, REFERENCES

P. L. Combettes and J. Pesquet, Proximal splitting methods in signal processing, " in Fixed-Point Algorithms for Inverse Problems in Science and Engineering, pp.185-212, 2010.

N. Komodakis and J. Pesquet, Playing with Duality: An overview of recent primal?dual approaches for solving large-scale optimization problems, IEEE Signal Processing Magazine, vol.32, issue.6, pp.31-54, 2015.
DOI : 10.1109/MSP.2014.2377273
URL : https://hal.archives-ouvertes.fr/hal-01010437

P. L. Combettes, D. Dung, and B. C. V?uv?u, Dualization of signal recovery problems Set-Valued Var, Anal, vol.18, issue.3, pp.373-404, 2010.

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, 2013.
DOI : 10.1081/NFA-120003674
URL : https://hal.archives-ouvertes.fr/hal-00609728

S. R. Becker and P. L. Combettes, An algorithm for splitting parallel sums of linearly composed monotone operators, with applications to signal recovery, J. Nonlinear Convex Anal, vol.15, issue.1, pp.137-159, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00825885

C. Couprie, L. Grady, L. Najman, J. Pesquet, and H. Talbot, Dual Constrained TV-based Regularization on Graphs, SIAM Journal on Imaging Sciences, vol.6, issue.3, pp.1246-1273, 2013.
DOI : 10.1137/120895068
URL : https://hal.archives-ouvertes.fr/hal-00743968

A. Jezierska, E. Chouzenoux, J. Pesquet, and H. Talbot, A primaldual proximal splitting approach for restoring data corrupted with poisson-gaussian noise, IEEE Int. Conf. Acoust. Speech and Signal Process, pp.25-30, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00687634

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, 2010.
DOI : 10.1007/978-3-540-74936-3_22
URL : https://hal.archives-ouvertes.fr/hal-00490826

P. L. Combettes, L. Condat, J. Pesquet, and B. C. V?uv?u, A forwardbackward view of some primal-dual optimization methods in image recovery, IEEE Int. Conf. Image Process. (ICIP 2014), pp.27-30, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01098038

R. I. Bot¸andbot¸bot¸and and C. Hendrich, Convergence analysis for a primal-dual monotone + skew splitting algorithm with applications to total variation minimization, J. Math. Imaging Vision, vol.49, issue.3, pp.551-568, 2014.

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.

R. I. Bot¸andbot¸bot¸and and C. Hendrich, A Douglas-Rachford type primal-dual method for solving inclusions with mixtures of composite and parallelsum type monotone operators, SIAM J. Optim, vol.23, issue.4, pp.2541-2565, 2013.

P. L. Combettes and J. Pesquet, Stochastic Quasi-Fej??r Block-Coordinate Fixed Point Iterations with Random Sweeping, SIAM Journal on Optimization, vol.25, issue.2, pp.1221-1248, 2015.
DOI : 10.1137/140971233

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers, Foundations and Trends?? in Machine Learning, vol.3, issue.1, pp.1-122, 2011.
DOI : 10.1561/2200000016

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

D. Davis, Convergence Rate Analysis of Primal-Dual Splitting Schemes, SIAM Journal on Optimization, vol.25, issue.3, pp.1912-1943, 2015.
DOI : 10.1137/151003076

L. Rosasco, S. Villa, B. C. V?uv?u, S. Shalev-shwartz, and T. Zhang, A First-Order Stochastic Primal-Dual Algorithm with Correction Step, Numerical Functional Analysis and Optimization, vol.14, issue.5, pp.602-626, 2013.
DOI : 10.1007/s11590-015-0904-5

P. Bianchi, W. Hachem, and F. Iutzeler, A Coordinate Descent Primal-Dual Algorithm and Application to Distributed Asynchronous Optimization, IEEE Transactions on Automatic Control, vol.61, issue.10, pp.2947-2957, 2016.
DOI : 10.1109/TAC.2015.2512043
URL : https://hal.archives-ouvertes.fr/hal-01237226

Z. Qu, P. Richtárik, and T. Zhang, Randomized dual coordinate ascent with arbitrary sampling, Adv. Neural Inf. Process. Syst, pp.7-12, 2015.

