G. Acosta and R. G. Duràn, An optimal Poincaré inequality in L 1 for convex domains, Proc. Amer, pp.195-202, 2004.

A. Almansa, C. Ballester, V. Caselles, and G. Haro, A TV Based Restoration Model with Local Constraints, Journal of Scientific Computing, vol.17, issue.1, pp.209-236, 2008.
DOI : 10.1007/s10915-007-9160-x

F. Alter, V. Caselles, and A. Chambolle, Evolution of characteristic functions of convex sets in the plane by the minimizing total variation flow, Interfaces and Free Boundaries, Mathematical Modelling, Analysis and Computation, vol.7, issue.1, pp.29-53, 2005.

F. Alter, V. Caselles, and A. Chambolle, A characterization of convex calibrable sets in, Mathematische Annalen, vol.7, issue.2, pp.329-366, 2005.
DOI : 10.1007/s00208-004-0628-9

L. Alvarez, F. Guichard, P. Lions, and J. Morel, Axioms and fundamental equations of image processing, Archive for Rational Mechanics and Analysis, pp.199-257, 1993.

F. Andreu, V. Caselles, J. I. Diaz, and J. M. Mazon, Some Qualitative Properties for the Total Variation Flow, Journal of Functional Analysis, vol.188, issue.2, pp.516-547, 2002.
DOI : 10.1006/jfan.2001.3829

L. Ambrosio, N. Fusco, and D. Pallara, Free Discontinuity Problems and Special Functions with Bounded Variation, 2000.
DOI : 10.1007/978-3-0348-8974-2_2

J. Aujol, G. Aubert, L. Blanc-féraud, 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, Some First-Order Algorithms for Total Variation Based Image Restoration, Journal of Mathematical Imaging and Vision, vol.33, issue.2, pp.307-327, 2009.
DOI : 10.1007/s10851-009-0149-y

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

G. Bellettini, V. Caselles, and M. Novaga, The Total Variation Flow in RN, Journal of Differential Equations, vol.184, issue.2, pp.475-525, 2002.
DOI : 10.1006/jdeq.2001.4150

M. Bertalmio, V. Caselles, B. Rougé, and A. Solé, A TV based restoration model with local constraints, J. Sci. Comput, vol.19, pp.1-3, 2003.

J. Besag, Statistical analysis of dirty pictures*, Journal of Applied Statistics, vol.6, issue.5-6, pp.259-302, 1986.
DOI : 10.1016/0031-3203(83)90012-2

P. Blomgren, T. F. Chan, P. Mulet, and C. Wong, Total variation image restoration: numerical methods and extensions, Proceedings of International Conference on Image Processing, pp.384-387, 1997.
DOI : 10.1109/ICIP.1997.632128

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.54.7197

T. Brox and D. Cremers, Iterated nonlocal means for texture restoration, Scale-Space and Variational Methods, pp.13-24, 2007.
DOI : 10.1007/978-3-540-72823-8_2

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

A. Buades, B. Coll, and J. Morel, The staircasing effect in neighborhood filters and its solution, IEEE Transactions on Image Processing, vol.15, issue.6, pp.1499-1595, 2006.
DOI : 10.1109/TIP.2006.871137

URL : https://hal.archives-ouvertes.fr/hal-00271143

J. Carter, Dual methods for total-variation based image restoration, 2001.

V. Caselles and A. Chambolle, Anisotropic curvature-driven flow of convex sets, Nonlinear Analysis: Theory, Methods & Applications, vol.65, issue.8, 2006.
DOI : 10.1016/j.na.2005.10.029

V. Caselles, A. Chambolle, and M. Novaga, The Discontinuity Set of Solutions of the TV Denoising Problem and Some Extensions, Multiscale Modeling & Simulation, vol.6, issue.3, pp.879-894, 2007.
DOI : 10.1137/070683003

A. Chambolle and P. Lions, Image recovery via total variation minimization and related problems, Numerische Mathematik, vol.76, issue.2, pp.167-188, 1997.
DOI : 10.1007/s002110050258

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

A. Chambolle, Total Variation Minimization and a Class of Binary MRF Models, Proc. Energy Minimization Methods ? Computer Vision and Pattern Recognition, pp.136-152, 2005.
DOI : 10.1007/11585978_10

T. 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. 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. Chan, A. Yip, and F. 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

T. Chan, J. Shen, and H. Zhou, Total Variation Wavelet Inpainting, Journal of Mathematical Imaging and Vision, vol.11, issue.7, pp.107-125, 2006.
DOI : 10.1007/s10851-006-5257-3

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1.4485

T. F. Chan, S. Esedoglu, and F. E. Park, Image decomposition combining staircase reduction and texture extraction, Journal of Visual Communication and Image Representation, vol.18, issue.6, pp.464-486, 2007.
DOI : 10.1016/j.jvcir.2006.12.004

P. Chatterjee and P. Milanfar, Clustering-Based Denoising With Locally Learned Dictionaries, IEEE Transactions on Image Processing, vol.18, issue.7, pp.1548-1451, 2009.
DOI : 10.1109/TIP.2009.2018575

