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Suprema of Chaos Processes and the Restricted Isometry Property
Author(s) -
Krahmer Felix,
Mendelson Shahar,
Rauhut Holger
Publication year - 2014
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21504
Subject(s) - mathematics , restricted isometry property , chaining , isometry (riemannian geometry) , circulant matrix , combinatorics , property (philosophy) , row , upper and lower bounds , wavelet , set (abstract data type) , pure mathematics , discrete mathematics , algorithm , mathematical analysis , compressed sensing , psychology , philosophy , epistemology , database , artificial intelligence , computer science , psychotherapist , programming language
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 log 2 s log 2 n . © 2014 Wiley Periodicals, Inc.