R. 1. Combettes and J. Pesquet, Proximal Splitting Methods in Signal Processing, Fixed- Point Algorithms for Inverse Problems in Science and Engineering, pp.185-212, 2011.
DOI : 10.1007/978-1-4419-9569-8_10
URL : https://hal.archives-ouvertes.fr/hal-00643807

N. Parikh and S. Boyd, Proximal Algorithms, Foundations and Trends?? in Optimization, vol.1, issue.3, pp.123-231, 2013.
DOI : 10.1561/2400000003

M. Guerquin-kern, M. Häberlin, K. P. Pruessmann, and M. Unser, A Fast Wavelet-Based Reconstruction Method for Magnetic Resonance Imaging, IEEE Transactions on Medical Imaging, vol.30, issue.9, pp.1649-1660, 2011.
DOI : 10.1109/TMI.2011.2140121

F. Dupé, M. J. Fadili, and J. Starck, A Proximal Iteration for Deconvolving Poisson Noisy Images Using Sparse Representations, IEEE Transactions on Image Processing, vol.18, issue.2, pp.310-321, 2009.
DOI : 10.1109/TIP.2008.2008223

J. Aujol, G. Gilboa, T. Chan, and S. Osher, Structure-Texture Image Decomposition???Modeling, Algorithms, and Parameter Selection, International Journal of Computer Vision, vol.4, issue.2, pp.111-136, 2006.
DOI : 10.1007/s11263-006-4331-z
URL : https://hal.archives-ouvertes.fr/hal-00201977

L. M. Briceño-arias, P. L. Combettes, J. Pesquet, and N. Pustelnik, Proximal Algorithms for Multicomponent Image Recovery Problems, Journal of Mathematical Imaging and Vision, vol.30, issue.1-2, pp.3-22, 2011.
DOI : 10.1007/s10851-010-0243-1

S. Theodoridis, K. Slavakis, and I. Yamada, Adaptive Learning in a World of Projections, IEEE Signal Processing Magazine, vol.28, issue.1, pp.97-123, 2011.
DOI : 10.1109/MSP.2010.938752

C. Chaux, M. El-gheche, J. Farah, J. Pesquet, and B. Pesquet-popescu, A Parallel Proximal Splitting Method for Disparity Estimation from Multicomponent Images Under Illumination Variation, Journal of Mathematical Imaging and Vision, vol.28, issue.4, pp.167-178, 2013.
DOI : 10.1007/s10851-012-0361-z
URL : https://hal.archives-ouvertes.fr/hal-00733454

S. Mallat, A wavelet tour of signal processing, 1997.

L. Jacques, L. Duval, C. Chaux, and G. Peyré, A panorama on multiscale geometric representations, intertwining spatial, directional and frequency selectivity, Signal Processing, vol.91, issue.12, pp.2699-2730, 2011.
DOI : 10.1016/j.sigpro.2011.04.025
URL : https://hal.archives-ouvertes.fr/hal-00588381

E. Van-den, M. P. Berg, and . Friedlander, Probing the Pareto Frontier for Basis Pursuit Solutions, SIAM Journal on Scientific Computing, vol.31, issue.2, pp.890-912, 2008.
DOI : 10.1137/080714488

R. Ciak, B. Shafei, and G. Steidl, Homogeneous Penalizers and Constraints in Convex Image Restoration, Journal of Mathematical Imaging and Vision, vol.21, issue.4, 2012.
DOI : 10.1007/s10851-012-0392-5

D. C. Youla and H. Webb, Image Restoration by the Method of Convex Projections: Part 1ߞTheory, IEEE Transactions on Medical Imaging, vol.1, issue.2, pp.81-94, 1982.
DOI : 10.1109/TMI.1982.4307555

H. J. Trussell and M. R. Civanlar, The feasible solution in signal restoration, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.32, issue.2, pp.201-212, 1984.
DOI : 10.1109/TASSP.1984.1164297

P. L. Combettes, Inconsistent signal feasibility problems: least-squares solutions in a product space, IEEE Transactions on Signal Processing, vol.42, issue.11, pp.2955-2966, 1994.
DOI : 10.1109/78.330356

T. Teuber, G. Steidl, and R. H. Chan, -divergence constraints, Inverse Problems, vol.29, issue.3, p.35007, 2013.
DOI : 10.1088/0266-5611/29/3/035007
URL : https://hal.archives-ouvertes.fr/hal-00868432

R. Stück, M. Burger, and T. Hohage, The iteratively regularized Gauss???Newton method with convex constraints and applications in 4Pi microscopy, Inverse Problems, vol.28, issue.1, 2012.
DOI : 10.1088/0266-5611/28/1/015012

S. Ono and I. Yamada, Poisson image restoration with likelihood constraint via hybrid steepest descent method, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, pp.5929-5933, 2013.
DOI : 10.1109/ICASSP.2013.6638802

S. Harizanov, J. Pesquet, and G. Steidl, Epigraphical Projection for Solving Least Squares Anscombe Transformed Constrained Optimization Problems, Scale Space and Variational Methods in Computer Vision, pp.125-136, 2013.
DOI : 10.1007/978-3-642-38267-3_11

S. Ono and I. Yamada, Second-order total Generalized Variation constraint, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2014.
DOI : 10.1109/ICASSP.2014.6854541

M. Tofighi, K. Kose, and A. E. Cetin, Signal reconstruction framework based on Projections onto Epigraph Set of a Convex cost function (PESC), 2014.

