Abstract
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.
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Communicated by Thomas Strohmer.
H.R. acknowledges support by the European Union’s Human Potential Programme through an Individual Marie Curie Fellowship, contract number MEIF CT-2006-022811.
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Pfander, G.E., Rauhut, H. Sparsity in Time-Frequency Representations. J Fourier Anal Appl 16, 233–260 (2010). https://doi.org/10.1007/s00041-009-9086-9
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DOI: https://doi.org/10.1007/s00041-009-9086-9
Keywords
- Time-frequency representations
- Sparse representations
- Sparse signal recovery
- Basis Pursuit
- Operator identification
- Random matrices