R. Abergel, C. Louchet, L. Moisan, and T. Zeng, Total Variation Restoration of Images Corrupted by Poisson Noise with Iterated Conditional Expectations, Proceedings of the International Conference on Scale Space and Variational Methods in Computer Vision, pp.178-190, 2015.
DOI : 10.1007/978-3-319-18461-6_15

URL : https://hal.archives-ouvertes.fr/hal-01275813

A. Aldroubi, M. Unser, and M. Eden, Cardinal spline filters: Stability and convergence to the ideal sinc interpolator, Signal Processing, vol.28, issue.2, pp.127-138, 1992.
DOI : 10.1016/0165-1684(92)90030-Z

K. J. Arrow, L. Hurwicz, H. Uzawa, and H. B. Chenery, Studies in linear and non-linear programming, 1958.

J. Aujol and A. Chambolle, Dual Norms and Image Decomposition Models, International Journal of Computer Vision, vol.19, issue.3, pp.85-104, 2005.
DOI : 10.1007/s11263-005-4948-3

URL : https://hal.archives-ouvertes.fr/inria-00071453

S. Babacan, R. Molina, and A. Katsaggelos, Total variation super resolution using a variational approach, 2008 15th IEEE International Conference on Image Processing, pp.641-644, 2008.
DOI : 10.1109/ICIP.2008.4711836

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

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

S. Boyd and L. Vandenberghe, Convex optimization, 2004.

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

T. Briand and J. Vacher, Linear filtering : From the continuous spectral definition to the numerical computations . IPOL preprint, 2015.

A. Chambolle, An algorithm for total variation minimization and applications, Journal of Mathematical Imaging and Vision, vol.20, issue.12, pp.89-97, 2004.

A. Chambolle, Total variation minimization and a class of binary MRF models. In Energy minimization methods in computer vision and pattern recognition, pp.136-152, 2005.

A. Chambolle, V. Caselles, D. Cremers, M. Novaga, and T. Pock, An introduction to total variation for image analysis. Theoretical foundations and numerical methods for sparse recovery, pp.263-340, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00437581

A. Chambolle, S. E. Levine, and B. J. Lucier, An Upwind Finite-Difference Method for Total Variation???Based Image Smoothing, SIAM Journal on Imaging Sciences, vol.4, issue.1, pp.277-299, 2011.
DOI : 10.1137/090752754

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

T. Chan, A. Marquina, and P. Mulet, High-Order Total Variation-Based Image Restoration, SIAM Journal on Scientific Computing, vol.22, issue.2, pp.503-516, 2000.
DOI : 10.1137/S1064827598344169

T. F. Chan and C. Wong, Total variation blind deconvolution, IEEE Transactions on Image Processing, vol.7, issue.3, pp.370-375, 1998.
DOI : 10.1109/83.661187

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.54.1221

T. F. Chan, A. M. Yip, and F. E. Park, Simultaneous total variation image inpainting and blind deconvolution, International Journal of Imaging Systems and Technology, vol.8, issue.1, pp.92-102, 2005.
DOI : 10.1002/ima.20041

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1.2218

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, 2011.

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

L. Condat, Discrete Total Variation: New Definition and Minimization, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01309685

J. Darbon and M. Sigelle, Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization, Journal of Mathematical Imaging and Vision, vol.2, issue.4, pp.261-276, 2006.
DOI : 10.1007/s10851-006-8803-0

Y. Drori, S. Sabach, and M. Teboulle, A simple algorithm for a class of nonsmooth convex???concave saddle-point problems, Operations Research Letters, vol.43, issue.2, pp.209-214, 2015.
DOI : 10.1016/j.orl.2015.02.001

I. Ekeland and R. Témam, Convex Analysis and Variational Problems, SIAM, vol.28, 1999.
DOI : 10.1137/1.9781611971088

G. Facciolo-furlan, A. Almansa, J. Aujol, and V. Caselles, Irregular to Regular Sampling, Denoising, and Deconvolution, Multiscale Modeling & Simulation, vol.7, issue.4, pp.1574-1608, 2009.
DOI : 10.1137/080719443

