimization, which, however, leads to significantly increased computational cost. In this article, we propose an efficient motion compensation (MOCO) scheme for CS SAR using measured antenna phase center (APC) data. Specifically, we exploit the motion error measured by the navigation device to correct the CS SAR observation model. Then, we use the corrected model to formulate a new sparse SAR reconstruction problem. This leads to substantially lower computational cost than the existing MOCO methods in CS SAR. To further achieve fast image recovery, we design a fast imaging algorithm for CS SAR with MOCO to speed up some matrix–vector products involved in the reconstruction problem. The experimental results demonstrate that the proposed method can efficiently reconstruct SAR images from CS SAR data with motion errors.