Suprema of Chaos Processes and the Restricted Isometry Property

Felix Krahmer; Shahar Mendelson; Holger Rauhut

Suprema of Chaos Processes and the Restricted Isometry Property

Probability 2013-09-20 v3 Information Theory math.IT

Authors: Felix Krahmer , Shahar Mendelson , Holger Rauhut

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 $m \gtrsim s \log^2 s \log^2 n$ .

Keywords

chaos processes suprema restricted isometry property random circulant matrices chaining method

Cite

@article{arxiv.1207.0235,
  title  = {Suprema of Chaos Processes and the Restricted Isometry Property},
  author = {Felix Krahmer and Shahar Mendelson and Holger Rauhut},
  journal= {arXiv preprint arXiv:1207.0235},
  year   = {2013}
}

Comments

revised version, accepted for publication in Communications on Pure and Applied Mathematics, a number of typos removed

Suprema of Chaos Processes and the Restricted Isometry Property

Abstract

Keywords

Cite

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