D. L. Donoho, For most large underdetermined systems of linear equations the minimal ???1-norm solution is also the sparsest solution, Communications on Pure and Applied Mathematics, vol.50, issue.6, pp.797-829, 2006.
DOI : 10.1002/cpa.20132

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

M. Zibulevsky and B. A. Pearlmutter, Blind Source Separation by Sparse Decomposition in a Signal Dictionary, Neural Computation, vol.1, issue.4, pp.863-882, 2001.
DOI : 10.1016/S0042-6989(97)00169-7

D. L. Donoho, M. Elad, and V. Temlyakov, Stable recovery of sparse overcomplete representations in the presence of noise, IEEE Transactions on Information Theory, vol.52, issue.1
DOI : 10.1109/TIT.2005.860430

M. Davies and N. Mitianoudis, Simple mixture model for sparse overcomplete ICA, Proc. Inst. Electr. Eng.?Vis. Image Signal Process, pp.35-43, 2004.
DOI : 10.1049/ip-vis:20040304

Y. Q. Li, S. Amari, A. Cichocki, D. W. Ho, and S. Xie, Underdetermined blind source separation based on sparse representation, IEEE Trans. Signal Process, vol.54, issue.2, pp.423-437, 2006.

P. G. Georgiev, F. J. Theis, and A. Cichocki, Sparse Component Analysis and Blind Source Separation of Underdetermined Mixtures, IEEE Transactions on Neural Networks, vol.16, issue.4, pp.992-996, 2005.
DOI : 10.1109/TNN.2005.849840

R. Gribonval and S. Lesage, A survey of sparse component analysis for blind source separation: Principles, perspectives, and new challenges, Proc. Eur. Symp. Artificial Neuran Networks (ESANN), pp.323-330, 2006.
URL : https://hal.archives-ouvertes.fr/inria-00544897

S. 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

J. L. Stark, M. Elad, and D. Donoho, Image decomposition via the combination of sparse representations and a variational approach, IEEE Transactions on Image Processing, vol.14, issue.10, pp.1570-1582, 2005.
DOI : 10.1109/TIP.2005.852206

M. Elad, R. Goldenberg, and R. Kimmel, Low Bit-Rate Compression of Facial Images, IEEE Transactions on Image Processing, vol.16, issue.9, pp.2379-2383, 2007.
DOI : 10.1109/TIP.2007.903259

M. Elad and M. Aharon, Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries, IEEE Transactions on Image Processing, vol.15, issue.12, pp.3736-3745, 2006.
DOI : 10.1109/TIP.2006.881969

O. G. Guleryuz, Nonlinear approximation based image recovery using adaptive sparse reconstructions and iterated denoising-part I: theory, IEEE Transactions on Image Processing, vol.15, issue.3, pp.539-554, 2006.
DOI : 10.1109/TIP.2005.863057

E. J. Candès and T. Tao, Decoding by Linear Programming, IEEE Transactions on Information Theory, vol.51, issue.12, pp.4203-4215, 2005.
DOI : 10.1109/TIT.2005.858979

M. Akcakaya and V. Tarokh, On Sparsity, Redundancy and Quality of Frame Representations, 2007 IEEE International Symposium on Information Theory, pp.951-955, 2007.
DOI : 10.1109/ISIT.2007.4557114

H. Zayyani, M. Babaie-zadeh, and C. Jutten, Decoding real-field codes by an iterative Expectation-Maximization (EM) algorithm, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, pp.3169-3172, 2008.
DOI : 10.1109/ICASSP.2008.4518323

URL : https://hal.archives-ouvertes.fr/hal-00271360

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

T. Blumensath and M. Davis, Compressed Sensing and Source Separation, Proc. IEEE Int. Conf. Acoustics (ICA), pp.341-348, 2007.
DOI : 10.1007/978-3-540-74494-8_43

L. Vielva, D. Erdogmus, and C. Principe, Underdetermined blind source separation using a probabilistic source sparsity model, Proc

C. Fevotte and S. J. , A Bayesian Approach for Blind Separation of Sparse Sources, IEEE Transactions on Audio, Speech and Language Processing, vol.14, issue.6, pp.2174-2188, 2006.
DOI : 10.1109/TSA.2005.858523

I. F. Gorodnitski 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

M. Babaie-zadeh, C. Jutten, and A. Mansour, Sparse ICA via cluster-wise PCA, Neurocomputing, vol.69, issue.13-15, pp.1458-1466, 2006.
DOI : 10.1016/j.neucom.2005.12.022

URL : https://hal.archives-ouvertes.fr/hal-00097157

A. A. Amini, M. Babaie-zadeh, and C. Jutten, A Fast Method for Sparse Component Analysis Based on Iterative Detection-Estimation, AIP Conference Proceedings, pp.123-130, 2006.
DOI : 10.1063/1.2423268

H. Zayyani, M. Babaie-zadeh, and C. Jutten, Source Estimation in Noisy Sparse Component Analysis, 2007 15th International Conference on Digital Signal Processing, pp.219-222, 2007.
DOI : 10.1109/ICDSP.2007.4288558

