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A Butterfly Algorithm for Synthetic Aperture Radar Imaging

Author(s)
Demanet, Laurent; Ferrara, Matthew; Maxwell, Nicholas; Poulson, Jack; Ying, Lexing
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Abstract
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 $O(N \log N \log(1/\epsilon))$ 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 $\log N$ and $\log(1/\epsilon)$ that are not observed in practice.
Date issued
2012-02
URI
http://hdl.handle.net/1721.1/71780
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
SIAM Journal on Imaging Sciences
Publisher
Society for Industrial and Applied Mathematics
Citation
Demanet, Laurent et al. “A Butterfly Algorithm for Synthetic Aperture Radar Imaging.” SIAM Journal on Imaging Sciences 5.1 (2012): 203–243. Copyright © 2012 Society for Industrial and Applied Mathematics
Version: Final published version
ISSN
1936-4954
1936-4954

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