L. Armijo, Minimization of functions having Lipschitz continuous first partial derivatives, Pacific Journal of Mathematics, vol.16, issue.1, pp.1-3, 1966.
DOI : 10.2140/pjm.1966.16.1

J. Aujol and C. Dossal, Stability of Over-Relaxations for the Forward-Backward Algorithm, Application to FISTA, SIAM Journal on Optimization, vol.25, issue.4, pp.2408-2433, 2015.
DOI : 10.1137/140994964

URL : https://hal.archives-ouvertes.fr/hal-01163432

A. Beck and M. Teboulle, Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems, IEEE Transactions on Image Processing, vol.18, issue.11, pp.2419-2434, 2009.
DOI : 10.1109/TIP.2009.2028250

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.231.6217

S. Bonettini, F. Porta, and V. Ruggiero, A Variable Metric Forward-Backward Method with Extrapolation, SIAM Journal on Scientific Computing, vol.38, issue.4, pp.2558-2584, 2016.
DOI : 10.1137/15M1025098

URL : http://arxiv.org/pdf/1506.02900

M. Burger, A. Sawatzky, and G. Steidl, First Order Algorithms in Variational Image Processing, pp.345-407, 2016.
DOI : 10.1117/12.772826

URL : http://arxiv.org/abs/1412.4237

A. Chambolle, An algorithm for total variation minimization and applications, Journal of Mathematical Imaging and Vision, vol.20, issue.1, pp.89-97, 2004.

A. Chambolle and C. Dossal, On the Convergence of the Iterates of the ???Fast Iterative Shrinkage/Thresholding Algorithm???, Journal of Optimization Theory and Applications, vol.155, issue.2, pp.968-982, 2015.
DOI : 10.1007/978-1-4419-9467-7

A. Chambolle, M. J. Ehrhardt, P. Richtarik, and C. Schönlieb, Stochastic primal-dual hybrid gradient algorithm with arbitrary sampling and imaging applications, arXiv preprint, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01569426

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, issue.11, pp.29-54, 2015.
DOI : 10.5802/smai-jcm.3

URL : https://hal.archives-ouvertes.fr/hal-01099182

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

Q. Ferocq and Q. Zheng, Restarting accelerated gradient methods with a rough strong convexity estimate, arXiv preprint, 2016.

M. I. Florea and S. Vorobyov, An accelerated composite gradient method for large-scale composite objective problems, (2016), arXiv preprint: https://arxiv.org/pdf/1612.02352. 15. , A generalized accelerated composite gradient method: uniting Nesterov's fast gradient method and FISTA, arXiv preprint, 2017.

A. A. Goldstein, Convex programming in Hilbert space, Bulletin of the American Mathematical Society, vol.70, issue.5, pp.709-710, 1964.
DOI : 10.1090/S0002-9904-1964-11178-2

O. Güler, New Proximal Point Algorithms for Convex Minimization, SIAM Journal on Optimization, vol.2, issue.4, pp.649-664, 1992.
DOI : 10.1137/0802032

H. Lin, J. Mairal, and Z. Harchaoui, A universal catalyst for first-order optimization, Proceedings of the 28th International Conference on Neural Information Processing Systems NIPS'15, pp.3384-3392, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01160728

Y. Nesterov, A method for solving the convex programming problem with convergence rate Introductory lectures on convex optimization 21. , Smooth minimization of non-smooth functions, Gradient methods for minimizing composite functions, Mathematical Programming, pp.543-547, 1983.

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

S. Salzo and S. Villa, Inexact and accelerated proximal point algorithms, Journal of Convex Analysis, vol.19, issue.4, pp.1167-1192, 2012.

A. Sawatzky, (nonlocal) total variation in medical imaging, 2011.

K. Scheinberg, D. Goldfarb, and X. Bai, Fast First-Order Methods for Composite Convex Optimization with Backtracking, Foundations of Computational Mathematics, vol.68, issue.3, pp.389-417, 2014.
DOI : 10.1111/j.1467-9868.2005.00532.x

M. Schmidt, N. Roux, and F. Bach, Convergence rates of inexact proximal-gradient methods for convex optimization Advances in Neural Information Processing Systems 24, pp.1458-1466, 2011.

S. Tao, D. Boley, and S. Zhang, Local Linear Convergence of ISTA and FISTA on the LASSO Problem, SIAM Journal on Optimization, vol.26, issue.1, pp.313-336, 2016.
DOI : 10.1137/151004549

P. Tseng, On accelerated proximal gradient methods for convex-concave optimization, 2008.

S. Villa, S. Salzo, L. Baldassarre, and A. Verri, Accelerated and Inexact Forward-Backward Algorithms, SIAM Journal on Optimization, vol.23, issue.3, pp.1607-1633, 2013.
DOI : 10.1137/110844805

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.416.3633