URL : https://hal.archives-ouvertes.fr/hal-00173337

G. H. Mohimani, M. Babaie-zadeh, and C. Jutten, A Fast Approach for Overcomplete Sparse Decomposition Based on Smoothed <formula formulatype="inline"><tex Notation="TeX">$\ell ^{0}$</tex></formula> Norm, IEEE Transactions on Signal Processing, vol.57, issue.1, pp.289-301, 2009.
DOI : 10.1109/TSP.2008.2007606

G. H. Mohimani, M. Babaie-zadeh, and C. Jutten, Fast sparse representation based on smoothed`-smoothed`smoothed`-norm, Proc. IEEE Int. Conf. Acoustics (ICA), pp.389-396, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00173357

H. Zayyani, M. Babaie-zadeh, G. H. Mohimani, and C. Jutten, Sparse Component Analysis in Presence of Noise Using an Iterative EM-MAP Algorithm, Proc. IEEE Int. Conf. Acoustics (ICA), pp.438-445, 2007.
DOI : 10.1007/978-3-540-74494-8_55

URL : https://hal.archives-ouvertes.fr/hal-00173379

S. Mallat and Z. Zhang, Matching pursuits with time-frequency dictionaries, IEEE Transactions on Signal Processing, vol.41, issue.12, pp.3397-3415, 1993.
DOI : 10.1109/78.258082

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.335.5769

M. Lewicki and T. J. Sejnowski, Learning Overcomplete Representations, Neural Computation, vol.33, issue.2, pp.337-365, 2000.
DOI : 10.1109/18.119725

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.164.7690

S. Krstulovic and R. Gribonval, Mptk: Matching Pursuit Made Tractable, 2006 IEEE International Conference on Acoustics Speed and Signal Processing Proceedings, pp.496-499, 2006.
DOI : 10.1109/ICASSP.2006.1660699

URL : https://hal.archives-ouvertes.fr/inria-00544919

Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad, Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers, pp.40-44, 1993.
DOI : 10.1109/ACSSC.1993.342465

D. L. Donoho, Y. Tsaig, I. Drori, J. L. Starck, and B. D. Rao, Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit Sparse Bayesian learning for basis selection, Tech. Rep. IEEE Trans. Signal Process, vol.52, issue.8, pp.2153-2164, 2004.

S. Ji, Y. Xue, and L. Carin, Bayesian Compressive Sensing, IEEE Transactions on Signal Processing, vol.56, issue.6, pp.2346-2356, 2008.
DOI : 10.1109/TSP.2007.914345

T. Blumensath and M. Davies, Gradient Pursuits, IEEE Transactions on Signal Processing, vol.56, issue.6, pp.2370-2382, 2008.
DOI : 10.1109/TSP.2007.916124

M. A. Figueirado, R. D. Nowak, S. J. Wright, and J. Sel, Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems Topics Signal Process Maximum likelihood estimation from incomplete data via the EM algorithm, J. Roy. Statist. Soc. B, vol.39, pp.1-38, 1977.

M. A. Figueirado and R. D. Nowak, An EM algorithm for wavelet-based image restoration, IEEE Transactions on Image Processing, vol.12, issue.8, pp.906-916, 2003.
DOI : 10.1109/TIP.2003.814255

H. L. Taylor, S. C. Banks, and J. F. Mccoy, Deconvolution with the ???1 norm, GEOPHYSICS, vol.44, issue.1, pp.39-52, 1979.
DOI : 10.1190/1.1440921

J. J. Kormylo and J. M. , Maximum likelihood detection and estimation of Bernoulli - Gaussian processes, IEEE Transactions on Information Theory, vol.28, issue.3, pp.482-488, 1982.
DOI : 10.1109/TIT.1982.1056496

M. Lavielle, Bayesian deconvolution of Bernoulli-Gaussian processes, Signal Processing, vol.33, issue.1, pp.67-79, 1993.
DOI : 10.1016/0165-1684(93)90079-P

I. Santamaria-caballero, C. J. Pantaleon-prieto, and A. Artes-rodriguez, Sparse deconvolution using adaptive mixed-Gaussian models, Signal Processing, vol.54, issue.2, pp.161-172, 1996.
DOI : 10.1016/S0165-1684(96)00105-3

A. M. Djafari, Bayesian source separation: Beyond PCA and ICA, Proc. Eur. Symp. Artificial Neuran Networks (ESANN), pp.313-322, 2006.

F. Labeau, J. C. Chiang, M. Kieffer, P. Duhamel, L. Vandendorpe et al., Oversampled filter banks as error correcting codes, The 5th International Symposium on Wireless Personal Multimedia Communications, pp.4619-4630, 2005.
DOI : 10.1109/WPMC.2002.1088382

E. Larsson and Y. Selen, Linear Regression With a Sparse Parameter Vector, IEEE Transactions on Signal Processing, vol.55, issue.2, pp.451-460, 2007.
DOI : 10.1109/TSP.2006.887109

A. M. Tomasi, B. D. Anderson, and J. B. Moore, Estimating Gaussian Mixture Density With EM?A Tutorial [Online] Available: http://www.cs.duke Optimal Filtering, 1979.

A. Blake and A. Zisserman, Visual Reconstruction, 1987.