J. M. Fadili and G. Peyré, Total Variation Projection With First Order Schemes, IEEE Transactions on Image Processing, vol.20, issue.3, pp.657-669, 2011.
DOI : 10.1109/TIP.2010.2072512

URL : https://hal.archives-ouvertes.fr/hal-00401251

M. Frigo and S. G. Johnson, The Design and Implementation of FFTW3, Proceedings of the IEEE, vol.93, issue.2, pp.216-231, 2005.
DOI : 10.1109/JPROC.2004.840301

P. Getreuer, Linear Methods for Image Interpolation, Image Processing On Line, vol.1, 2011.
DOI : 10.5201/ipol.2011.g_lmii

G. Gilboa, A Spectral Approach to Total Variation, Proceedings of the International Conference on Scale Space and Variational Methods in Computer Vision, Lecture Rémy Abergel, pp.36-47, 2013.
DOI : 10.1007/978-3-642-38267-3_4

F. Guichard and F. Malgouyres, Total variation based interpolation, Proceedings of the European signal processing conference, pp.1741-1744, 1998.

P. J. Huber, Robust Estimation of a Location Parameter, The Annals of Mathematical Statistics, vol.35, issue.1, pp.73-101, 1964.
DOI : 10.1214/aoms/1177703732

P. J. Huber, Robust regression: asymptotics, conjectures and Monte Carlo. The Annals of Statistics, pp.799-821, 1973.

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

C. Louchet and L. Moisan, Total variation denoising using iterated conditional expectation, Proceedings of the European signal processing conference, pp.1592-1596, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01214735

F. Malgouyres and F. Guichard, Edge Direction Preserving Image Zooming: A Mathematical and Numerical Analysis, SIAM Journal on Numerical Analysis, vol.39, issue.1, pp.1-37, 2001.
DOI : 10.1137/S0036142999362286

W. Miled, J. Pesquet, and M. Parent, A Convex Optimization Approach for Depth Estimation Under Illumination Variation, IEEE Transactions on Image Processing, vol.18, issue.4, pp.813-830, 2009.
DOI : 10.1109/TIP.2008.2011386

URL : https://hal.archives-ouvertes.fr/hal-00692900

L. Moisan, How to discretize the Total Variation of an image?, the 6th International Congress on Industrial Applied Mathematics Proceedings in Applied Mathematics and Mechanics, pp.1041907-1041908, 2007.
DOI : 10.1002/pamm.200700424

URL : https://hal.archives-ouvertes.fr/hal-00624503

L. Moisan, Periodic Plus Smooth Image Decomposition, Journal of Mathematical Imaging and Vision, vol.4, issue.1, pp.161-179, 2011.
DOI : 10.1007/s10851-010-0227-1

URL : https://hal.archives-ouvertes.fr/hal-00388020

J. Moreau, Proximité et dualité dans un espace hilbertien Bulletin de la Société mathématique de France, pp.273-299, 1965.

Y. Nesterov, A method of solving a convex programming problem with convergence rate, Soviet Mathematics Doklady, pp.372-376, 1983.

M. Nikolova, Local Strong Homogeneity of a Regularized Estimator, SIAM Journal on Applied Mathematics, vol.61, issue.2, pp.633-658, 2000.
DOI : 10.1137/S0036139997327794

P. Ochs, Y. Chen, T. Brox, and T. Pock, iPiano: Inertial Proximal Algorithm for Nonconvex Optimization, SIAM Journal on Imaging Sciences, vol.7, issue.2, pp.1388-1419, 2014.
DOI : 10.1137/130942954

