D. L. Donoho, Compressed sensing, IEEE Transactions on Information Theory, vol.52, issue.4, pp.1289-1306, 2006.
DOI : 10.1109/TIT.2006.871582

URL : https://hal.archives-ouvertes.fr/inria-00369486

R. G. Baraniuk, M. Davenport, R. A. Devore, and M. Wakin, A Simple Proof of the Restricted Isometry Property for Random Matrices, Constructive Approximation, vol.159, issue.2, pp.253-263, 2008.
DOI : 10.1007/s00365-007-9003-x

E. J. Candès and T. Tao, Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?, IEEE Transactions on Information Theory, vol.52, issue.12, pp.5406-5425, 2006.
DOI : 10.1109/TIT.2006.885507

H. Rauhut, Stability Results for Random Sampling of Sparse Trigonometric Polynomials, IEEE Transactions on Information Theory, vol.54, issue.12, pp.5661-5670, 2008.
DOI : 10.1109/TIT.2008.2006382

M. Rudelson and R. Vershynin, Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements, 2006 40th Annual Conference on Information Sciences and Systems, 2006.
DOI : 10.1109/CISS.2006.286463

URL : http://arxiv.org/abs/math/0602559

W. Bajwa, J. Haupt, G. Raz, S. Wright, and R. Nowak, Toeplitzstructured compressed sensing matrices, IEEE Workshop SSP, 2007.

J. Romberg, Compressive Sensing by Random Convolution, SIAM Journal on Imaging Sciences, vol.2, issue.4, 2008.
DOI : 10.1137/08072975X

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.329.5393

W. U. Bajwa, J. Haupt, G. Raz, and R. Nowak, Compressed channel sensing, 2008 42nd Annual Conference on Information Sciences and Systems, 2008.
DOI : 10.1109/CISS.2008.4558485

S. Boyd and L. Vandenberghe, Convex Optimization, 2004.

B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, Least angle regression, Ann. Statist, vol.32, issue.2, pp.407-499, 2004.

G. Davis, S. Mallat, and M. Avellaneda, Adaptive greedy approximations, Constructive Approximation, vol.21, issue.1, pp.57-98, 1997.
DOI : 10.1007/BF02678430

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.47.7530

E. J. Candès, J. , T. Tao, J. Romberg, D. L. Donoho et al., Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information, IEEE Transactions on Information Theory, vol.52, issue.2, pp.489-509, 2006.
DOI : 10.1109/TIT.2005.862083

R. Gribonval and M. Nielsen, Sparse representations in unions of bases, IEEE Transactions on Information Theory, vol.49, issue.12, pp.3320-3325, 2003.
DOI : 10.1109/TIT.2003.820031

URL : https://hal.archives-ouvertes.fr/inria-00570057

H. Rauhut, Random sampling of sparse trigonometric polynomials, Applied and Computational Harmonic Analysis, vol.22, issue.1, pp.16-42, 2007.
DOI : 10.1016/j.acha.2006.05.002

E. J. Candès, The restricted isometry property and its implications for compressed sensing, Compte Rendus de l'Academie des Sciences, pp.589-592, 2008.
DOI : 10.1016/j.crma.2008.03.014

S. Foucart and M. Lai, Sparsest solutions of underdetermined linear systems via ?q-minimization for 0 < q ? 1, Appl. Comput. Harmon. Anal

J. Tropp, M. Wakin, M. Duarte, D. Baron, and R. Baraniuk, Random Filters for Compressive Sampling and Reconstruction, 2006 IEEE International Conference on Acoustics Speed and Signal Processing Proceedings, pp.872-875, 2006.
DOI : 10.1109/ICASSP.2006.1660793

J. J. Fuchs, On Sparse Representations in Arbitrary Redundant Bases, IEEE Transactions on Information Theory, vol.50, issue.6, pp.1341-1344, 2004.
DOI : 10.1109/TIT.2004.828141

J. A. Tropp, Recovery of Short, Complex Linear Combinations Via<tex>$ell _1$</tex>Minimization, IEEE Transactions on Information Theory, vol.51, issue.4, pp.1568-1570, 2005.
DOI : 10.1109/TIT.2005.844057

A. Buchholz, Operator Khintchine inequality in non-commutative probability, Mathematische Annalen, vol.319, issue.1, pp.1-16, 2001.
DOI : 10.1007/PL00004425

J. Bourgain and L. Tzafriri, Invertibility of ???large??? submatrices with applications to the geometry of Banach spaces and harmonic analysis, Israel Journal of Mathematics, vol.16, issue.5, pp.137-224, 1987.
DOI : 10.1007/BF02772174

V. H. De-la-peña and E. Giné, Decoupling, From dependence to independence, ser. Probability and its Applications, 1999.

T. R. Mcconnell and M. S. Taqqu, Decoupling Inequalities for Multilinear Forms in Independent Symmetric Random Variables, The Annals of Probability, vol.14, issue.3, pp.943-951, 1986.
DOI : 10.1214/aop/1176992449