M. Advani and S. Ganguli, An equivalence between high dimensional Bayes optimal inference and M-estimation. arXiv, 2016.

A. Antoniadis, Wavelet methods in statistics: some recent developments and their applications, Statistics Surveys, vol.1, issue.0, pp.16-55, 2007.
DOI : 10.1214/07-SS014
URL : https://hal.archives-ouvertes.fr/hal-00853883

F. Bach, Optimization with Sparsity-Inducing Penalties, Machine Learning, pp.1-106, 2011.
DOI : 10.1561/2200000015
URL : https://hal.archives-ouvertes.fr/hal-00613125

S. Bakin, Adaptive regression and model selection in data mining problems, 1999.

S. Boyd and L. Vandenberghe, Convex optimization, 2009.

P. Stephen, J. Boyd, L. Duchi, . Vandenberghe, and . Subgradients, Notes for EE364b, 2014.

L. M. Bregman, The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming, USSR Computational Mathematics and Mathematical Physics, vol.7, issue.3, pp.200-217, 1967.
DOI : 10.1016/0041-5553(67)90040-7

T. Tony, C. Bernard, and W. Silverman, Incorporating information on neighbouring coefficients into wavelet estimation, Sankhyà: The Indian Journal of Statistics, Series B, vol.63, pp.127-148, 1960.

H. Cartan, Cours de calcul différentiel. Collection Méthodes, Editions Hermann, 1977.

Y. Censor and S. A. Zenios, On the proximal minimization algorithm with D-Functions, Linear Algebra and its Applications, vol.167, issue.3, pp.451-464, 1992.
DOI : 10.1016/0024-3795(92)90349-F

L. Patrick, J. Combettes, and . Pesquet, Proximal Thresholding Algorithm for Minimization over Orthonormal Bases, SIAM J. Optim, vol.18, pp.1351-1376, 2007.

L. Asen, R. Dontchev, and . Tyrrell-rockafellar, Implicit Functions and Solution Mappings. Springer Series in Operations Research and Financial Engineering

I. Ekeland and T. Turnbull, Infinite-dimensional optimization and convexity, Chicago Lectures in Mathematics, 1983.

C. Févotte and M. Kowalski, Hybrid sparse and low-rank time-frequency signal decomposition, 2015 23rd European Signal Processing Conference (EUSIPCO), pp.464-468, 2015.
DOI : 10.1109/EUSIPCO.2015.7362426

R. Gribonval, Should Penalized Least Squares Regression be Interpreted as Maximum A Posteriori Estimation?, IEEE Transactions on Signal Processing, vol.59, issue.5, pp.2405-2410, 2011.
DOI : 10.1109/TSP.2011.2107908
URL : https://hal.archives-ouvertes.fr/inria-00486840

R. Gribonval, P. Machart-in, C. Burges, . Bottou, . Welling et al., Reconciling " priors " and " priors " without prejudice?, Advances in Neural Information Processing Systems 26 (NIPS), pp.2193-2201, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00751996

R. Gribonval and M. Nikolova, On bayesian estimation and proximity operators, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01835108

P. Hall, I. Spiridon, G. Penev, D. Kerkyacharian, and . Picard, Numerical performance of block thresholded wavelet estimators, Statistics and Computing, 1997.

J. Hiriart-urruty and C. Lemaréchal, Convex analysis and Minimization Algorithms, 1996.
DOI : 10.1007/978-3-662-02796-7

M. Kowalski, K. Siedenburg, and M. Dörfler, Social Sparsity! Neighborhood Systems Enrich Structured Shrinkage Operators, IEEE Transactions on Signal Processing, vol.61, issue.10, 2013.
DOI : 10.1109/TSP.2013.2250967
URL : https://hal.archives-ouvertes.fr/hal-00691774

M. Kowalski and B. Torrésani, Sparsity and persistence: mixed norms provide simple signal models with dependent coefficients. Signal, Image and Video Processing, pp.251-264, 2009.
DOI : 10.1007/s11760-008-0076-1
URL : https://hal.archives-ouvertes.fr/hal-00206245

M. Kowalski and B. Torrésani, Structured Sparsity: from Mixed Norms to Structured Shrinkage, SPARS'09 -Signal Processing with Adaptive Sparse Structured Representations, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00369577

C. Louchet and L. Moisan, Posterior Expectation of the Total Variation Model: Properties and Experiments, SIAM Journal on Imaging Sciences, vol.6, issue.4, pp.2640-2684, 2013.
DOI : 10.1137/120902276
URL : https://hal.archives-ouvertes.fr/hal-00764175

D. Luenberger, Optimization by vector space methods, 1969.

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
URL : https://hal.archives-ouvertes.fr/hal-01740635/file/Proximit%C3%A9_dualit%C3%A9_espace_hilbertien_Moreau_1965.pdf

M. Nikolova, Estimation of binary images by minimizing convex criteria, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269), pp.108-112, 1998.

A. Parekh, W. Ivan, and . Selesnick, Convex Denoising using Non-Convex Tight Frame Regularization, IEEE Signal Processing Letters, vol.22, issue.10, 2015.
DOI : 10.1109/LSP.2015.2432095
URL : http://arxiv.org/pdf/1504.00976

R. Tyrrell, R. , and R. J. Wets, Variational Analysis, volume 317 of Grundlehren der mathematischen Wissenschaften, 1998.

R. Rockafellar, On the maximal monotonicity of subdifferential mappings, Pacific Journal of Mathematics, vol.33, issue.1, pp.209-216, 1970.
DOI : 10.2140/pjm.1970.33.209

W. Ivan and . Selesnick, Sparse Regularization via Convex Analysis, IEEE Trans. Signal Processing, vol.65, issue.17, pp.4481-4494, 2017.

K. Siedenburg and M. Dörfler, Structured sparsity for audio signals, Proc. 14th Int. Conf. on Digital Audio Effects (DAFx-11), 2011.

K. Siedenburg, M. Kowalski, and M. Dörfler, Audio declipping with social sparsity, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp.1577-1581, 2014.
DOI : 10.1109/ICASSP.2014.6853863
URL : https://hal.archives-ouvertes.fr/hal-01002998

G. Varoquaux, M. Kowalski, and B. Thirion, Social-sparsity brain decoders: faster spatial sparsity, 2016 International Workshop on Pattern Recognition in Neuroimaging (PRNI), 2016.
DOI : 10.1109/PRNI.2016.7552352
URL : https://hal.archives-ouvertes.fr/hal-01334551

C. Villani, Optimal Transport -Old and New, volume 338 of Grundlehren der mathematischen Wissenschaften -A series of Comprehensive Studies in Mathematics, 2009.

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
URL : http://www2.isye.gatech.edu/~myuan/papers/glasso.final.pdf