Suprema of Chaos Processes and the Restricted Isometry Property |
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| Authors: | Felix Krahmer Shahar Mendelson Holger Rauhut |
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| Institution: | 1. Institute for Numerical and Applied Mathematics, University of G?ttingen, G?ttingen, Germany;2. Department of Mathematics Technion, Haifa, Israel;3. RWTH Aachen University Lehrstuhl C für Mathematik (Analysis), Aachen, Germany |
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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. © 2014 Wiley Periodicals, Inc. |
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