Near-optimal sparse Fourier representations via sampling (2002)
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| Venue: | In STOC |
| Citations: | 57 - 14 self |
BibTeX
@INPROCEEDINGS{Gilbert02near-optimalsparse,
author = {A. C. Gilbert and S. Guha and P. Indyk and S. Muthukrishnan and M. Strauss},
title = {Near-optimal sparse Fourier representations via sampling},
booktitle = {In STOC},
year = {2002},
pages = {152--161}
}
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Abstract
We give an algorithm for nding a Fourier representation R ofBterms for a given discrete signal A of lengthN, such thatkA,Rk 2 2 is within the factor (1 +) of best possible kA,Roptk 2 2. Our algorithm can access A by reading its values on a sample setT [0;N), chosen randomly from a (non-product) distribution of our choice, independent of A. That is, we sample non-adaptively. The total time cost of the algorithm is polynomial inB log(N) log(M) = (where M is the ratio of largest to smallest numerical quantity encountered), which implies a similar bound for the number of samples. 1.
