A Butterfly Algorithm for Synthetic Aperture Radar Imaging
Name
Demanet-2012-A Butterfly Algorithm for Synthetic Aperture Radar Imaging.pdf
Size
7.03 MB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Demanet, Laurent
Ferrara, Matthew
Maxwell, Nicholas
Poulson, Jack
Ying, Lexing
Date Issued
February 2012
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1137/100811593
