T. Buades, B. Coll, and J. M. , A Review of Image Denoising Algorithms, with a New One, SIAM, Multiscale modeling and Simulation, pp.490-530, 2005.
DOI : 10.1137/040616024
URL : https://hal.archives-ouvertes.fr/hal-00271141

D. L. Donoho and I. M. Johnstone, Ideal spatial adaptation by wavelet shrinkage, Biometrika, vol.81, issue.3, pp.425-455, 1994.
DOI : 10.1093/biomet/81.3.425

S. Mallat, A Wavelet Tour of Signal Processing, 1998.

L. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena, vol.60, issue.1-4, pp.259-268, 1992.
DOI : 10.1016/0167-2789(92)90242-F

Y. Meyer, Oscillating paterns in image processing and in some nonlinear evolution equation, 2001.

F. Malgouyres, Minimizing the total variation under a general convex constraint for image restoration, IEEE Transactions on Image Processing, vol.11, issue.12, pp.1450-1456, 2002.
DOI : 10.1109/TIP.2002.806241

E. Candes and F. Guo, New multiscale transforms, minimun total variation synthesis: application to edge regularization in image compression, Signal Processing, issue.11, pp.821519-1543, 2002.

F. Malgouyres, Mathematical analysis of a model which combines total variation and wavelet for image restoration, Journal of information processes, vol.2, issue.1, pp.1-10, 2002.

S. Lintner and F. Malgouyres, Solving a variational image restoration model which involves l ? contraints, Inverse Problem, pp.815-831, 2004.

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
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.113.7694

J. Starck, M. Elad, and D. L. 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. Brown and N. P. Costen, Exploratory basis pursuit classification, Pattern Recognition Letters, vol.26, issue.12, pp.1907-1915, 2005.
DOI : 10.1016/j.patrec.2005.03.012

B. Matalon, M. Elad, and M. Zibulevsky, Image denoising with the contourlet transform, Proceedings of SPARSE'05, 2005.

M. J. Wainwright, V. Portilla, E. P. Strela, and . Simoncelli, Image enoising using scale mixtures of gaussians in the wavelet domain, IEEE Trans. Image Process, vol.12, issue.11, pp.1338-1351, 2003.

D. 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, pp.6-18, 2006.
DOI : 10.1109/TIT.2005.860430

D. Donoho and J. Tanner, Sparse nonegative solution of underdetermined linear equations by linear programming, 2005.

F. Malgouyres, Rank related properties for Basis Pursuit and total variation regularization, Signal Processing, vol.87, issue.11, 2006.
DOI : 10.1016/j.sigpro.2007.04.019
URL : https://hal.archives-ouvertes.fr/hal-00020801

F. Malgouyres, Projecting onto a polytope simplifies data distributions, 2006.

I. Daubechies, M. Defrise, and C. Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Communications on Pure and Applied Mathematics, vol.58, issue.11, pp.1413-1457, 2004.
DOI : 10.1002/cpa.20042

P. L. Combettes and J. Pesquet, Proximal Thresholding Algorithm for Minimization over Orthonormal Bases, SIAM Journal on Optimization, vol.18, issue.4
DOI : 10.1137/060669498
URL : https://hal.archives-ouvertes.fr/hal-00621819

J. Bect, L. Blanc-féraud, G. Aubert, and A. Chambolle, A l1-unified variational framework for image restoration, Proc. ECCV, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00217251

M. Figueiredo and R. Nowak, A bound optimization approach to wavelet-based image deconvolution, IEEE International Conference on Image Processing 2005, pp.782-785, 2005.
DOI : 10.1109/ICIP.2005.1530172

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

S. Sardy, A. G. Bruce, and P. Tseng, Block coordinate relaxation methods for nonparametric wavelet denoising, Journal of Computational and Graphical Statistics, vol.9, issue.2, pp.361-379, 2000.

