M. Elad, P. Milanfar, and R. Rubinstein, Analysis versus synthesis in signal priors, Inverse Problems, vol.23, issue.3, pp.947-968, 2007.
DOI : 10.1088/0266-5611/23/3/007

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, 1998.
DOI : 10.1137/S1064827596304010

I. Tosic and P. Frossard, Dictionary Learning, IEEE Signal Processing Magazine, vol.28, issue.2, pp.27-38, 2011.
DOI : 10.1109/MSP.2010.939537

M. Yaghoobi and M. Davies, Dictionary Learning for Sparse Representations: A Pareto Curve Root Finding Approach, Lecture notes in computer science, pp.410-417, 2010.
DOI : 10.1007/978-3-642-15995-4_51

URL : https://hal.archives-ouvertes.fr/inria-00567528

M. Yaghoobi, T. Blumensath, and M. Davies, Dictionary Learning for Sparse Approximations With the Majorization Method, IEEE Transactions on Signal Processing, vol.57, issue.6, pp.2178-2191, 2009.
DOI : 10.1109/TSP.2009.2016257

R. Gribonval and K. Schnass, Dictionary identification sparse matrix-factorisation via ?1 minimisation, IEEE Trans. on Info. Theory, vol.56, issue.7, pp.3523-3539, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00541297

J. Mairal, F. Bach, J. Ponce, and G. Sapiro, Online learning for matrix factorization and sparse coding, Journal of Machine Learning Research, vol.11, pp.19-60, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00408716

Q. Geng, H. Wang, and J. Wright, On the local correctness of l1 minimization for dictionary learning, 2011.

S. Nam, M. E. Davies, M. Elad, and R. Gribonval, The cosparse analysis model and algorithms, Applied and Computational Harmonic Analysis, vol.34, issue.1, 2011.
DOI : 10.1016/j.acha.2012.03.006

URL : https://hal.archives-ouvertes.fr/inria-00602205

E. J. Candès, Y. C. Eldar, D. Needell, and P. Randall, Compressed sensing with coherent and redundant dictionaries, Applied and Computational Harmonic Analysis, vol.31, issue.1, pp.59-73, 2011.
DOI : 10.1016/j.acha.2010.10.002

G. Peyre and J. Fadili, Learning analysis sparsity priors, Proc. of Sampta'11, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00542016

M. Yaghoobi, S. Nam, R. Gribonval, and M. Davies, Analysis operator learning for overcomplete cosparse representations, EUSIPCO, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00583133

B. Ophir, M. Elad, N. Bertin, and M. D. Plumbley, Sequential minimal eigenvalues an approach to analysis dictionary learning, Proceedings of EUSIPCO, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00577231

J. Eckstein and D. P. Bertsekas, On the Douglas???Rachford splitting method and the proximal point algorithm for maximal monotone operators, Mathematical Programming, pp.293-318, 1992.
DOI : 10.1007/BF01581204

M. Afonso, J. Bioucas-dias, and M. Figueiredo, Fast Image Recovery Using Variable Splitting and Constrained Optimization, IEEE Transactions on Image Processing, vol.19, issue.9, pp.2345-2356, 2010.
DOI : 10.1109/TIP.2010.2047910

URL : http://arxiv.org/abs/0910.4887

T. Goldstein and S. Osher, The Split Bregman Method for L1-Regularized Problems, SIAM Journal on Imaging Sciences, vol.2, issue.2, pp.323-343, 2009.
DOI : 10.1137/080725891

S. Setzer, Split Bregman Algorithm, Douglas-Rachford Splitting and Frame Shrinkage, 2009.
DOI : 10.1137/080724265

R. T. Rockafellar, Augmented Lagrange Multiplier Functions and Duality in Nonconvex Programming, SIAM Journal on Control, vol.12, issue.2, pp.268-286, 1974.
DOI : 10.1137/0312021

K. C. Lee, J. Ho, and D. Kriegman, Acquiring linear subspaces for face recognition under variable lighting, pp.684-698, 2005.