Suprema of Chaos Processes and the Restricted Isometry Property

Suprema of Chaos Processes and the Restricted Isometry Property

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 r...

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Veröffentlicht in:Communications on pure and applied mathematics 2014-11, Vol.67 (11), p.1877-1904
Hauptverfasser: Krahmer, Felix, Mendelson, Shahar, Rauhut, Holger
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Sprache:eng
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Algebra
Estimating techniques
Matrix
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creator Krahmer, Felix
Mendelson, Shahar
Rauhut, Holger
description 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. © 2014 Wiley Periodicals, Inc.
doi_str_mv 10.1002/cpa.21504
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subjects Algebra
Estimating techniques
Matrix
title Suprema of Chaos Processes and the Restricted Isometry Property
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