J. Aujol, 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 : 10.1023/B:JMIV.0000011320.81911.38
URL : https://hal.archives-ouvertes.fr/hal-00202001

F. R. Bach, Consistency of the Group Lasso and Multiple Kernel Learning, Journal of Machine Learning Research, vol.9, pp.1179-1225, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00164735

F. R. Bach, Consistency of Trace Norm Minimization, Journal of Machine Learning Research, vol.9, pp.1019-1048, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00179522

H. H. Bauschke and P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00643354

J. F. Bonnans and A. Shapiro, Perturbation analysis of optimization problems. Springer Series in Operations Research and Financial Engineering, 2000.

M. Burger and S. Osher, Convergence rates of convex variational regularization, Inverse Problems, vol.20, issue.5, p.1411, 2004.
DOI : 10.1088/0266-5611/20/5/005

E. Candès and B. English, Exact Matrix Completion via Convex Optimization, In: Foundations of Computational Mathematics, vol.96, pp.717-772, 2009.

E. J. Candès, Robust principal component analysis?, Journal of the ACM, vol.58, issue.3, pp.1-11, 2011.
DOI : 10.1145/1970392.1970395

E. J. Candès and Y. Plan, Matrix Completion With Noise, Proceedings of the IEEE 98, pp.925-936, 2010.
DOI : 10.1109/JPROC.2009.2035722

E. J. Candès and B. Recht, Simple bounds for recovering low-complexity models, Mathematical Programming, vol.52, issue.3, pp.577-589, 2013.
DOI : 10.1137/070697835

E. J. Candès, T. Strohmer, and V. Voroninski, PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming, Communications on Pure and Applied Mathematics, vol.38, issue.5, pp.1241-1274, 2013.
DOI : 10.1109/9.554402

E. J. Candès and T. Tao, The Power of Convex Relaxation: Near-Optimal Matrix Completion, IEEE Transactions on Information Theory, vol.56, issue.5, pp.2053-2080, 2009.
DOI : 10.1109/TIT.2010.2044061

S. S. Chen, D. L. Donoho, and M. A. Saunders, Atomic decomposition by basis pursuit, In: SIAM journal on scientific computing, vol.201, pp.33-61, 1999.

A. Daniilidis, J. Malick, and H. Sendov, Spectral (isotropic) manifolds and their dimension, Journal d'Analyse Math??matique, vol.207, issue.1, 2014.
DOI : 10.1016/0024-3795(94)90009-4

V. Duval and G. Peyré, Exact Support Recovery for Sparse Spikes Deconvolution, Foundations of Computational Mathematics, vol.15, issue.5, 2013.
DOI : 10.1109/TIT.2012.2233859
URL : https://hal.archives-ouvertes.fr/hal-00839635

M. Elad, P. Milanfar, and R. Rubinstein, Analysis versus synthesis in signal priors, Inverse Problems, vol.23, issue.3, pp.947-957, 2007.
DOI : 10.1088/0266-5611/23/3/007

J. Fadili, Stable Recovery with Analysis Decomposable Priors, Proc. Sampta'13. 2013, pp.113-116
URL : https://hal.archives-ouvertes.fr/hal-00926727

M. Fazel, Matrix rank minimization with applications, 2002.

J. J. Fuchs, On Sparse Representations in Arbitrary Redundant Bases, IEEE Transactions on Information Theory, vol.50, issue.6, pp.1341-1344, 2004.
DOI : 10.1109/TIT.2004.828141

M. Golbabaee and P. Vandergheynst, Hyperspectral image compressed sensing via low-rank and joint-sparse matrix recovery, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp.2741-2744, 2012.
DOI : 10.1109/ICASSP.2012.6288484
URL : https://hal.archives-ouvertes.fr/hal-00705915

M. Grasmair, Linear convergence rates for Tikhonov regularization with positively homogeneous functionals, Inverse Problems, vol.27, issue.7, p.75014, 2011.
DOI : 10.1088/0266-5611/27/7/075014

M. Grasmair, O. Scherzer, and M. Haltmeier, Necessary and sufficient conditions for linear convergence of ???1-regularization, Communications on Pure and Applied Mathematics, vol.52, issue.3, pp.161-182, 2011.
DOI : 10.1515/9783110920291

E. Grave, G. Obozinski, and F. Bach, Trace Lasso: a trace norm regularization for correlated designs, Proc. NIPS. Ed. by John Shawe-Taylor et al. 2011, pp.2187-2195
URL : https://hal.archives-ouvertes.fr/hal-00620197

W. L. Hare, Nonsmooth optimization with smooth substructure, 2005.

W. L. Hare and A. S. Lewis, Identifying active constraints via partial smoothness and prox-regularity, J. Convex Anal, vol.11, issue.2, pp.251-266, 2004.

M. A. Herman and T. Strohmer, General Deviants: An Analysis of Perturbations in Compressed Sensing, Selected Topics in Signal Processing, pp.342-349, 2010.
DOI : 10.1109/JSTSP.2009.2039170

Y. Sun, J. D. Lee, and Y. E. Taylor, On model selection consistency of regularized M -estimators, In: Electronic Journal of Statistics, vol.9, pp.608-642, 2015.

