, Volume 28, Issue 3, pp 277-289
Date: 12 Feb 2008

Uniform Uncertainty Principle for Bernoulli and Subgaussian Ensembles

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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.

Communicated by Emmanuel J. Candes.