M. Elad, Why Simple Shrinkage Is Still Relevant for Redundant Representations?, IEEE Transactions on Information Theory, vol.52, issue.12, pp.5559-5569, 2006.
DOI : 10.1109/TIT.2006.885522

M. Elad, B. Matalon, and M. Zibulevsky, Coordinate and subspace optimization methods for linear least squares with non-quadratic regularization, Applied and Computational Harmonic Analysis, vol.23, issue.3, 2007.
DOI : 10.1016/j.acha.2007.02.002

S. Maria and J. J. Fuchs, Application of the Global Matched Filter to Stap Data an Efficient Algorithmic Approach, 2006 IEEE International Conference on Acoustics Speed and Signal Processing Proceedings, pp.1013-1016, 2006.
DOI : 10.1109/ICASSP.2006.1661143
URL : https://hal.archives-ouvertes.fr/inria-00504570

D. Donoho and Y. Tsaig, Fast solution of l1 -norm minimization problems when the solution may be sparse, 2006.

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

S. Qian, D. Chen, and K. Chen, Signal approximation via data-adaptive normalized Gaussian functions and its applications for speech processing, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing, pp.141-144, 1992.
DOI : 10.1109/ICASSP.1992.225952

Y. C. Pati, R. Rezaiifar, and K. P. , 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
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.348.5735

. Kreutz-delgado, J. K. Murray, B. Rao, K. Engan, T. Lee et al., Dictionary Learning Algorithms for Sparse Representation, Neural Computation, vol.15, issue.2, pp.349-396, 2003.
DOI : 10.1162/089976601300014385
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2944020

P. Jost, P. Vandergheynst, S. Lesage, and R. Gribonval, MoTIF: An Efficient Algorithm for Learning Translation Invariant Dictionaries, 2006 IEEE International Conference on Acoustics Speed and Signal Processing Proceedings, 2006.
DOI : 10.1109/ICASSP.2006.1661411
URL : https://hal.archives-ouvertes.fr/inria-00544911

M. Aharon, M. Elad, and A. Bruckstein, <tex>$rm K$</tex>-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation, IEEE Transactions on Signal Processing, vol.54, issue.11, pp.4311-4322, 2006.
DOI : 10.1109/TSP.2006.881199

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
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.109.6477

J. Mairal, M. Elad, and G. Sapiro, Sparse Representation for Color Image Restoration, IEEE Transactions on Image Processing, vol.17, issue.1
DOI : 10.1109/TIP.2007.911828
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.102.6724

J. F. Aujol, G. Aubert, L. Blanc-ferraud, and A. Chambolle, Image Decomposition into a Bounded Variation Component and an Oscillating Component, Journal of Mathematical Imaging and Vision, vol.15, issue.3, pp.71-88, 2005.
DOI : 10.1007/s10851-005-4783-8
URL : https://hal.archives-ouvertes.fr/hal-00202001

T. Zeng and F. Malgouyres, Using gabor dictionaries in a tv ? l ? model, for denoising, Proceedings of ICASSP 2006, pp.865-868, 2006.

S. Lintner and F. Malgouyres, Solving a variational image restoration model which involves l ? contraints, Inverse Problem, pp.815-831, 2004.
DOI : 10.1088/0266-5611/20/3/010
URL : http://authors.library.caltech.edu/11772/1/LINip04.pdf

R. Acar and C. Vogel, Analysis of bounded variation penalty methods for ill-posed problems, Inverse Problems, vol.10, issue.6, pp.1217-1229, 1994.
DOI : 10.1088/0266-5611/10/6/003

J. F. Aujol, G. Gilboa, and S. Osher, Structure-texture image decomposition -modeling , algorithms and parameter section, 2005.
DOI : 10.1007/s11263-006-4331-z

