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, N2 log2 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 N2 log2 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.