P. Arias, V. Caselles, and G. Sapiro, A variational framework for non-local image inpainting , in Energy Minimization Methods in Computer Vision and Pattern Recognition, pp.345-358, 2009.

J. Aujol, Some First-Order Algorithms for Total Variation Based Image Restoration, Journal of Mathematical Imaging and Vision, vol.33, issue.2, pp.34-37, 2009.
DOI : 10.1007/s10851-009-0149-y

URL : https://hal.archives-ouvertes.fr/hal-00260494

J. Aujol, G. Aubert, L. Blanc-feraud, and A. Chambolle, Image Decomposition into a Bounded Variation Component and an Oscillating Component, Journal of Mathematical Imaging and Vision, vol.15, issue.3, pp.71-88, 2005.
DOI : 10.1007/s10851-005-4783-8

URL : https://hal.archives-ouvertes.fr/hal-00202001

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

J. Aujol and G. Gilboa, Constrained and SNR-Based Solutions for TV-Hilbert Space Image Denoising, Journal of Mathematical Imaging and Vision, vol.17, issue.10, pp.217-237, 2006.
DOI : 10.1007/s10851-006-7801-6

URL : https://hal.archives-ouvertes.fr/hal-00201844

J. Aujol, G. Gilboa, T. Chan, and S. Osher, Structure-Texture Image Decomposition???Modeling, Algorithms, and Parameter Selection, International Journal of Computer Vision, vol.4, issue.2, pp.111-136, 2006.
DOI : 10.1007/s11263-006-4331-z

URL : https://hal.archives-ouvertes.fr/hal-00201977

J. Aujol and S. H. Kang, Color image decomposition and restoration, Journal of Visual Communication and Image Representation, vol.17, issue.4, pp.916-928, 2006.
DOI : 10.1016/j.jvcir.2005.02.001

URL : https://hal.archives-ouvertes.fr/hal-00201973

J. Aujol, S. Ladjal, and S. Masnou, Exemplar-Based Inpainting from a Variational Point of View, SIAM Journal on Mathematical Analysis, vol.42, issue.3, pp.42-1246, 2010.
DOI : 10.1137/080743883

URL : https://hal.archives-ouvertes.fr/hal-00392011

J. Bect, L. Blanc-féraud, G. Aubert, and A. Chambolle, A l 1-Unified Variational Framework for Image Restoration, Proc. of ECCV04, pp.1-13, 2004.
DOI : 10.1007/978-3-540-24673-2_1

URL : https://hal.archives-ouvertes.fr/hal-00217251

M. Bertalmio, L. Vese, G. Sapiro, and S. Osher, Simultaneous structure and texture image inpainting, IEEE Transactions on Image Processing, vol.12, issue.8, pp.882-889, 2003.
DOI : 10.1109/TIP.2003.815261

X. Bresson and T. 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

A. Buades, B. Coll, and J. M. , On image denoising methods, SIAM Multiscale Modeling and Simulation, To Appear, 2005.

E. Candès and D. Donoho, singularities, Communications on Pure and Applied Mathematics, vol.9, issue.7, pp.219-266, 2004.
DOI : 10.1002/cpa.10116

E. J. Candès, L. Demanet, D. L. Donoho, and L. Ying, Fast Discrete Curvelet Transforms, Multiscale Modeling & Simulation, vol.5, issue.3, pp.861-899, 2005.
DOI : 10.1137/05064182X

F. Cao, Y. Gousseau, S. Masnou, and P. Pérez, Geometrically Guided Exemplar-Based Inpainting, SIAM Journal on Imaging Sciences, vol.4, issue.4, 2009.
DOI : 10.1137/110823572

URL : https://hal.archives-ouvertes.fr/hal-00392018

A. Chambolle, An algorithm for total variation minimization and applications, J. Math. Imaging Vis, vol.20, pp.89-97, 2004.

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, 2010.
DOI : 10.1007/s10851-010-0251-1

URL : https://hal.archives-ouvertes.fr/hal-00490826

T. Chan and J. Shen, Mathematical models for local nontexture inpaintings, SIAM J. Appl. Math, vol.62, pp.1019-1043, 2002.

T. F. Chan, S. H. Kang, and J. Shen, Total Variation Denoising and Enhancement of Color Images Based on the CB and HSV Color Models, Journal of Visual Communication and Image Representation, vol.12, issue.4, 2000.
DOI : 10.1006/jvci.2001.0491

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

A. Criminisi, P. Perez, and K. Toyama, Region Filling and Object Removal by Exemplar-Based Image Inpainting, IEEE Transactions on Image Processing, vol.13, issue.9, pp.1200-1212, 2004.
DOI : 10.1109/TIP.2004.833105

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, Image denoising by sparse 3d transform-domain collaborative filtering, IEEE Trans. Image Proc, p.16, 2007.

