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.
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Communicated by Emmanuel J. Candes.
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Mendelson, S., Pajor, A. & Tomczak-Jaegermann, N. Uniform Uncertainty Principle for Bernoulli and Subgaussian Ensembles. Constr Approx 28, 277–289 (2008). https://doi.org/10.1007/s00365-007-9005-8
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DOI: https://doi.org/10.1007/s00365-007-9005-8