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Uncertainty principles and ideal atomic decomposition
Abstract
Suppose a discrete-time signal S(t), 0/spl les/t<N, is a superposition of atoms taken from a combined time-frequency dictionary made of spike sequences 1/sub {t=/spl tau/}/ and sinusoids exp{2/spl pi/iwt/N}//spl radic/N. Can one recover, from knowledge of S alone, the precise collection of atoms going to make up S? Because every discrete-time signal can be represented as a superposition of spikes alone, or as a superposition of sinusoids alone, there is no unique way of writing S as a sum of spikes and sinusoids in general. We prove that if S is representable as a highly sparse superposition of atoms from this time-frequency dictionary, then there is only one such highly sparse representation of S, and it can be obtained by solving the convex optimization problem of minimizing the l/sup 1/ norm of the coefficients among all decompositions. Here "highly sparse" means that N/sub t/+N/sub w/
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Cites
Daubechies, I. (1992) · doi:10.1137/1.9781611970104 · Cited by 15,979
Cited by
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Metadata
- Authors
- Donoho, D. L., & Huo, X.
- Venue
- IEEE Transactions on Information Theory
- Published
- 2001
- Volume
- 47
- Issue
- 7
- Pages
- 2845-2862
- ISSN
- 0018-9448 (ISSN-L)
- OpenAlex
- W2099641086
- Cited by
- 1,949
- References
- 1
- FWCI
- 23.60
- Type
- journal article
- Language
- en
- Open access
- closed
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