The restricted isometry property for time-frequency structured random matrices

Details The restricted isometry property for time-frequency structured random matrices The restricted isometry property for time-frequency structured random matrices

2011-06-16

arxiv.org/abs/1106.3184v1

Computer Science

Information Theory

25 pages

Scientific paper

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 $n \times n^2$ Gabor synthesis matrix is small provided $s \leq c \, n^{2/3} / \log^2 n$. This improves on previous estimates that exhibit quadratic scaling of $n$ in $s$. Our proof develops bounds for a corresponding chaos process.

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