Constructive Approximation

, Volume 28, Issue 3, pp 277–289

Uniform Uncertainty Principle for Bernoulli and Subgaussian Ensembles

  • Shahar Mendelson
  • Alain Pajor
  • Nicole Tomczak-Jaegermann
Article

DOI: 10.1007/s00365-007-9005-8

Cite this article as:
Mendelson, S., Pajor, A. & Tomczak-Jaegermann, N. Constr Approx (2008) 28: 277. doi:10.1007/s00365-007-9005-8

Abstract

The paper considers random matrices with independent subgaussian columns and provides a new elementary proof of the Uniform Uncertainty Principle for such matrices. The Principle was introduced by Candes, Romberg and Tao in 2004; for subgaussian random matrices it was carlier proved by the present authors, as a consequence of a general result based on a generic chaining method of Talagrand. The present proof combines a simple measure concentration and a covering argument, which are standard tools of high-dimensional convexity.

Keywords

Uniform uncertainty principle Approximate reconstruction Random matrices Generic chaining 

Mathematics Subject Classification (2000)

46B07 41A45 94B75 52B05 62G99 

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Shahar Mendelson
    • 1
    • 2
  • Alain Pajor
    • 3
  • Nicole Tomczak-Jaegermann
    • 4
  1. 1.Centre for Mathematics and its ApplicationsThe Australian National UniversityCanberraAustralia
  2. 2.Department of MathematicsTechnion, I.I.T.HaifaIsrael
  3. 3.Laboratoire d’Analyse et Mathématiques AppliquéesUniversité Paris-EstMarne-la-Vallee Cedex 2France
  4. 4.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada

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