H. Akaike, A new look at the statistical model identification, IEEE Transactions on Automatic Control, vol.19, issue.6, pp.716-723, 1974.
DOI : 10.1109/TAC.1974.1100705

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, vol.7, issue.1, pp.29-53, 2005.
DOI : 10.4171/IFB/112

F. Alter, S. Durand, and J. Froment, Adapted Total Variation for Artifact Free Decompression of JPEG Images, Journal of Mathematical Imaging and Vision, vol.25, issue.9, pp.199-211, 2005.
DOI : 10.1007/s10851-005-6467-9

URL : https://hal.archives-ouvertes.fr/hal-00712138

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

L. Ambrosio, N. Fusco, and D. Pallara, Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs, 2000.

F. Andreu, C. Ballester, V. Caselles, and J. M. And-mazòn, Minimizing total variation flow. Comptes Rendus de l, Académie des Sciences, issue.11, pp.331867-872, 2000.
DOI : 10.1016/s0764-4442(00)01729-8

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.142.311

C. Andrieu and ´. E. Moulines, On the ergodicity properties of some adaptive MCMC algorithms, The Annals of Applied Probability, vol.16, issue.3, pp.1462-1505, 2006.
DOI : 10.1214/105051606000000286

S. Arulampalam, S. Maskell, G. , and N. , A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking, IEEE Transactions on Signal Processing, vol.50, issue.2, pp.174-188, 2002.
DOI : 10.1109/78.978374

G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, of Applied Mathematical Sciences, 2006.

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 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, 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

S. Awate and R. Whitaker, Higher-order image statistics for unsupervised, informationtheoretic , adaptive, image filtering, CVPR05, pages II, pp.44-51, 2005.

S. Awate and R. Whitaker, Unsupervised, information-theoretic, adaptive image filtering for image restoration, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.28, issue.3, pp.364-376, 2006.
DOI : 10.1109/TPAMI.2006.64

N. Azzabou, N. Paragios, and F. Guichard, Image Denoising Based on Adapted Dictionary Computation, 2007 IEEE International Conference on Image Processing, pp.109-112, 2007.
DOI : 10.1109/ICIP.2007.4379258

N. Azzabou, N. Paragios, and F. Guichard, Uniform and textured regions separation in natural images towards MPM adaptive denoising. Scale Space and Variational Methods in Computer Vision, pp.418-429, 2008.

M. Bédard, Weak convergence of Metropolis algorithms for non-i.i.d. target distributions, The Annals of Applied Probability, vol.17, issue.4, pp.1222-1244, 2007.
DOI : 10.1214/105051607000000096

M. Bertalmio, V. Caselles, B. Rougé, and A. Solé, TV based image restoration with local constraints, J. Sci. Comput, vol.19, pp.1-395, 2003.

J. Besag, Spatial interaction and the statistical analysis of lattice systems, Journal of the Royal Statistical Society, Series B, vol.36, issue.2, pp.192-236, 1974.

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

J. Besag, Digital Image Processing, Journal of Applied Statistics, vol.74, issue.3, pp.395-407, 1989.
DOI : 10.2307/2289127

J. Besag, P. Green, D. Higdon, and K. Mengersen, Bayesian Computation and Stochastic Systems, Statistical Science, vol.10, issue.1, pp.3-41, 1995.
DOI : 10.1214/ss/1177010123

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.8854

L. Birgé and Y. Rozenholc, How many bins should be put in a regular histogram, ESAIM: Probability and Statistics, vol.10, pp.24-45, 2006.
DOI : 10.1051/ps:2006001

A. Blake and A. Zisserman, Visual Reconstruction, 1987.

G. Blanchet and . Ens-cachan, Etude des artefacts de flou, ringing et aliasing en imagerie numérique. ApplicationàApplication`Applicationà la restauration, 2006.

P. Blomgren, T. 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

A. Borghi, J. Darbon, S. Peyronnet, T. F. Chan, and S. Osher, A Simple Compressive Sensing Algorithm for Parallel Many-Core Architectures, Journal of Signal Processing Systems, vol.1, issue.1, 2008.
DOI : 10.1007/s11265-012-0671-9

URL : https://hal.archives-ouvertes.fr/hal-01086454

C. Bouman and K. Sauer, A generalized Gaussian image model for edge-preserving MAP estimation, IEEE Transactions on Image Processing, vol.2, issue.3, pp.296-310, 1993.
DOI : 10.1109/83.236536

