S. Mallat, [A wavelet tour of signal processing, 1998.

J. Guerrero-colon, L. Mancera, and J. Portilla, Image Restoration Using Space-Variant Gaussian Scale Mixtures in Overcomplete Pyramids, IEEE Transactions on Image Processing, vol.17, issue.1, pp.27-41, 2008.
DOI : 10.1109/TIP.2007.911473

J. Pesquet, A. Benazza-benyahia, C. , and C. , A SURE Approach for Digital Signal/Image Deconvolution Problems, IEEE Transactions on Signal Processing, vol.57, issue.12, 2009.
DOI : 10.1109/TSP.2009.2026077

URL : https://hal.archives-ouvertes.fr/hal-00621942

C. Vonesch and M. Unser, A Fast Multilevel Algorithm for Wavelet-Regularized Image Restoration, IEEE Transactions on Image Processing, vol.18, issue.3, pp.509-523, 2009.
DOI : 10.1109/TIP.2008.2008073

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.193.6699

E. Candès, L. Demanet, D. Donoho, Y. , and L. , Fast Discrete Curvelet Transforms, Multiscale Modeling & Simulation, vol.5, issue.3, pp.861-899, 2006.
DOI : 10.1137/05064182X

I. W. Selesnick, R. G. Baraniuk, and N. G. Kingsbury, The dual-tree complex wavelet transform, IEEE Signal Processing Magazine, vol.22, issue.6, pp.123-151, 2005.
DOI : 10.1109/MSP.2005.1550194

S. Mallat, Geometrical grouplets, Applied and Computational Harmonic Analysis, vol.26, issue.2, pp.161-180, 2009.
DOI : 10.1016/j.acha.2008.03.004

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

M. Carlavan, P. Weiss, L. Blanc-féraud, and J. Zerubia, Algorithme rapide pour la restauration d'image rgularise sur les coefficients d'ondelettes, Proc. GRETSI, 2009.

Y. Nesterov, Gradient methods for minimizing composite objective function, CORE Discussion paper, vol.76, 2007.

P. L. Combettes, D. Dung, C. Vu, and B. , Dualization of Signal Recovery Problems, Set-Valued and Variational Analysis, vol.1, issue.3-4, 2009.
DOI : 10.1007/s11228-010-0147-7

C. Chaux, P. L. Combettes, J. Pesquet, and V. R. Wajs, A variational formulation for frame-based inverse problems, Inverse Problems, vol.23, issue.4, pp.1495-1518, 2007.
DOI : 10.1088/0266-5611/23/4/008

URL : https://hal.archives-ouvertes.fr/hal-00621883

P. L. Combettes and J. Pesquet, A proximal decomposition method for solving convex variational inverse problems, Inverse Problems, vol.24, issue.6, 2008.
DOI : 10.1088/0266-5611/24/6/065014

URL : https://hal.archives-ouvertes.fr/hal-00692901

J. J. Moreau, Proximit?? et dualit?? dans un espace hilbertien, Bulletin de la Société mathématique de France, vol.79, pp.273-299, 1965.
DOI : 10.24033/bsmf.1625

A. Tikhonov, Tikhonov regularization of incorrectly posed problems, Soviet Mathematics Doklady, vol.4, pp.1624-1627, 1963.

P. Weiss, L. Blanc-fraud, A. , and G. , Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing, SIAM Journal on Scientific Computing, vol.31, issue.3, pp.2047-2080, 2008.
DOI : 10.1137/070696143

URL : https://hal.archives-ouvertes.fr/inria-00166096

I. Daubechies, M. Defrise, and C. D. 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, A Douglas???Rachford Splitting Approach to Nonsmooth Convex Variational Signal Recovery, IEEE Journal of Selected Topics in Signal Processing, vol.1, issue.4, pp.564-574, 2007.
DOI : 10.1109/JSTSP.2007.910264

URL : https://hal.archives-ouvertes.fr/hal-00621820

H. H. Bauschke and P. L. Combettes, A Dykstra-like algorithm for two monotone operators, Pacific Journal of Optimization, 2008.

J. J. Moreau, Fonctions convexes duales et points proximaux dans un espace hilbertien, C. R. Acad. Sci, vol.255, pp.2897-2899, 1962.

P. L. Combettes and V. R. Wajs, Signal Recovery by Proximal Forward-Backward Splitting, Multiscale Modeling & Simulation, vol.4, issue.4, pp.1168-1200, 2005.
DOI : 10.1137/050626090

URL : https://hal.archives-ouvertes.fr/hal-00017649

C. Z?-alinescu, [Convex analysis in general vector spaces], World Scientific, 2002.

R. L. De-queiroz, T. Q. Nguyen, and K. R. Rao, The GenLOT: generalized linear-phase lapped orthogonal transform, IEEE Transactions on Signal Processing, vol.44, issue.3, pp.497-507, 1996.
DOI : 10.1109/78.489023

J. Gauthier, L. Duval, and J. Pesquet, Optimization of Synthesis Oversampled Complex Filter Banks, IEEE Transactions on Signal Processing, vol.57, issue.10, 2009.
DOI : 10.1109/TSP.2009.2023947

URL : https://hal.archives-ouvertes.fr/hal-00405293

R. Coifman and D. Donoho, Translation-Invariant De-Noising, Lecture Notes in Statistics, vol.103, pp.125-150, 1995.
DOI : 10.1007/978-1-4612-2544-7_9

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.125.3682