A Butterfly Algorithm for Synthetic Aperture Radar Imaging

In spite of an extensive literature on fast algorithms for synthetic aperture radar (SAR) imaging, it is not currently known if it is possible to accurately form an image from N data points in provable near-linear time complexity. This paper seeks to close this gap by proposing an algorithm which runs in complexity O(N logN log(1/epsilon)) without making the far-field approximation or imposing the beam pattern approximation required by time-domain backprojection, with epsilon the desired pixelwise accuracy. It is based on the butterfly scheme, which unlike the FFT works for vastly more general oscillatory integrals than the discrete Fourier transform. A complete error analysis is provided: the rigorous complexity bound has additional powers of logN and log(1/epsilon) that are not observed in practice.