L. A. Breyer and G. O. Roberts, From metropolis to diffusions: Gibbs states and optimal scaling, Stochastic Processes and their Applications, vol.90, issue.2, pp.181-206, 2000.
DOI : 10.1016/S0304-4149(00)00041-7

URL : http://doi.org/10.1016/s0304-4149(00)00041-7

H. R. Brezis, Les opérateurs monotones. Séminaire Choquet, InitiationàInitiation`Initiationà l'analyse, 1965.

T. Brox and J. Weickert, A TV flow based local scale estimate and its application to texture discrimination, Journal of Visual Communication and Image Representation, vol.17, issue.5, pp.1053-1073, 2006.
DOI : 10.1016/j.jvcir.2005.06.001

A. Buades, B. Coll, J. Lisani, and C. Sbert, Conditional image diffusion, Inverse Problems and Imaging, vol.1, issue.4, pp.593-608, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00271145

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, Neighborhood filters and PDE???s, Numerische Mathematik, vol.23, issue.1, pp.1-34, 2006.
DOI : 10.1007/s00211-006-0029-y

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.1499-1505, 2006.
DOI : 10.1109/TIP.2006.871137

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

A. Buades, B. Coll, and J. Morel, Nonlocal Image and Movie Denoising, International Journal of Computer Vision, vol.14, issue.1, pp.123-139, 2008.
DOI : 10.1007/s11263-007-0052-1

URL : https://hal.archives-ouvertes.fr/hal-00271147

R. W. Buccigrossi and E. P. Simoncelli, Image compression via joint statistical characterization in the wavelet domain, IEEE Transactions on Image Processing, vol.8, issue.12, pp.1688-1701, 1999.
DOI : 10.1109/83.806616

L. A. Caffarelli and X. Cabré, Fully Nonlinear Elliptic Equations, 1995.
DOI : 10.1090/coll/043

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

F. Catté, F. Dibos, and G. Koepfler, A Morphological Scheme for Mean Curvature Motion and Applications to Anisotropic Diffusion and Motion of Level Sets, SIAM Journal on Numerical Analysis, vol.32, issue.6, pp.1895-1909, 1995.
DOI : 10.1137/0732085

B. Chalmond, Modeling and Inverse Problems in Image Analysis, Applied Mathematical Science, vol.155, 2003.

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, EMMCVPR, pp.136-152, 2005.
DOI : 10.1007/11585978_10

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

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 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, 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

R. R. Coifman and D. L. Donoho, Translation-Invariant De-Noising, Lecture notes in statistics: Wavelets and statistics, pp.125-150, 1995.
DOI : 10.1007/978-1-4612-2544-7_9

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.125.3682

P. L. Combettes and J. C. Pesquet, Image Restoration Subject to a Total Variation Constraint, IEEE Transactions on Image Processing, vol.13, issue.9, pp.1213-1222, 2004.
DOI : 10.1109/TIP.2004.832922

URL : https://hal.archives-ouvertes.fr/hal-00017934

P. L. Combettes and V. R. Wajs, Theoretical analysis of some regularized image denoising methods, 2004 International Conference on Image Processing, 2004. ICIP '04., pp.969-972, 2004.
DOI : 10.1109/ICIP.2004.1419462

URL : https://hal.archives-ouvertes.fr/hal-00017847

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

I. Csiszar and Z. Talata, Consistent estimation of the basic neighborhood of Markov random fields. The Annals of Statistics, pp.123-145, 2006.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, Image denoising with blockmatchig and 3D filtering, Electronic Imaging'06, Proc. SPIE 6064, 2006.

J. Darbon and M. Sigelle, A Fast and Exact Algorithm for Total Variation Minimization, 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

J. Darbon and M. Sigelle, Image Restoration with Discrete Constrained Total Variation Part II: Levelable Functions, Convex Priors and Non-Convex Cases, Journal of Mathematical Imaging and Vision, vol.39, issue.4, pp.277-291, 2006.
DOI : 10.1007/s10851-006-0644-3

A. Desolneux, L. Moisan, and J. Morel, From Gestalt Theory to Image Analysis: a probabilistic approach, 2008.
DOI : 10.1007/978-0-387-74378-3

URL : https://hal.archives-ouvertes.fr/hal-00259077

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 J. Froment, Reconstruction of Wavelet Coefficients Using Total Variation Minimization, SIAM Journal on Scientific Computing, vol.24, issue.5, pp.1754-1767, 2003.
DOI : 10.1137/S1064827501397792