N. Parikh and S. Boyd, Proximal algorithms. Foundations and Trends in optimization, pp.123-231, 2013.

J. Preciozzi, P. Musé, A. Almansa, S. Durand, A. Khazaal et al., A Sparsity-Based Variational Approach for the Restoration of SMOS Images From L1A Data, IEEE International Geoscience and Remote Sensing Symposium, pp.2487-2490, 2014.
DOI : 10.1109/TGRS.2017.2654864

URL : https://hal.archives-ouvertes.fr/hal-01341839

H. Raguet, J. M. Fadili, and G. Peyré, A Generalized Forward-Backward Splitting, SIAM Journal on Imaging Sciences, vol.6, issue.3, pp.1199-1226, 2013.
DOI : 10.1137/120872802

URL : https://hal.archives-ouvertes.fr/hal-00613637

W. Ring, Structural Properties of Solutions to Total Variation Regularization Problems, ESAIM: Modélisation Mathématique et Analyse Numérique, pp.799-810, 2000.
DOI : 10.1051/m2an:2000104

R. T. Rockafellar, Convex analysis. Princeton university press, 1997.

B. Rougé and A. Seghier, <title>Nonlinear spectral extrapolation: new results and their application to spatial and medical imaging</title>, Neural, Morphological, and Stochastic Methods in Image and Signal Processing, pp.279-289, 1995.
DOI : 10.1117/12.216364

D. L. Ruderman, The statistics of natural images. Network: computation in neural systems, pp.517-548, 1994.

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

L. Simon and J. Morel, Influence of Unknown Exterior Samples on Interpolated Values for Band-Limited Images, SIAM Journal on Imaging Sciences, vol.9, issue.1, pp.152-184, 2016.
DOI : 10.1137/140978338

URL : https://hal.archives-ouvertes.fr/hal-01287218

M. Unser, Sampling-50 years after Shannon, Proceedings of the IEEE, pp.569-587, 2000.
DOI : 10.1109/5.843002

M. Unser, A. Aldroubi, and M. Eden, Fast B-spline transforms for continuous image representation and interpolation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.13, issue.3, pp.277-285, 1991.
DOI : 10.1109/34.75515

M. A. Unser, Ten good reasons for using spline wavelets, Optical Science, Engineering and Instrumentation'97 International Society for Optics and Photonics, pp.422-431, 1997.

L. A. Vese and S. J. Osher, Modeling textures with total variation minimization and oscillating patterns in image processing, Journal of Scientific Computing, vol.19, issue.1/3, pp.553-572, 2003.
DOI : 10.1023/A:1025384832106

C. Vogel and M. Oman, Fast, robust total variation-based reconstruction of noisy, blurred images, IEEE Transactions on Image Processing, vol.7, issue.6, pp.813-824, 1998.
DOI : 10.1109/83.679423

P. Weiss and L. Blanc-féraud, A proximal method for inverse problems in image processing, Proceedings of the European signal processing conference, pp.1374-1378, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00417712

P. Weiss, L. Blanc-féraud, and G. Aubert, Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing, SIAM Journal on Scientific Computing, vol.31, issue.3, pp.312047-2080, 2009.
DOI : 10.1137/070696143

URL : https://hal.archives-ouvertes.fr/inria-00166096

M. Werlberger, W. Trobin, T. Pock, A. Wedel, D. Cremers et al., Anisotropic Huber-L1 Optical Flow, Procedings of the British Machine Vision Conference 2009, p.3, 2009.
DOI : 10.5244/C.23.108

L. Yaroslavsky, Signal sinc???interpolation: A fast computer algorithm, Bioimaging, vol.4, issue.4, pp.225-231, 1996.
DOI : 10.1002/1361-6374(199612)4:4<225::AID-BIO1>3.0.CO;2-G

K. Yosida, Functional Analysis Originally published as volume 123 in the series: Grundlehren der mathematischen Wissenschaften, 1968.

M. Zhu and T. Chan, An efficient primal-dual hybrid gradient algorithm for total variation image restoration, UCLA CAM Report, 2008.