Sparsity in time-frequency representations

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Sparsity in time-frequency representations
We consider signals and operators in finite dimension which have sparse time-frequency representations. As main result we show that an S-sparse Gabor representation in Cn with respect to a random unimodular window can be recovered by Basis Pursuit with high probability provided that S ≤ Cn/ log(n). Our results are applicable to the channel estimation problem in wireless communications and they establish the usefulness of a class of measurement matrices for compressive sensing. Keywords. Time-frequency representations, sparse representations, sparse signal recovery, Basis Pursuit, operator identification, random matrices. AMS Subject Classification. 42C40, 15A52, 90C25.
Götz E. Pfander, Holger Rauhut
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2007
Where CORR
Authors Götz E. Pfander, Holger Rauhut
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