A. Miller, Subset Selection in Regression, 2002.

E. J. Candes 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

B. D. Jeffs and M. Gunsay, Restoration of blurred star field images by maximally sparse optimization, IEEE Transactions on Image Processing, vol.2, issue.2, pp.202-211, 1993.
DOI : 10.1109/83.217223

J. Bobin, J. L. Starck, J. M. Fadili, Y. Moudden, and D. L. Donoho, Morphological Component Analysis: An Adaptive Thresholding Strategy, IEEE Transactions on Image Processing, vol.16, issue.11, pp.2675-2681, 2007.
DOI : 10.1109/TIP.2007.907073

URL : https://hal.archives-ouvertes.fr/hal-00196076

B. K. Natarajan, Sparse Approximate Solutions to Linear Systems, SIAM Journal on Computing, vol.24, issue.2, pp.227-234, 1995.
DOI : 10.1137/S0097539792240406

J. John, J. M. Kormylo, and . Mendel, Maximum likelihood detection and estimation of Bernoulli-Gaussian processes, IEEE Transactions on Information Theory, vol.28, pp.482-488, 1982.

C. Soussen, J. Idier, D. Brie, and J. Duan, From Bernoulli–Gaussian Deconvolution to Sparse Signal Restoration, IEEE Transactions on Signal Processing, vol.59, issue.10, pp.4572-4584, 2011.
DOI : 10.1109/TSP.2011.2160633

I. Barbu, C. Herzet, and E. Mémin, Sparse models and pursuit algorithms for piv tomography, Forum on recent developments in Volume Reconstruction techniques applied to 3D fluid and solid mechanics, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00683436

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

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

I. Gorodnitsky and D. R. Bhaskar, 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

S. G. 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

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, 1993.
DOI : 10.1109/ACSSC.1993.342465

D. L. Donoho, Y. Tsaig, I. Drori, and J. L. Starck, Sparse Solution of Underdetermined Systems of Linear Equations by Stagewise Orthogonal Matching Pursuit, IEEE Transactions on Information Theory, vol.58, issue.2, 2006.
DOI : 10.1109/TIT.2011.2173241

S. Chen, S. A. Billings, and W. Luo, Orthogonal least squares methods and their application to non-linear system identification, International Journal of Control, vol.10, issue.5, pp.1873-1896, 1989.
DOI : 10.2307/2284566

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

T. Blumensath and M. E. Davies, Iterative Thresholding for Sparse Approximations, Journal of Fourier Analysis and Applications, vol.73, issue.10, pp.629-654, 2008.
DOI : 10.1007/s00041-008-9035-z

S. Foucart, Hard Thresholding Pursuit: An Algorithm for Compressive Sensing, SIAM Journal on Numerical Analysis, vol.49, issue.6, 2011.
DOI : 10.1137/100806278

D. Needell and J. A. Tropp, CoSaMP, Communications of the ACM, vol.53, issue.12, pp.301-321, 2009.
DOI : 10.1145/1859204.1859229

W. Dai and O. Milenkovic, Subspace Pursuit for Compressive Sensing Signal Reconstruction, IEEE Transactions on Information Theory, vol.55, issue.5, 2009.
DOI : 10.1109/TIT.2009.2016006

URL : http://arxiv.org/abs/0803.0811

B. A. Olshausen and D. J. Field, Sparse coding with an overcomplete basis set: A strategy employed by V1?, Vision Research, vol.37, issue.23, pp.3311-3325, 1997.
DOI : 10.1016/S0042-6989(97)00169-7

M. Girolami, A Variational Method for Learning Sparse and Overcomplete Representations, Neural Computation, vol.22, issue.10, pp.2517-2532, 2001.
DOI : 10.1109/18.119725

C. Févotte and S. J. , Blind Separation of Sparse Sources Using Jeffrey???s Inverse Prior and the EM Algorithm, Proc.?6th International Conference on Independent Component Analysis and Blind Source Separation, pp.593-600, 2006.
DOI : 10.1007/11679363_74

