Sparse SAR Imaging and Doppler Rate Estimation for Azimuth Downsampled Echo Data via Complex Approximated Message Passing

Airborne synthetic aperture radar (SAR) systems are commonly susceptible to trajectory deviations, resulting in distinct azimuth phase errors in the collected echo. SAR autofocus technology can compensate for phase error and produce a well-focused image based on echo data. However, due to the influence of unfavorable factors such as radar interruption and electromagnetic interference, the echo data may be downsampled in azimuth, which reduces the phase error estimation accuracy of traditional autofocus methods. By introducing compressed sensing (CS) to SAR data processing, sparse SAR imaging shows outstanding performance in acquiring high-resolution images utilizing downsampled echo. However, the phase error existing in the azimuth direction will reduce the sparsity of the observed scene, and the precision of sparse reconstruction is consequently decreased. This article aims to enhance the Doppler rate error estimation precision when echo is downsampled in azimuth and proposes a novel sparse imaging method combined with Doppler rate estimation. During each iteration of the complex approximated message passing (CAMP) algorithm, the Doppler rate error is estimated according to the nonsparse solution by the fractional Fourier transform (FrFT). Then, the phase error is compensated to the nonsparse solution, and the azimuth matched filtering (MF) operator is upgraded. The aforementioned steps are performed iteratively until a well-focused sparse SAR image is generated. It should be noted that the Armijo rule and the random sample consensus algorithm (RANSAC) are introduced to guarantee the fast and precise reconstruction of the observed scene. Experiments from simulated and airborne data prove the enhancement in Doppler rate estimation precision by the proposed method than traditional estimator when used data are azimuth downsampled.