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arXiv · 1207.0235

Suprema of Chaos Processes and the Restricted Isometry Property

Felix Krahmer·Shahar Mendelson·Holger Rauhut
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Abstract

We present a new bound for suprema of a special type of chaos processes indexed by a set of matrices, which is based on a chaining method. As applications we show significantly improved estimates for the restricted isometry constants of partial random circulant matrices and time-frequency structured random matrices. In both cases the required condition on the number $m$ of rows in terms of the sparsity $s$ and the vector length $n$ is $m \gtrsim s \log^2 s \log^2 n$.

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Felix Krahmer, Shahar Mendelson, Holger Rauhut. 2013-09-19. Suprema of Chaos Processes and the Restricted Isometry Property. https://arxiv.org/abs/1207.0235

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