G. Chen and M. Teboulle, A proximal-based decomposition method for convex minimization problems, Mathematical Programming, vol.29, issue.1-3, pp.81-101, 1994.
DOI : 10.1007/BF01582566

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

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 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

M. Figueiredo, R. Nowak, and S. Wright, Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems, IEEE Journal of Selected Topics in Signal Processing, vol.1, issue.4, pp.586-598, 2007.
DOI : 10.1109/JSTSP.2007.910281

A. Beck and M. Teboulle, A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems, SIAM Journal on Imaging Sciences, vol.2, issue.1, pp.183-202, 2009.
DOI : 10.1137/080716542

M. Fornasier and C. Schönlieb, Subspace Correction Methods for Total Variation and $\ell_1$-Minimization, SIAM Journal on Numerical Analysis, vol.47, issue.5, pp.3397-3428, 2009.
DOI : 10.1137/070710779

G. Steidl and T. Teuber, Removing Multiplicative Noise by Douglas-Rachford Splitting Methods, Journal of Mathematical Imaging and Vision, vol.11, issue.11, pp.168-184, 2010.
DOI : 10.1007/s10851-009-0179-5

J. Pesquet and N. Pustelnik, A parallel inertial proximal optimization method, Pac. J. Optim, vol.8, issue.2, pp.273-305, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00790702

E. Esser, X. Zhang, and T. Chan, A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science, SIAM Journal on Imaging Sciences, vol.3, issue.4, pp.1015-1046, 2010.
DOI : 10.1137/09076934X

A. Chambolle and T. Pock, A First-Order Primal-Dual Algorithm for Convex Problems with??Applications to Imaging, Journal of Mathematical Imaging and Vision, vol.60, issue.5, pp.120-145, 2011.
DOI : 10.1007/s10851-010-0251-1
URL : https://hal.archives-ouvertes.fr/hal-00490826

L. M. Briceño-arias and P. L. Combettes, A Monotone+Skew Splitting Model for Composite Monotone Inclusions in Duality, SIAM Journal on Optimization, vol.21, issue.4, pp.1230-1250, 2011.
DOI : 10.1137/10081602X

P. L. Combettes and J. Pesquet, Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators. Set-Valued Var, Anal, vol.20, issue.2, pp.307-330, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00794044

B. C. V?uv?u, A splitting algorithm for dual monotone inclusions involving cocoercive operators, Adv. Comput. Math, vol.38, issue.3, pp.667-681, 2013.

L. Condat, A Primal???Dual Splitting Method for Convex Optimization Involving Lipschitzian, Proximable and Linear Composite Terms, Journal of Optimization Theory and Applications, vol.23, issue.1???2, pp.460-479, 2012.
DOI : 10.1007/s10957-012-0245-9
URL : https://hal.archives-ouvertes.fr/hal-00609728

P. Chen, J. Huang, and X. Zhang, A primal???dual fixed point algorithm for convex separable minimization with applications to image restoration, Inverse Problems, vol.29, issue.2, p.2013
DOI : 10.1088/0266-5611/29/2/025011

M. A. Alghamdi, A. Alotaibi, P. L. Combettes, and N. Shahzad, A primal-dual method of partial inverses for composite inclusions, Optimization Letters, vol.38, issue.8, 2014.
DOI : 10.1007/s11590-014-0734-x
URL : https://hal.archives-ouvertes.fr/hal-01158985

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

H. H. Bauschke and P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, 2011.
DOI : 10.1007/978-1-4419-9467-7
URL : https://hal.archives-ouvertes.fr/hal-00643354

P. L. Combettes, A block-iterative surrogate constraint splitting method for quadratic signal recovery, IEEE Transactions on Signal Processing, vol.51, issue.7, pp.1771-1782, 2003.
DOI : 10.1109/TSP.2003.812846

Y. Kopsinis, K. Slavakis, and S. Theodoridis, Online sparse system identification and signal reconstruction using projections onto weighted 1 balls, pp.936-952, 2011.

