Uniform uncertainty principle for Bernoulli and subgaussian ensembles

Shahar Mendelson (1) , Alain Pajor (2) , Nicole Tomczak-Jaegermann (3)

1 Technion - Israel Institute of Technology [Haifa]
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
3 University of Alberta

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 earlier proved by the present authors, as a consequence of a deep 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.

Mots clés: uniform uncertainty principle; approximate reconstruction; random matrices; generic chaining.; generic chaining

Domaines: Analyse fonctionnelle [math.FA]

Shahar Mendelson, Alain Pajor, Nicole Tomczak-Jaegermann. Uniform uncertainty principle for Bernoulli and subgaussian ensembles. Constructive Approximation, 2008, 28 (3), pp.277-289. ⟨hal-00793740⟩