URL : https://hal.archives-ouvertes.fr/hal-00712152

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

R. Durrett, Probability: theory and examples, 1996.
DOI : 10.1017/CBO9780511779398

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

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

H. Federer, Geometric measure theory, 1969.
DOI : 10.1007/978-3-642-62010-2

J. A. Fessler, Mean and variance of implicitly defined biased estimators (such as penalized maximum likelihood): applications to tomography, IEEE Transactions on Image Processing, vol.5, issue.3, pp.493-506, 1996.
DOI : 10.1109/83.491322

G. Fort, E. Moulines, G. O. Roberts, and J. S. Rosenthal, On the geometric ergodicity of hybrid samplers, Journal of Applied Probability, vol.55, issue.01, pp.123-146, 2003.
DOI : 10.1093/biomet/83.1.95

H. Fu, M. K. Ng, M. Nikolova, and J. L. Barlow, Efficient Minimization Methods of Mixed l2-l1 and l1-l1 Norms for Image Restoration, SIAM Journal on Scientific Computing, vol.27, issue.6, pp.271881-1902, 2006.
DOI : 10.1137/040615079

H. Fu, M. K. Ng, M. Nikolova, J. L. Barlow, C. et al., Fast Algorithms for l1 Norm/Mixed l1 and l2 Norms for Image Restoration, Lecture Notes in Computer Science, vol.3483, issue.4, pp.843-851, 2005.
DOI : 10.1007/11424925_88

A. Gelman, G. O. Roberts, and W. R. Gilks, Efficient Metropolis jumping rules, Bayesian statistics, pp.599-607, 1994.

D. Geman and A. Koloydenko, Invariant statistics and coding of natural microimages, CVPR 99, 1999.

D. Geman and C. Yang, Nonlinear image recovery with half-quadratic regularization, IEEE Transactions on Image Processing, vol.4, issue.7, pp.932-946, 1995.
DOI : 10.1109/83.392335

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.53.7349

S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images In Readings in computer vision: issues, problems, principles, and paradigms, pp.564-584, 1987.

C. Geyer, Practical Markov Chain Monte Carlo, Statistical Science, vol.7, issue.4, pp.473-483, 1992.
DOI : 10.1214/ss/1177011137

URL : http://projecteuclid.org/download/pdf_1/euclid.ss/1177011137

G. Gilboa, N. Sochen, and Y. Y. Zeevi, Texture preserving variational denoising using an adaptive fidelity term, pp.137-144, 2003.

G. Gilboa, N. Sochen, and Y. Y. Zeevi, Variational denoising of partly textured images by spatially varying constraints, IEEE Transactions on Image Processing, vol.15, issue.8, pp.152281-2289, 2006.
DOI : 10.1109/TIP.2006.875247

D. Goldfarb and W. Yin, Second-order Cone Programming Methods for Total Variation-Based Image Restoration, SIAM Journal on Scientific Computing, vol.27, issue.2, pp.622-645, 2005.
DOI : 10.1137/040608982

N. Gordon, D. Salmond, and A. F. Smith, Novel approach to non-linear and non-Gaussian Bayesian state estimation. Radar and Signal Processing, IEEE Proceedings-F, vol.140, issue.2, pp.107-113, 1993.

Y. Gousseau and J. Morel, Are Natural Images of Bounded Variation?, SIAM Journal on Mathematical Analysis, vol.33, issue.3, pp.634-648, 2001.
DOI : 10.1137/S0036141000371150

G. R. Grimmett and D. R. Stirzaker, Probability and random processes, 2001.

F. Guichard and F. Malgouyres, Total variation based interpolation, Proceedings of Eusipco'98, pp.1741-1744, 1998.

F. Guichard, L. Moisan, and J. Morel, A review of P.D.E. models in image processing and image analysis, Journal de Physique IV (Proceedings), vol.12, issue.1, pp.137-154, 2002.
DOI : 10.1051/jp42002006

F. Guichard and J. Morel, Image analysis and PDE's, 2001.

J. M. Hammersley and P. Clifford, Markov field on finite graphs and lattices. (Unpub- lished), 1971.

W. K. Hastings, Monte Carlo sampling methods using Markov chains and their applications, Biometrika, vol.57, issue.1, pp.97-109, 1970.
DOI : 10.1093/biomet/57.1.97

T. Hida and H. Nomoto, Gaussian measure on the projective limit space of spheres, Proc. Japan Acad, pp.301-304, 1964.
DOI : 10.3792/pja/1195522741

J. Hiriart-urruty and C. Lemaréchal, Convex analysis and minimization algorithms: A review of PDE models in image image processing and image analysis, pp.305-306, 1993.
DOI : 10.1007/978-3-662-02796-7

D. S. Hochbaum, An efficient algorithm for image segmentation, Markov random fields and related problems, Journal of the ACM, vol.48, issue.4, pp.686-701, 2001.
DOI : 10.1145/502090.502093

G. Huang, A. B. Lee, and D. Mumford, Statistics of range images, Proceedings of CVPR, pp.541-547, 2000.

G. Huang and D. Mumford, Image statistics for the British aerospace segmented database, MTPC preprint, 1999.

G. Huang and D. Mumford, The statistics of natural images and models, Proceedings of IEEE Comp. Vision and Pattern Recognition, pp.541-547, 1999.

