D. C. Youla and H. Webb, Image Restoration by the Method of Convex Projections: Part 1ߞTheory, IEEE Transactions on Medical Imaging, vol.1, issue.2, pp.81-94, 1982.
DOI : 10.1109/TMI.1982.4307555

H. J. Trussell and M. R. Civanlar, The feasible solution in signal restoration, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.32, issue.2, pp.201-212, 1984.
DOI : 10.1109/TASSP.1984.1164297

P. L. Combettes, Inconsistent signal feasibility problems: least-squares solutions in a product space, IEEE Transactions on Signal Processing, vol.42, issue.11, pp.2955-2966, 1994.
DOI : 10.1109/78.330356

K. Kose, V. Cevher, and A. E. Cetin, Filtered Variation method for denoising and sparse signal processing, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp.3329-3332, 2012.
DOI : 10.1109/ICASSP.2012.6288628

T. Teuber, G. Steidl, and R. H. Chan, -divergence constraints, Inverse Problems, vol.29, issue.3, 2012.
DOI : 10.1088/0266-5611/29/3/035007
URL : https://hal.archives-ouvertes.fr/hal-00929638

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

G. Gilboa and S. Osher, Nonlocal Operators with Applications to Image Processing, Multiscale Modeling & Simulation, vol.7, issue.3, p.1005, 2009.
DOI : 10.1137/070698592

S. Mallat, A wavelet tour of signal processing, 1997.

J. Cai, B. Dong, S. Osher, and Z. Shen, Image restoration: Total variation, wavelet frames, and beyond, Journal of the American Mathematical Society, vol.25, issue.4, pp.1033-1089, 2012.
DOI : 10.1090/S0894-0347-2012-00740-1

G. Peyré, S. Bougleux, and L. D. Cohen, Non-local Regularization of Inverse Problems, Inverse Problems and Imaging, vol.5, issue.2, pp.511-530, 2011.
DOI : 10.1007/978-3-540-88690-7_5

G. Peyré, A Review of Adaptive Image Representations, IEEE Journal of Selected Topics in Signal Processing, vol.5, issue.5, pp.896-911, 2011.
DOI : 10.1109/JSTSP.2011.2120592

P. Blomgren and T. F. Chan, Color TV: total variation methods for restoration of vector-valued images, IEEE Transactions on Image Processing, vol.7, issue.3, pp.304-309, 1998.
DOI : 10.1109/83.661180

H. Attouch, G. Buttazzo, and G. Michaille, Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization, MPS-SIAM Series on Optimization, 2006.
DOI : 10.1137/1.9781611973488

C. Zach, T. Pock, and H. Bischof, A duality based approach for realtime TV-L1 optical flow, Proceedings of DAGM Symposium on Pattern Recognition, pp.214-223, 2007.

X. Bresson and T. F. Chan, Fast dual minimization of the vectorial total variation norm and applications to color image processing, Inverse Problems and Imaging, vol.2, issue.4, pp.455-484, 2008.
DOI : 10.3934/ipi.2008.2.455

V. Duval, J. Aujol, and L. Vese, Projected gradient based color image decomposition A note on the gradient of a multi-image, Scale Space and Variational Methods in Computer Vision, pp.295-306, 1986.

G. Sapiro and D. L. Ringach, Anisotropic diffusion of multivalued images with applications to color filtering, IEEE Transactions on Image Processing, vol.5, issue.11, pp.1582-1586, 1996.
DOI : 10.1109/83.541429

N. Sochen, R. Kimmel, and R. Malladi, A general framework for low level vision, IEEE Transactions on Image Processing, vol.7, issue.3, pp.310-318, 1998.
DOI : 10.1109/83.661181

J. Weickert, Coherence-enhancing diffusion of colour images, Image and Vision Computing, vol.17, issue.3-4, pp.201-212, 1999.
DOI : 10.1016/S0262-8856(98)00102-4

D. Tschumperlé and R. Deriche, Constrained and unconstrained PDE's for vector image restoration, Scandinavian Conference on Image Analysis, 2001.

B. Goldluecke, E. Strekalovskiy, and D. Cremers, The Natural Vectorial Total Variation Which Arises from Geometric Measure Theory, SIAM Journal on Imaging Sciences, vol.5, issue.2, pp.537-563, 2012.
DOI : 10.1137/110823766

E. Van-den, M. P. Berg, and . Friedlander, Probing the Pareto Frontier for Basis Pursuit Solutions, SIAM Journal on Scientific Computing, vol.31, issue.2, pp.890-912, 2008.
DOI : 10.1137/080714488

A. Quattoni, X. Carreras, M. Collins, and T. Darrell, An efficient projection for 1,? regularization, International Conference on Machine Learning, pp.857-864, 2009.

A. Buades, B. Coll, and J. Morel, A Review of Image Denoising Algorithms, with a New One, Multiscale Modeling & Simulation, vol.4, issue.2, pp.490-530, 2005.
DOI : 10.1137/040616024
URL : https://hal.archives-ouvertes.fr/hal-00271141

G. Gilboa and S. Osher, Nonlocal Linear Image Regularization and Supervised Segmentation, Multiscale Modeling & Simulation, vol.6, issue.2, pp.595-630, 2007.
DOI : 10.1137/060669358

A. Foi and G. Boracchi, Foveated self-similarity in nonlocal image filtering, Human Vision and Electronic Imaging XVII, p.12, 2012.
DOI : 10.1117/12.912217

G. Chierchia, N. Pustelnik, J. Pesquet, and B. Pesquet-popescu, Epigraphical projection and proximal tools for solving constrained convex optimization problems, Signal, Image and Video Processing, vol.18, issue.4, p.24, 2012.
DOI : 10.1007/s11760-014-0664-1
URL : https://hal.archives-ouvertes.fr/hal-00744603

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.