A. T. Cemgil, C. Févotte, and S. J. , Variational and stochastic inference for Bayesian source separation, Digital Signal Processing, vol.17, issue.5, pp.891-913, 2007.
DOI : 10.1016/j.dsp.2007.03.008

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.333.9835

D. P. Wipf and B. D. Rao, Sparse Bayesian Learning for Basis Selection, IEEE Transactions on Signal Processing, vol.52, issue.8, pp.2153-2164, 2004.
DOI : 10.1109/TSP.2004.831016

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.6861

D. P. Wipf, J. A. Palmer, and B. D. Rao, Perspectives on sparse Bayesian learning, Neural Inform. Process. Syst, 2004.

E. G. Larrson 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

P. Schniter, L. C. Potter, and J. Ziniel, Fast bayesian matching pursuit, 2008 Information Theory and Applications Workshop, pp.326-333, 2008.
DOI : 10.1109/ITA.2008.4601068

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.120.3231

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, 2008.
DOI : 10.1109/ICASSP.2008.4518323

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

D. Baron, S. Sarvotham, and R. G. Baraniuk, Bayesian Compressive Sensing Via Belief Propagation, IEEE Transactions on Signal Processing, vol.58, issue.1, 2009.
DOI : 10.1109/TSP.2009.2027773

C. Herzet and A. Drémeau, Sparse representation algorithms based on mean-field approximations, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing, 2010.
DOI : 10.1109/ICASSP.2010.5494965

URL : https://hal.archives-ouvertes.fr/inria-00589354

C. Herzet and A. Drémeau, Bayesian pursuit algorithms, EURASIP European Signal Processing Conference, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00673801

A. Drémeau and C. Herzet, Soft Bayesian pursuit algorithm for sparse representations, 2011 IEEE Statistical Signal Processing Workshop (SSP), 2011.
DOI : 10.1109/SSP.2011.5967699

K. Qiu and A. Dogandzic, ECME thresholding methods for sparse signal reconstruction, 2011.
DOI : 10.1109/ciss.2010.5464879

A. J. Miller, Subset Selection in Regression, 2002.

C. Couvreur and Y. Bresler, On the Optimality of the Backward Greedy Algorithm for the Subset Selection Problem, SIAM Journal on Matrix Analysis and Applications, vol.21, issue.3, pp.797-808, 2000.
DOI : 10.1137/S0895479898332928

N. Kenneth and . Berk, Forward and backward stepping in variable selection, Journal of Statistical Computation and Simulation, vol.10, issue.3-4, pp.177-185, 1980.

P. M. Broersen, Subset Regression with Stepwise Directed Search, Applied Statistics, vol.35, issue.2, pp.168-177, 1986.
DOI : 10.2307/2347267

D. Haugland, A Bidirectional Greedy Heuristic for the Subspace Selection Problem, Lecture Notes in Computer Science, vol.4638, pp.162-176, 2007.
DOI : 10.1007/978-3-540-74446-7_12

T. Zhang, Adaptive Forward-Backward Greedy Algorithm for Learning Sparse Representations, IEEE Transactions on Information Theory, vol.57, issue.7, 2011.
DOI : 10.1109/TIT.2011.2146690

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.388.4812

F. R. Kschischang, B. J. Frey, and H. A. Loeliger, Factor graphs and the sum-product algorithm, IEEE Transactions on Information Theory, vol.47, issue.2, pp.498-519, 2001.
DOI : 10.1109/18.910572

M. J. Beal and Z. Ghahramani, The variational bayesian em algorithm for incomplete data: with application to scoring graphical model structures, Bayesian Statistics, vol.7, 2003.

D. Ge, J. Idier, and E. L. Carpentier, Enhanced sampling schemes for MCMC based blind Bernoulli???Gaussian deconvolution, Signal Processing, vol.91, issue.4, pp.759-772, 2011.
DOI : 10.1016/j.sigpro.2010.08.009

URL : https://hal.archives-ouvertes.fr/hal-00517861

H. Zayyani, M. Babaie-zadeh, and C. Jutten, Bayesian Pursuit algorithm for sparse representation, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing, 2009.
DOI : 10.1109/ICASSP.2009.4959892

URL : https://hal.archives-ouvertes.fr/hal-00400478