A. Jalobeanu, L. Blanc-féraud, and J. Zerubia, Estimation d'hyperparamètres pour la restauration d'images satellitaires par une méthode MCMCML, Research Report, vol.3469, 1998.

S. F. Jarner and E. Hansen, Geometric ergodicity of Metropolis algorithms, Stochastic Processes and their Applications, vol.85, issue.2, pp.341-361, 2000.
DOI : 10.1016/S0304-4149(99)00082-4

C. Kervrann and J. Boulanger, Optimal Spatial Adaptation for Patch-Based Image Denoising, IEEE Transactions on Image Processing, vol.15, issue.10, pp.2866-2878, 2006.
DOI : 10.1109/TIP.2006.877529

C. Kervrann and J. Boulanger, Local adaptivity to variable smoothness for exemplarbased image denoising and representation, International Journal of Computer Vision, 2007.
DOI : 10.1007/s11263-007-0096-2

URL : https://hal.archives-ouvertes.fr/inria-00070384

C. Kervrann, J. Boulanger, C. , and P. , Bayesian Non-local Means Filter, Image Redundancy and Adaptive Dictionaries for Noise Removal, Proc. Conf. Scale-Space and Variational Meth. (SSVM' 07), pp.520-532, 2007.
DOI : 10.1007/978-3-540-72823-8_45

URL : https://hal.archives-ouvertes.fr/hal-00645444

S. Kindermann, S. Osher, and P. W. Jones, Deblurring and Denoising of Images by Nonlocal Functionals, Multiscale Modeling & Simulation, vol.4, issue.4, pp.1091-1115, 2005.
DOI : 10.1137/050622249

C. Kipnis and S. R. Varadhan, Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions, Communications in Mathematical Physics, vol.28, issue.1, pp.1-19, 1986.
DOI : 10.1007/BF01210789

A. A. Koloydenko, Modeling natural microimage statistics, 2000.

A. A. Koloydenko, Adaptive coding of microstructure of natural images. Eurandom seminar, 2004.

S. Lafon, Y. Keller, and R. R. Coifman, Data Fusion and Multicue Data Matching by Diffusion Maps, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.28, issue.11, pp.1784-1797, 2006.
DOI : 10.1109/TPAMI.2006.223

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.419.1814

A. B. Lee, K. S. Pedersen, and D. Mumford, The nonlinear statistics of high-contrast patches in natural images, Int. J. Comput. Vision, vol.54, pp.1-383, 2003.

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

B. Luo, J. Aujol, Y. Gousseau, S. Ladjal, and H. Ma??trema??tre, Resolution- Independent Characteristic Scale Dedicated to Satellite Images, IEEE Transactions on Image Processing, vol.16, issue.10, pp.162503-2514, 2007.
DOI : 10.1109/TIP.2007.906004

URL : https://hal.archives-ouvertes.fr/hal-00176968

F. Malgouyres, Minimizing the total variation under a general convex constraint for image restoration, IEEE Transactions on Image Processing, vol.11, issue.12, pp.1450-1456, 2002.
DOI : 10.1109/TIP.2002.806241

B. Malgouyres and F. , Rank related properties for basis pursuit and total variation regularization . Signal Process, pp.2695-2707, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00020801

S. Mallat, A wavelet tour of signal processing, 1998.

B. Maurey, Inégalité de Brunn-Minkowski-Lusternik, et autres inégalités géométriques et fonctionnelles, Séminaire Bourbaki, issue.299 928, pp.95-113, 2003.

K. L. Mengersen and R. L. Tweedie, Rates of convergence of the Hastings and Metropolis algorithms, The Annals of Statistics, vol.24, issue.1, pp.101-121, 1996.
DOI : 10.1214/aos/1033066201

Y. Meyer, Oscillating patterns in image processing and nonlinear evolution equations, volume 22 of University Lecture Series, 2001.