A. Quattoni, X. Carreras, M. Collins, and T. Darrell, An efficient projection for 1,? regularization, International Conference on Machine Learning, 2009.
DOI : 10.1145/1553374.1553484
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.149.6140

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

G. Gilboa and S. Osher, Nonlocal Operators with Applications to Image Processing, Multiscale Modeling & Simulation, vol.7, issue.3, p.1005, 2009.
DOI : 10.1137/070698592

R. Gaetano, G. Chierchia, and B. Pesquet-popescu, Parallel implementations of a disparity estimation algorithm based on a Proximal splitting method, 2012 Visual Communications and Image Processing, 2012.
DOI : 10.1109/VCIP.2012.6410734

E. J. Candès, M. B. Wakin, and S. Boyd, Enhancing Sparsity by Reweighted ??? 1 Minimization, Journal of Fourier Analysis and Applications, vol.7, issue.3, pp.877-905, 2008.
DOI : 10.1007/s00041-008-9045-x

A. Tikhonov, Regularization of incorrectly posed problems, Sov. Math. Dokl, vol.4, pp.1624-1627, 1963.

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. Wu, F. Liu, L. C. Jiao, X. Wang, and B. Hou, Multivariate Compressive Sensing for Image Reconstruction in the Wavelet Domain: Using Scale Mixture Models, IEEE Transactions on Image Processing, vol.20, issue.12, pp.3483-3494, 2011.
DOI : 10.1109/TIP.2011.2150231

B. A. Turlach, W. N. Venables, and S. J. Wright, Simultaneous Variable Selection, Technometrics, vol.47, issue.3, pp.349-363, 2005.
DOI : 10.1198/004017005000000139

Y. Chen and A. O. Hero, Recursive <formula formulatype="inline"><tex Notation="TeX">$\ell_{1,\infty}$</tex> </formula> Group Lasso, IEEE Transactions on Signal Processing, vol.60, issue.8, pp.3978-3987, 2012.
DOI : 10.1109/TSP.2012.2192924

C. Studer, T. Goldstein, W. Yin, and R. G. Baraniuk, Democratic representations, 2014.

M. V. Afonso, J. M. Bioucas-dias, and M. A. Figueiredo, An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems, IEEE Transactions on Image Processing, vol.20, issue.3, pp.681-695, 2011.
DOI : 10.1109/TIP.2010.2076294

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Machine Learn, pp.1-122, 2011.

C. Ding, D. F. Sun, and K. Toh, An introduction to a class of matrix cone programming, Mathematical Programming, vol.20, issue.1-2, pp.1-39, 2012.
DOI : 10.1007/s10107-012-0619-7

D. L. Donoho, De-noising by soft-thresholding, IEEE Transactions on Information Theory, vol.41, issue.3, pp.613-627, 1995.
DOI : 10.1109/18.382009

F. Bach, R. Jenatton, J. Mairal, and G. Obozinski, Optimization with Sparsity-Inducing Penalties, Machine Learning, pp.1-106, 2012.
DOI : 10.1561/2200000015
URL : https://hal.archives-ouvertes.fr/hal-00613125

K. Bredies, K. Kunisch, and T. Pock, Total Generalized Variation, SIAM Journal on Imaging Sciences, vol.3, issue.3, pp.492-526, 2010.
DOI : 10.1137/090769521

A. Buades, B. Coll, and J. Morel, A Review of Image Denoising Algorithms, with a New One, Multiscale Modeling & Simulation, vol.4, issue.2, pp.490-530, 2005.
DOI : 10.1137/040616024
URL : https://hal.archives-ouvertes.fr/hal-00271141

G. Gilboa and S. Osher, Nonlocal Linear Image Regularization and Supervised Segmentation, Multiscale Modeling & Simulation, vol.6, issue.2, pp.595-630, 2007.
DOI : 10.1137/060669358

A. Foi and G. Boracchi, Foveated self-similarity in nonlocal image filtering, Human Vision and Electronic Imaging XVII, 2012.
DOI : 10.1117/12.912217

Y. Li and S. Osher, A new median formula with applications to PDE based denoising, Communications in Mathematical Sciences, vol.7, issue.3, pp.741-753, 2009.
DOI : 10.4310/CMS.2009.v7.n3.a11

X. Bresson and T. F. Chan, Fast dual minimization of the vectorial total variation norm and applications to color image processing, Inverse Problems and Imaging, vol.2, issue.4, pp.455-484, 2008.
DOI : 10.3934/ipi.2008.2.455

T. Miyata and Y. Sakai, Vectorized total variation defined by weighted L infinity norm for utilizing inter channel dependency, 2012 19th IEEE International Conference on Image Processing, pp.3057-3060, 2012.
DOI : 10.1109/ICIP.2012.6467545

Z. Wang and A. C. Bovik, Mean squared error: Love it or leave it? A new look at Signal Fidelity Measures, IEEE Signal Processing Magazine, vol.26, issue.1, pp.98-117, 2009.
DOI : 10.1109/MSP.2008.930649

M. Yuan and Y. Lin, Model selection and estimation in regression with grouped variables, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.58, issue.1, pp.49-67, 2006.
DOI : 10.1198/016214502753479356

I. Ekeland and R. Témam, Convex analysis and variational problems, SIAM, 1999.
DOI : 10.1137/1.9781611971088

P. L. Combettes and J. Pesquet, Proximal Thresholding Algorithm for Minimization over Orthonormal Bases, SIAM Journal on Optimization, vol.18, issue.4, pp.1351-1376, 2007.
DOI : 10.1137/060669498
URL : https://hal.archives-ouvertes.fr/hal-00621819