I. Daubechies and G. Tescke, Variational image restoration by means of wavelets: Simultaneous decomposition, deblurring, and denoising, Applied and Computational Harmonic Analysis, vol.19, issue.1, pp.1-16, 2005.
DOI : 10.1016/j.acha.2004.12.004

I. Daubechies, G. Tescke, and L. Vese, On Some Iterative Concepts for Image Restoration, Advances in Imaging and Electronics, pp.2-52, 2008.
DOI : 10.1016/S1076-5670(07)00001-8

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.417.9268

D. Donoho and I. Johnstone, Ideal spatial adaptation via wavelet shrinkage, Biometrika, pp.81-425, 1994.

I. Drori, D. Cohen-or, and H. Yeshurun, Fragment-based image completion, ACM Transactions on Graphics, vol.22, issue.3, pp.303-312, 2003.
DOI : 10.1145/882262.882267

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.185.198

V. Duval, J. Aujol, and Y. Gousseau, The TVL1 Model: A Geometric Point of View, Multiscale Modeling & Simulation, vol.8, issue.1, pp.154-189, 2009.
DOI : 10.1137/090757083

URL : https://hal.archives-ouvertes.fr/hal-00380195

V. Duval, J. Aujol, and L. A. Vese, Mathematical Modeling of Textures: Application to Color Image Decomposition with a Projected Gradient Algorithm, Journal of Mathematical Imaging and Vision, vol.33, issue.2, pp.232-248, 2010.
DOI : 10.1007/s10851-010-0203-9

URL : https://hal.archives-ouvertes.fr/hal-00292898

A. A. Efros and T. K. Leung, Texture synthesis by non-parametric sampling, Proceedings of the Seventh IEEE International Conference on Computer Vision, p.1033, 1999.
DOI : 10.1109/ICCV.1999.790383

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.2805

M. Elad, J. Starck, P. Querre, and D. Donoho, Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA), Applied and Computational Harmonic Analysis, vol.19, issue.3, pp.340-358, 2005.
DOI : 10.1016/j.acha.2005.03.005

M. J. Fadili, J. Starck, and F. Murtagh, Inpainting and Zooming Using Sparse Representations, The Computer Journal, vol.52, issue.1, 2006.
DOI : 10.1093/comjnl/bxm055

URL : https://hal.archives-ouvertes.fr/hal-00091746

Y. Kim and L. Vese, Image recovery using functions of bounded variation and Sobolev spaces of negative differentiability, Inverse Problems and Imaging, vol.3, issue.1, pp.43-68, 2009.
DOI : 10.3934/ipi.2009.3.43

N. Komodakis, Image Completion Using Global Optimization, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Volume 1 (CVPR'06), pp.442-452, 2006.
DOI : 10.1109/CVPR.2006.141

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.98.9858

V. Kwatra, I. Essa, A. Bobick, and N. Kwatra, Texture optimization for example-based synthesis, ACM Transactions on Graphics, vol.24, issue.3, pp.795-802, 2005.
DOI : 10.1145/1073204.1073263

E. Le, S. Pennec, and . Mallat, Bandelet image approximation and compression, SIAM Journal of Multiscale Modeling and Simulation, vol.4, 2005.

S. Masnou, Disocclusion: a variational approach using level lines, IEEE Transactions on Image Processing, vol.11, issue.2, pp.68-76, 2002.
DOI : 10.1109/83.982815

Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations, 2001.
DOI : 10.1090/ulect/022

Y. Nesterov, Smooth minimization of non-smooth functions, Mathematical Programming, vol.269, issue.1, pp.127-152, 2005.
DOI : 10.1007/s10107-004-0552-5

P. Pérez, M. Gangnet, and A. Blake, Patchworks: Example-based region tiling for image editing, tech. report, Microsoft Research, 2004.

G. Peyré, Texture Synthesis with Grouplets, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.32, issue.4, 2009.
DOI : 10.1109/TPAMI.2009.54

G. Peyré and S. Mallat, A Review of Bandlet Methods for Geometrical Image Representation , Numerical Algorithms, pp.205-234, 2007.

J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, Image denoising using scale mixtures of gaussians in the wavelet domain, IEEE Transactions on Image Processing, vol.12, issue.11, pp.1338-1351, 2003.
DOI : 10.1109/TIP.2003.818640

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

J. Shen, S. H. Kang, and T. Chan, Euler's Elastica and Curvature-Based Inpainting, SIAM Journal on Applied Mathematics, vol.63, issue.2, pp.564-592, 2003.
DOI : 10.1137/S0036139901390088

J. Starck, M. Elad, and D. L. Donoho, Redundant multiscale transforms and their application for morphological component analysis, Advances in Imaging and Electron Physics, p.132, 2004.

J. Sun, L. Yuan, J. Jia, and H. Shum, Image completion with structure propagation, SIGGRAPH '05, pp.861-868, 2005.

J. A. Tropp, Algorithms for simultaneous sparse approximation. part II: Convex relaxation, Signal Processing, special issue " Sparse approximations in signal and image processing, pp.86-589, 2006.
DOI : 10.1016/j.sigpro.2005.05.030

P. Tseng, Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization, Journal of Optimization Theory and Applications, vol.109, issue.3, pp.475-494, 2001.
DOI : 10.1023/A:1017501703105

L. Vese and S. 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

L. Wei and M. Levoy, Fast texture synthesis using tree-structured vector quantization, Proceedings of the 27th annual conference on Computer graphics and interactive techniques , SIGGRAPH '00, pp.479-488, 2000.
DOI : 10.1145/344779.345009

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.124.5631