J. Jia and B. Yu, On model selection consistency of the elastic net when p n, Statistica Sinica, vol.20, pp.595-611, 2010.
DOI : 10.21236/ADA485557

K. Knight and W. Fu, Asymptotics for Lasso-Type Estimators, The Annals of Statistics, vol.285, pp.1356-1378, 2000.

C. Lemaréchal, F. Oustry, and C. Sagastizábal, The U -Lagrangian of a convex function, Transactions of the American Mathematical Society, vol.352, issue.02, pp.711-729, 2000.
DOI : 10.1090/S0002-9947-99-02243-6

A. S. Lewis, Active Sets, Nonsmoothness, and Sensitivity, SIAM Journal on Optimization, vol.13, issue.3, pp.702-725, 2003.
DOI : 10.1137/S1052623401387623

A. S. Lewis, The mathematics of eigenvalue optimization, Mathematical Programming, vol.97, issue.1, pp.155-176, 2003.
DOI : 10.1007/s10107-003-0441-3

A. S. Lewis and J. Malick, Alternating Projections on Manifolds, Mathematics of Operations Research, vol.33, issue.1, pp.216-234, 2008.
DOI : 10.1287/moor.1070.0291
URL : https://hal.archives-ouvertes.fr/hal-00317157

A. S. Lewis and S. Zhang, Partial Smoothness, Tilt Stability, and Generalized Hessians, SIAM Journal on Optimization, vol.23, issue.1, pp.74-94, 2013.
DOI : 10.1137/110852103

J. Liang, M. J. Fadili, and G. Peyré, Local Linear Convergence of Forward?Backward under Partial Smoothness, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01150460

P. Loh and M. J. Wainwright, Highdimensional regression with noisy and missing data: Provable guarantees with nonconvexity, In: The Annals of Statistics, vol.403, pp.1637-1664, 2012.

B. S. Mordukhovich, Sensitivity analysis in nonsmooth optimization In: Theoretical Aspects of Industrial De- 14 sign, SIAM Volumes in Applied Mathematics, pp.32-46, 1992.

Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course, Science & Business Media, vol.87, 2004.
DOI : 10.1007/978-1-4419-8853-9

S. Oymak, Simultaneously Structured Models With Application to Sparse and Low-Rank Matrices, IEEE Transactions on Information Theory, vol.61, issue.5, 2012.
DOI : 10.1109/TIT.2015.2401574

G. Peyré, M. J. Fadili, and J. Starck, Learning the Morphological Diversity, SIAM Journal on Imaging Sciences, vol.3, issue.3, pp.646-669, 2010.
DOI : 10.1137/090770783

R. A. Poliquin, R. T. Rockafellar, and L. Thibault, Local differentiability of distance functions, Transactions of the American Mathematical Society, vol.352, issue.11, pp.5231-5249, 2000.
DOI : 10.1090/S0002-9947-00-02550-2

B. Recht, M. Fazel, and P. A. Parrilo, Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization, SIAM Review, vol.52, issue.3, pp.471-501, 2010.
DOI : 10.1137/070697835

E. Richard, F. R. Bach, and J. Vert, Intersecting singularities for multi-structured estimation, Proc. ICML JMLR Proceedings. JMLR.org, pp.1157-1165, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00918253

M. Rosenbaum and A. B. Tsybakov, Sparse recovery under matrix uncertainty, The Annals of Statistics, vol.38, issue.5, pp.2620-2651, 2010.
DOI : 10.1214/10-AOS793
URL : https://hal.archives-ouvertes.fr/hal-00533272

L. I. 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

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

R. Tibshirani, Regression shrinkage and selection via the Lasso, Journal of the Royal Statistical Society. Series B. Methodological, vol.581, pp.267-288, 1996.

R. Tibshirani, Sparsity and smoothness via the fused lasso, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.99, issue.1, pp.91-108, 2005.
DOI : 10.1016/S0140-6736(02)07746-2

S. Vaiter, Model selection with low complexity priors, Information and Inference, 2013.
DOI : 10.1093/imaiai/iav005
URL : https://hal.archives-ouvertes.fr/hal-00842603

S. Vaiter, Robust Sparse Analysis Regularization, IEEE Transactions on Information Theory, vol.59, issue.4, pp.2001-2016, 2013.
DOI : 10.1109/TIT.2012.2233859
URL : https://hal.archives-ouvertes.fr/hal-00627452

M. J. Wainwright, Sharp Thresholds for High-Dimensional and Noisy Sparsity Recovery Using $\ell _{1}$-Constrained Quadratic Programming (Lasso), IEEE Transactions on Information Theory, vol.55, issue.5, pp.2183-2202, 2009.
DOI : 10.1109/TIT.2009.2016018

S. J. Wright, Identifiable Surfaces in Constrained Optimization, SIAM Journal on Control and Optimization, vol.31, issue.4, pp.1063-1079, 1993.
DOI : 10.1137/0331048

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, 2005.
DOI : 10.1198/016214502753479356

P. Zhao and B. Yu, On Model Selection Consistency of Lasso, J. Mach. Learn. Res, vol.7, pp.2541-2563, 2006.