M. Jaggi, V. Smith, J. Takac, S. Terhorst, T. Krishnan et al., Communication-efficient distributed dual coordinate ascent, Adv. Neural Inf. Process. Syst, pp.3068-3076, 2014.

F. Abboud, E. Chouzenoux, J. Pesquet, J. Chenot, and L. Laborelli, A dual block coordinate proximal algorithm with application to deconvolution of interlaced video sequences, 2015 IEEE International Conference on Image Processing (ICIP), pp.27-30, 2015.
DOI : 10.1109/ICIP.2015.7351742

A. Chambolle and T. Pock, A remark on accelerated block coordinate descent for computing the proximity operators of a sum of convex functions, SMAI Journal of Computational Mathematics, vol.1, pp.29-57, 2015.
DOI : 10.5802/smai-jcm.3
URL : https://hal.archives-ouvertes.fr/hal-01099182

J. Pesquet and A. Repetti, A class of randomized primal-dual algorithms for distributed optimization, J. Nonlinear Convex Anal, vol.16, issue.12, pp.2453-2490, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01077615

F. Iutzeler, P. Bianchi, P. Ciblat, and W. Hachem, Explicit Convergence Rate of a Distributed Alternating Direction Method of Multipliers, IEEE Transactions on Automatic Control, vol.61, issue.4, pp.892-904, 2016.
DOI : 10.1109/TAC.2015.2448011

P. Richtárik and M. Takác, Distributed coordinate descent method for learning with big data, J. Mach. Learn. Res, vol.17, issue.75, pp.1-25, 2016.

F. Abboud, E. Chouzenoux, J. Pesquet, J. Chenot, and L. Laborelli, Dual Block-Coordinate Forward-Backward Algorithm with Application to Deconvolution and Deinterlacing of Video Sequences, Journal of Mathematical Imaging and Vision, vol.13, issue.4, pp.415-431, 2017.
DOI : 10.1109/PCS.2010.5702567
URL : https://hal.archives-ouvertes.fr/hal-01418393

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

E. Chouzenoux, A. Jezierska, J. Pesquet, and H. Talbot, A Convex Approach for Image Restoration with Exact Poisson--Gaussian Likelihood, SIAM Journal on Imaging Sciences, vol.8, issue.4, pp.2662-2682, 2015.
DOI : 10.1137/15M1014395
URL : https://hal.archives-ouvertes.fr/hal-00922151

N. Pustelnik, A. Benazza-benhayia, Y. Zheng, and J. Pesquet, Wavelet-Based Image Deconvolution and Reconstruction, 2016.
DOI : 10.1109/83.392335
URL : https://hal.archives-ouvertes.fr/hal-01164833

N. Pustelnik, C. Chaux, and J. Pesquet, Parallel Proximal Algorithm for Image Restoration Using Hybrid Regularization, IEEE Transactions on Image Processing, vol.20, issue.9, pp.2450-2462, 2011.
DOI : 10.1109/TIP.2011.2128335
URL : https://hal.archives-ouvertes.fr/hal-00826121

F. Abboud, E. Chouzenoux, J. Pesquet, J. Chenot, and L. Laborelli, A distributed strategy for computing proximity operators, 2015 49th Asilomar Conference on Signals, Systems and Computers, pp.8-11, 2015.
DOI : 10.1109/ACSSC.2015.7421156
URL : https://hal.archives-ouvertes.fr/hal-01373644

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

, Message Passing Interface Forum MPI: A Message-Passing Interface standard, Tech. Rep, 1994.

W. Gropp, E. Lusk, and A. Skjellum, Using MPI: Portable Paral lel Programming with the Message Passing Interface, 1999.

G. M. , Validity of the single processor approach to achieving large scale computing capabilities, Proceedings of the April 18-20, 1967, spring joint computer conference on, AFIPS '67 (Spring), pp.18-20, 1967.
DOI : 10.1145/1465482.1465560