Sample-Optimal Fourier Sampling in Any Constant Dimension
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Sample-optimal.pdf
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422.69 KB
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Author(s)
Indyk, Piotr
Kapralov, Mikhail
Date Issued
December 2014
Journal
2014 IEEE 55th Annual Symposium on Foundations of Computer Science
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Indyk, Piotr, and Kapralov, Michael. “Sample-Optimal Fourier Sampling in Any Constant Dimension.” 2014 IEEE 55th Annual Symposium on Foundations of Computer Science, Philadelphia, Pennsylvania, USA, October 18-21 2014, Institute of Electrical and Electronics Engineers (IEEE), December 2014
Version
Original manuscript
Abstract
We give an algorithm for ℓ[subscript 2]/ℓ[subscript 2] sparse recovery from Fourier measurements using O(k log N) samples, matching the lower bound of Do Ba-Indyk-Price-Woodruff'10 for non-adaptive algorithms up to constant factors for any k ≤ N [superscript 1-δ]. The algorithm runs in Õ(N) time. Our algorithm extends to higher dimensions, leading to sample complexity of Õd(k log N), which is optimal up to constant factors for any d = O(1). These are the first sample optimal algorithms for these problems. A preliminary experimental evaluation indicates that our algorithm has empirical sampling complexity comparable to that of other recovery methods known in the literature, while providing strong provable guarantees on the recovery quality.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/FOCS.2014.61
