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CORR
2011
Springer

The restricted isometry property for time-frequency structured random matrices

7 years 9 months ago
The restricted isometry property for time-frequency structured random matrices
We establish the restricted isometry property for finite dimensional Gabor systems, that is, for families of time–frequency shifts of a randomly chosen window function. We show that the s-th order restricted isometry constant of the associated n×n2 Gabor synthesis matrix is small provided s ≤ c n2/3 / log2 n. This improves on previous estimates that exhibit quadratic scaling of n in s. Our proof develops bounds for a corresponding chaos process. Key Words: compressive sensing, restricted isometry property, Gabor system, time-frequency analysis, random matrix, chaos process. AMS Subject classification: 60B20, 42C40, 94A12
Götz E. Pfander, Holger Rauhut, Joel A. Tropp
Added 19 Aug 2011
Updated 19 Aug 2011
Type Journal
Year 2011
Where CORR
Authors Götz E. Pfander, Holger Rauhut, Joel A. Tropp
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