M. Turner, Texture discrimination by gabor functions, Biological Cybernetics, pp.71-82, 1986.

R. Maria, Sparse image approximation with application to flexible image coding, 2005.

J. S-taylor and N. Cristianini, Support Vector Machines and other kernel-based learning methods, 2000.

R. T. Rockafellar, Convex analysis, 1970.
DOI : 10.1515/9781400873173

F. Malgouyres, Increase in the resolution of digital images: Variational theory and applications, 2000.

D. Donoho, Neighborly polytopes and sparse solution of underdetermined linear equations, 2005.

R. T. Rockafellar, Monotone Operators and the Proximal Point Algorithm, SIAM Journal on Control and Optimization, vol.14, issue.5, pp.877-898, 1976.
DOI : 10.1137/0314056

O. Güler, On the Convergence of the Proximal Point Algorithm for Convex Minimization, SIAM Journal on Control and Optimization, vol.29, issue.2, 1991.
DOI : 10.1137/0329022

P. Ciarlet, Introduction to numerical linear algebra and optimisation, 1989.

C. Lemarechal and C. Sagastizabal, Practial aspects of the moreau-yoshida regularization 1 : theoretical properties, SIAM, J. optimization, 1997.

Y. Nesterov, Introductory lectures on convex optimization : A basic course, 2004.
DOI : 10.1007/978-1-4419-8853-9

J. M. Borwein and W. B. Moors, Essentially strictly differentiable lipschitz functions, Tech. Rep., CECM, pp.95-124
DOI : 10.1006/jfan.1997.3101
URL : http://doi.org/10.1006/jfan.1997.3101

J. M. Borwein and W. B. Moors, A chain rule for essentially strictly differentiable lipschitz functions, Tech. Rep., CECM, pp.96-057

L. David, M. Donoho, V. Elad, and . Temlyakov, Stable recovery of sparse overcomplete representations in the presence of noise Information Theory, IEEE Transactions on, vol.52, issue.1, pp.6-18, 2004.

G. Hong-ye, A. G. Gao, and . Bruce, Wavelet shrinkage denoising using the non-negative garrote Waveshrink with firm shrinkage, Journal of Computational and Graphical Statistics Statistica Sinica, vol.7, issue.7, pp.469-488, 1997.

Z. Zhao, Wavelet shrinkage denoising by generalized threshold function, Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, pp.18-21, 2005.

P. J. Huber, Projection Pursuit, The Annals of Statistics, vol.13, issue.2, pp.435-525, 1985.
DOI : 10.1214/aos/1176349519

A. W. Van and . Vaart, Asymptotic Statistics(Cambridge Series in Statistical and Probabilistic Mathematics) (Paperback), 2000.

A. P. Dempster, N. M. Laird, and D. B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society, B, vol.39, pp.1-38, 1977.

Y. Stéphanieallassonnì-ere, A. Amit, and . Trouvé, Towards a coherent statistical framework for dense deformable template estimation, Journal of the Royal Statistical Society, Series B, vol.69, issue.1, pp.3-29, 2007.

G. C. Wei and M. A. Tanner, A Monte Carlo Implementation of the EM Algorithm and the Poor Man's Data Augmentation Algorithms, Journal of the American Statistical Association, vol.51, issue.411, pp.699-704, 1990.
DOI : 10.1214/aos/1176346060

L. Devroye, Nonuniform Random Variate Generation, 1986.

E. Kuhn and M. Lavielle, Coupling a stochastic approximation version of EM with an MCMC procedure, ESAIM: Probability and Statistics, vol.8, pp.115-131, 2004.
DOI : 10.1051/ps:2004007

Z. Jordan, M. I. Ghahramani, T. S. Jaakkola, and L. K. Saul, Learning in Graphical Models, chapter An introduction to variational methods for graphical models, pp.105-162, 1998.

R. Gribonval and P. Vandergheynst, On the exponential convergence of matching pursuits in quasi-incoherent dictionaries, IEEE Transactions on Information Theory, vol.52, issue.1, pp.255-261, 2006.
DOI : 10.1109/TIT.2005.860474
URL : https://hal.archives-ouvertes.fr/inria-00544945