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

E. Candès, J. Romberg, and T. Tao, 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

E. Candès, The Restricted Isometry Property and its implications for Compressed Sensing Compte Rendus de l, Academie des Sciences, pp.589-592, 2008.

E. J. Candés, M. B. Wakin, and S. P. Boyd, Enhancing sparsity by reweighted ell-1 minimization, J. Fourier Anal. Appl, 2008.

S. Chen, D. L. Donoho, and M. A. Saunders, Atomic Decomposition by Basis Pursuit, SIAM Journal on Scientific Computing, vol.20, issue.1, pp.33-61, 1999.
DOI : 10.1137/S1064827596304010

O. Christensen, An introduction to frames and Riesz bases, Birkhauser, 2003.

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

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

D. L. Donoho and M. Elad, Optimally sparse representation from overcomplete dictionaries via ? 1 norm minimization, Proc. Natl. Acad. Sci. USA, pp.2197-2002, 2002.

D. Donoho and J. Tanner, Counting faces of randomly projected polytopes when the projection radically lowers dimension, Journal of the American Mathematical Society, vol.22, issue.1, 2008.
DOI : 10.1090/S0894-0347-08-00600-0

S. Foucart and M. Lai, Sparsest solutions of underdetermined linear systems via ? q minimization for 0 < q ? 1, 2008.

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

I. F. Gorodnitsky and B. D. Rao, Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm, IEEE Transactions on Signal Processing, vol.45, issue.3, pp.600-616, 1997.
DOI : 10.1109/78.558475

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

R. Gribonval and M. Nielsen, On the strong uniqueness of highly sparse expansions from redundant dictionaries, Proc. Int Conf. Independent Component Analysis, 2004.
URL : https://hal.archives-ouvertes.fr/inria-00567341

R. Gribonval and M. Nielsen, Highly sparse representations from dictionaries are unique and independent of the sparseness measure, Applied and Computational Harmonic Analysis, vol.22, issue.3, pp.335-355, 2003.
DOI : 10.1016/j.acha.2006.09.003

URL : https://hal.archives-ouvertes.fr/inria-00544779

J. Tropp, Just relax: convex programming methods for identifying sparse signals in noise, IEEE Transactions on Information Theory, vol.52, issue.3, pp.1030-1051, 2006.
DOI : 10.1109/TIT.2005.864420