A butterfly algorithm for synthetic aperture radar

Laurent Demanet; Matthew Ferrara; Nicholas Maxwell; Jack Poulson; Lexing Ying

doi:10.1117/12.888948

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4 May 2011 A butterfly algorithm for synthetic aperture radar

Laurent Demanet; Matthew Ferrara; Nicholas Maxwell; Jack Poulson; Lexing Ying

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Proceedings Volume 8051, Algorithms for Synthetic Aperture Radar Imagery XVIII; 805105 (2011) https://doi.org/10.1117/12.888948
Event: SPIE Defense, Security, and Sensing, 2011, Orlando, Florida, United States

Abstract

It is not currently known if it is possible to accurately form a synthetic aperture radar image from N data points in provable near-linear complexity, where accuracy is defined as the ℓ₂ error between the full O(N²) backprojection image and the approximate image. To bridge this gap, we present a backprojection algorithm with complexity O(log(1/ε)N log N), with ε the tunable pixelwise accuracy. It is based on the butterfly scheme, which works for vastly more general oscillatory integrals than the discrete Fourier transform. Unlike previous methods this algorithm allows the user to directly choose the amount of acceptable image error based on a well-defined metric. Additionally, the algorithm does not invoke the far-field approximation or place restrictions on the antenna flight path, nor does it impose the frequency-independent beampattern approximation required by time-domain backprojection techniques.

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Laurent Demanet, Matthew Ferrara, Nicholas Maxwell, Jack Poulson, and Lexing Ying "A butterfly algorithm for synthetic aperture radar", Proc. SPIE 8051, Algorithms for Synthetic Aperture Radar Imagery XVIII, 805105 (4 May 2011); https://doi.org/10.1117/12.888948

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