Sparsity-based autofocus for undersampled synthetic aperture radar

Motivated by the field of compressed sensing and sparse recovery, nonlinear algorithms have been proposed for the reconstruction of synthetic-aperture-radar images when the phase history is undersampled. These algorithms assume exact knowledge of the system acquisition model. In this paper we investigate the effects of acquisition-model phase errors when the phase history is undersampled. We show that the standard methods of autofocus, which are used as a postprocessing step on the reconstructed image, are typically not suitable. Instead of applying autofocus in postprocessing, we propose an algorithm that corrects phase errors during the image reconstruction. The performance of the algorithm is investigated quantitatively and qualitatively through numerical simulations on two practical scenarios where the phase histories contain phase errors and are undersampled.