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 ru...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics
2012
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| Online Access: | http://hdl.handle.net/1721.1/71780 https://orcid.org/0000-0001-7052-5097 |
| _version_ | 1811083072522682368 |
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| author | Demanet, Laurent Ferrara, Matthew Maxwell, Nicholas Poulson, Jack Ying, Lexing |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Demanet, Laurent Ferrara, Matthew Maxwell, Nicholas Poulson, Jack Ying, Lexing |
| author_sort | Demanet, Laurent |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T12:20:04Z |
| format | Article |
| id | mit-1721.1/71780 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:20:04Z |
| publishDate | 2012 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/717802022-09-28T01:02:20Z A Butterfly Algorithm for Synthetic Aperture Radar Imaging Demanet, Laurent Ferrara, Matthew Maxwell, Nicholas Poulson, Jack Ying, Lexing Massachusetts Institute of Technology. Department of Mathematics Demanet, Laurent Demanet, Laurent 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. 2012-07-24T15:45:17Z 2012-07-24T15:45:17Z 2012-02 2010-10 Article http://purl.org/eprint/type/JournalArticle 1936-4954 1936-4954 http://hdl.handle.net/1721.1/71780 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 https://orcid.org/0000-0001-7052-5097 en_US http://dx.doi.org/10.1137/100811593 SIAM Journal on Imaging Sciences 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. application/pdf Society for Industrial and Applied Mathematics SIAM |
| spellingShingle | Demanet, Laurent Ferrara, Matthew Maxwell, Nicholas Poulson, Jack Ying, Lexing A Butterfly Algorithm for Synthetic Aperture Radar Imaging |
| title | A Butterfly Algorithm for Synthetic Aperture Radar Imaging |
| title_full | A Butterfly Algorithm for Synthetic Aperture Radar Imaging |
| title_fullStr | A Butterfly Algorithm for Synthetic Aperture Radar Imaging |
| title_full_unstemmed | A Butterfly Algorithm for Synthetic Aperture Radar Imaging |
| title_short | A Butterfly Algorithm for Synthetic Aperture Radar Imaging |
| title_sort | butterfly algorithm for synthetic aperture radar imaging |
| url | http://hdl.handle.net/1721.1/71780 https://orcid.org/0000-0001-7052-5097 |
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