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 under-sampled. 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 under-sampled. We show that the standard methods of autofocus, which are used as a post-processing step on the reconstructed image, are typically not suitable. Instead of applying autofocus as a post-processor, 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 contains phase errors and are under-sampled.

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Iterative SAR image formation can visually improve image reconstructions from under-sampled phase histories by approximately solving a regularised least squares problem. For iterative inversion to be computationally feasible, fast algorithms for the observation matrix and its adjoint must be available. We demonstrate how fast, N 2 log 2 N complexity, (re/back)-projection algorithms can be used as accurate approximations for the observation matrix and its adjoint, without the limiting assumptions of other N 2 log 2 N methods, e.g. the polar format algorithm. Experimental results demonstrate the effectiveness of iterative methods using a publicly available SAR dataset. Matlab/C code implementations of the fast (re/back)-projection algorithms used in this paper have been made available.

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