Suprema of chaos processes and the restricted isometry property

Felix Krahmer; Shahar Mendelson; Holger Rauhut

doi:10.1002/cpa.21504

Suprema of chaos processes and the restricted isometry property

Felix Krahmer
, Shahar Mendelson
, Holger Rauhut

Research output: Contribution to journal › Article › peer-review

148 Scopus citations

Abstract

We present a new bound for suprema of a special type of chaos process 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 ≳ s log² s log² n.

Original language	English
Pages (from-to)	1877-1904
Number of pages	28
Journal	Communications on Pure and Applied Mathematics
Volume	67
Issue number	11
DOIs	https://doi.org/10.1002/cpa.21504
State	Published - 1 Nov 2014
Externally published	Yes

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10.1002/cpa.21504

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abstract = "We present a new bound for suprema of a special type of chaos process 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 ≳ s log2 s log2 n.",

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AB - We present a new bound for suprema of a special type of chaos process 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 ≳ s log2 s log2 n.

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Suprema of chaos processes and the restricted isometry property

Abstract

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