The restricted isometry property and its implications for compressed sensing

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 restrict...

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Published inComptes rendus. Mathématique Vol. 346; no. 9; pp. 589 - 592
Main Author CANDES, Emmanuel J
Format Journal Article
LanguageEnglish
Published Paris Elsevier SAS 01.05.2008
Elsevier
Subjects
Exact sciences and technology
General mathematics
General, history and biography
Mathematics
Sciences and techniques of general use
Measurement
Isometry
Mathematics
Matrices
Signal reconstruction
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Summary: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. To cite this article: E.J. Candès, C. R. Acad. Sci. Paris, Ser. I 346 (2008). 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. Pour citer cet article : E.J. Candès, C. R. Acad. Sci. Paris, Ser. I 346 (2008).
ISSN:1631-073X
1778-3569
1778-3569
DOI:10.1016/j.crma.2008.03.014