Theory of Signals/Mathematical Analysis
The restricted isometry property and its implications for compressed sensing
Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 589-592.

It is now well-known that one can reconstruct sparse or compressible signals accurately from a very limited number of measurements, possibly contaminated with noise. This technique known as “compressed sensing” or “compressive sampling” relies on properties of the sensing matrix such as the restricted isometry property. In this Note, we establish new results about the accuracy of the reconstruction from undersampled measurements which improve on earlier estimates, and have the advantage of being more elegant.

Il est maintenant bien connu que l'on peut reconstruire des signaux compressibles de manière précise à partir d'un nombre étonnamment petit de mesures, peut-être même bruitées. Cette technique appelée le “compressed sensing” ou “compressive sampling” utilise des propriétés de la matrice d'échantillonage comme la propriété d'isométrie restreinte. Dans cette Note, nous présentons de nouveaux résultats sur la reconstruction de signaux à partir de données incomplètes qui améliorent des travaux précedents et qui, en outre, ont l'avantage d'être plus élégants.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.03.014
Candès, Emmanuel J. 1

1 Applied & Computational Mathematics, California Institute of Technology, Pasadena, CA 91125-5000, USA
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Candès, Emmanuel J. The restricted isometry property and its implications for compressed sensing. Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 589-592. doi : 10.1016/j.crma.2008.03.014. http://www.numdam.org/articles/10.1016/j.crma.2008.03.014/

[1] Candès, E.J.; Romberg, J.; Tao, T. Stable signal recovery from incomplete and inaccurate measurements, Comm. Pure Appl. Math., Volume 59 (August 2006) no. 8, pp. 1207-1223

[2] Candès, E.J.; Tao, T. Decoding by linear programming, IEEE Trans. Inform. Theory, Volume 51 (December 2005) no. 12, pp. 4203-4215

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