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Near-optimal sparse fourier representations via sampling
Abstract
(MATH) We give an algorithm for finding a Fourier representation R of B terms for a given discrete signal signal A of length N, such that $\|\signal-\repn\|_2^2$ is within the factor (1 +ε) of best possible $\|\signal-\repn_\opt\|_2^2$. Our algorithm can access A by reading its values on a sample set T ⊆[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 in B log(N)log(M)ε (where M is the ratio of largest to smallest numerical quantity encountered), which implies a similar bound for the number of samples.
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Citations
Cited by
Donoho, D. L. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2006.871582 · Cited by 23,994
Candes, E. J., Romberg, J., & Tao, T. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2005.862083 · Cited by 15,639
A Simple Proof of the Restricted Isometry Property for Random Matrices
Baraniuk, R., Davenport, M., DeVore, R., & Wakin, M. (2008) · Constructive Approximation · doi:10.1007/s00365-007-9003-x · Cited by 2,372
Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals
Tropp, J. A., Laska, J. N., Duarte, M. F., Romberg, J. K., & Baraniuk, R. G. (2010) · IEEE Transactions on Information Theory · doi:10.1109/tit.2009.2034811 · Cited by 1,089
Data Streams: Algorithms and Applications
Muthukrishnan, S. (2005) · Foundations and Trends® in Theoretical Computer Science · doi:10.1561/0400000002 · Cited by 718
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Metadata
- Authors
- Gilbert, A. C., Guha, S., Indyk, P., Muthukrishnan, S., & Strauss, M.
- Venue
- Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
- Publisher
- ACM
- Published
- 2002-05-19
- Pages
- 152-161
- OpenAlex
- W2012365979
- Cited by
- 259
- References
- 0
- FWCI
- 8.75
- Type
- conference paper
- Language
- en
- Open access
- closed
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- Gilbert, A. C., Guha, S., Indyk, P., Muthukrishnan, S., & Strauss, M. (2002). Near-optimal sparse fourier representations via sampling. Proceedings of the thiry-fourth annual ACM symposium on Theory of computing. https://doi.org/10.1145/509907.509933
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