(Nearly) sample-optimal sparse fourier transform
Name
(Nearly) sample-optimal sparse fourier transform.pdf
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463.27 KB
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Checksum (MD5)
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Author(s)
Indyk, Piotr
Kapralov, Mikhail
Price, Eric C
Date Issued
January 2014
Journal
SODA '14 Proceedings of the twenty-fifth annual ACM-SIAM symposium on Discrete algorithms
Publisher
Association for Computing Machinery
Citation
Indyk, Piotr, Michael Kapralov, and Eric Price. "(Nearly) Sample-Optimal Sparse Fourier Transform." SODA '14 Proceedings of the Twenty-fifth Annual ACM-SIAM Symposium on Discrete Algorithms, 5-7 January, 2014, Pittsburgh, Pennsylvania, Association for Computing Machinery, 2014.
Version
Original manuscript
Abstract
We consider the problem of computing a k-sparse approximation to the discrete Fourier transform of an n-dimensional signal. Our main result is a randomized algorithm that computes such an approximation using O(k log n(log log n)[superscript O(1)]) signal samples in time O(k log[superscript 2] n(log log n)[superscript O(1)]), assuming that the entries of the signal are polynomially bounded. The sampling complexity improves over the recent bound of O(k log n log(n/k)) given in [15], and matches the lower bound of Ω(k log(n/k)/log log n) from the same paper up to poly(log log n) factors when k = O(n[superscript 1-δ]) for a constant δ > 0.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
http://dl.acm.org/citation.cfm?id=2634110