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.3425

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

P. 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

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, Image denoising by sparse 3D transform-domain collaborative filtering, IEEE Trans. Image Process, vol.16, issue.8, 2007.
DOI : 10.1109/tip.2007.901238

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.219.5398

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, BM3D image denoising with shape-adaptive principal component analysis, Proc. Workshop on Signal Processing with Adaptive Sparse Structured Representations (SPARS'09), 2009.
URL : https://hal.archives-ouvertes.fr/inria-00369582

J. Darbon and M. Sigelle, A Fast and Exact Algorithm for Total Variation Minimization, Trans. Iberian Conference on Pattern Recognition and Image Analysis, vol.1, pp.351-359, 2005.
DOI : 10.1007/11492429_43

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

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.331.2423

D. C. Dobson and F. Santosa, Recovery of Blocky Images from Noisy and Blurred Data, SIAM Journal on Applied Mathematics, vol.56, issue.4, pp.1181-1198, 1996.
DOI : 10.1137/S003613999427560X

S. Durand and M. Nikolova, Denoising of Frame Coefficients Using $\ell^1$ Data-Fidelity Term and Edge-Preserving Regularization, Multiscale Modeling & Simulation, vol.6, issue.2, pp.547-576, 2007.
DOI : 10.1137/06065828X

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

L. C. Evans and R. F. Gariepy, Measure theory and fine properties of functions, Studies in Advanced Mathematics, 1992.

E. Fisher, A Skorohod Representation and an Invariance Principle for Sums of Weighted i.i.d. Random Variables, Rocky Mountain Journal of Mathematics, vol.22, issue.1, pp.169-179, 1992.
DOI : 10.1216/rmjm/1181072802

F. Guichard and F. Malgouyres, Total variation based interpolation, Proc. European Signal Processing Conference, pp.1741-1744, 1998.

J. Hiriart-urruty and C. Lemaréchal, Convex analysis and minimization algorithms: A review of PDE models in image image processing and image analysis, Grundlehren der Mathematischen Wissenshaft [Fundamental Principles of Mathematical Sciences], pp.305-306, 1993.
DOI : 10.1007/978-3-662-02796-7

V. Katkovnik, A. Foi, K. Egiazarian, and J. Astola, Directional varying scale approximations for anisotropic signal processing, Proc. European Signal Processing Conference, pp.101-104, 2004.

C. Kervrann and J. Boulanger, Local Adaptivity to Variable Smoothness for Exemplar-Based Image Regularization and Representation, International Journal of Computer Vision, vol.27, issue.2, pp.45-69, 2008.
DOI : 10.1007/s11263-007-0096-2

S. Levine, Y. Chen, and J. Stanich, Image restoration via nonstandard diffusion, 2004.

C. Louchet and L. Moisan, Total variation denoising using posterior expectation, Proc. European Signal Processing Conference (electronic), 2008.
URL : https://hal.archives-ouvertes.fr/hal-00258849

J. Mairal, F. Bach, J. Ponce, G. Sapiro, and A. Zisserman, Non-local sparse models for image restoration, 2009 IEEE 12th International Conference on Computer Vision, 2009.
DOI : 10.1109/ICCV.2009.5459452

F. Malgouyres, Rank related properties for Basis Pursuit and total variation regularization, Signal Processing, vol.87, issue.11, pp.2695-2707, 2007.
DOI : 10.1016/j.sigpro.2007.04.019

URL : https://hal.archives-ouvertes.fr/hal-00020801

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

M. Nikolova, Weakly Constrained Minimization: Application to the Estimation of Images and Signals Involving Constant Regions, Journal of Mathematical Imaging and Vision, vol.21, issue.2, pp.155-175, 2004.
DOI : 10.1023/B:JMIV.0000035180.40477.bd

J. Orchard, M. Ebrahimi, and A. Wong, Efficient nonlocal-means denoising using the SVD, Int, Conf. on Image Processing, pp.1732-1735, 2008.

P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.12, issue.7, pp.629-639, 1990.
DOI : 10.1109/34.56205

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.108.2553

W. Ring, Structural Properties of Solutions to Total Variation Regularization Problems, ESAIM: Mathematical Modelling and Numerical Analysis, vol.34, issue.4, pp.799-840, 2000.
DOI : 10.1051/m2an:2000104

L. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena, vol.60, issue.1-4, pp.1-4, 1992.
DOI : 10.1016/0167-2789(92)90242-F

L. Rudin and S. Osher, Total variation based image restoration with free local constraints, Proceedings of 1st International Conference on Image Processing, pp.31-35, 1994.
DOI : 10.1109/ICIP.1994.413269

S. M. Smith and J. M. Brady, SUSAN?A new approach to low level image processing, International Journal of Computer Vision, vol.23, issue.1, pp.45-78, 1997.
DOI : 10.1023/A:1007963824710

D. M. Strong and T. F. Chan, Exact solutions to total variation regularization problems, UCLA CAM Report, pp.96-137, 1996.

C. Tomasi and R. Manduchi, Bilateral filtering for gray and color images, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271), pp.839-846, 1998.
DOI : 10.1109/ICCV.1998.710815

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.2047-2080, 2009.
DOI : 10.1137/070696143

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

L. Yaroslavsky and M. Eden, Digital picture processing ? an introduction, 1985.