S. Meyn and R. Tweedie, Markov Chains and Stochastic Stability, 1993.

L. Moisan, Affine plane curve evolution: a fully consistent scheme, IEEE Transactions on Image Processing, vol.7, issue.3, pp.411-420, 1998.
DOI : 10.1109/83.661191

L. Moisan, Extrapolation de spectre et variation totale pondérée. GRETSI'01, 2001.

L. Moisan, How to discretize the total variation of an image? ICIAM'07, 2007.

J. Moreau, Fonctions convexes duales et points proximaux dans un espace hilbertien, C.R. Acad. Sci. Paris Sér. A Math, vol.255, pp.2897-2899, 1962.

J. Moreau, Proximit?? et dualit?? dans un espace hilbertien, Bulletin de la Société mathématique de France, vol.79, pp.273-299, 1965.
DOI : 10.24033/bsmf.1625

URL : http://archive.numdam.org/article/BSMF_1965__93__273_0.pdf

D. Mumford and B. Gidas, Stochastic models for generic images, Quarterly of Applied Mathematics, vol.59, issue.1, pp.85-111, 2001.
DOI : 10.1090/qam/1811096

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.366.5210

P. Neal and G. Roberts, Optimal scaling for partially updating MCMC algorithms, The Annals of Applied Probability, vol.16, issue.2, pp.475-515, 2006.
DOI : 10.1214/105051605000000791

M. Nikolova, Estimées localement fortement homogènes. Compte-rendus de l'académie des sciences, t, pp.665-670, 1997.
DOI : 10.1016/s0764-4442(97)84780-5

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

M. Nikolova, Analysis of the Recovery of Edges in Images and Signals by Minimizing Nonconvex Regularized Least-Squares, Multiscale Modeling & Simulation, vol.4, issue.3, pp.960-991, 2005.
DOI : 10.1137/040619582

M. Nikolova, Model distortions in Bayesian MAP reconstruction, Inverse Problems and Imaging, vol.1, issue.2, pp.399-422, 2007.
DOI : 10.3934/ipi.2007.1.399

B. Olshausen and E. Simoncelli, Natural image statistics and neural representation, Annu. Rev. Neurosci, vol.24, pp.1193-1216, 2001.

E. Ordentlich, G. Seroussi, S. Verdú, M. J. Weinberger, and T. Weissman, A discrete universal denoiser and its application to binary images, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429), pp.117-120, 2003.
DOI : 10.1109/ICIP.2003.1246912

J. D. Owens, D. Luebke, N. Govindaraju, M. Harris, J. Kruger et al., A Survey of General-Purpose Computation on Graphics Hardware, Computer Graphics Forum, vol.7, issue.4, pp.80-113, 2007.
DOI : 10.1016/j.rti.2005.04.002

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

G. Peyré, Image processing with non-local spectral bases. to appear in SIAM Multiscale Modeling and Simulation, 2008.

K. Popat and R. Picard, Cluster-based probability model and its application to image and texture processing, IEEE Transactions on Image Processing, vol.6, issue.2, pp.268-284, 1997.
DOI : 10.1109/83.551697

J. Portilla and E. P. Simoncelli, A parametric texture model based on joint statistics of complex wavelet coefficients, International Journal of Computer Vision, vol.40, issue.1, pp.49-70, 2000.
DOI : 10.1023/A:1026553619983

A. Prékopa, On logarithmic concave measures and functions, Acta Scientiarum Mathematicarum, vol.34, pp.335-343, 1973.

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

C. Robert, Méthodes de Monte Carlo par cha??nescha??nes de Markov, Statistique Mathématique et Probabilité. [Mathematical Statistics and Probability]. ´ EditionsÉconomicaEditions´EditionsÉconomica, 1996.

G. O. Roberts and J. S. Rosenthal, Geometric Ergodicity and Hybrid Markov Chains, Electronic Communications in Probability, vol.2, issue.0, pp.13-25, 1997.
DOI : 10.1214/ECP.v2-981

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.29

G. O. Roberts and J. S. Rosenthal, Two convergence properties of hybrid samplers, The Annals of Applied Probability, vol.8, issue.2, pp.397-407, 1998.
DOI : 10.1214/aoap/1028903533

G. O. Roberts and J. S. Rosenthal, Optimal scaling for various Metropolis-Hastings algorithms, Statistical Science, vol.16, issue.4, pp.351-367, 2001.
DOI : 10.1214/ss/1015346320

G. O. Roberts and R. L. Tweedie, Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms, Biometrika, vol.83, issue.1, pp.95-110, 1996.
DOI : 10.1093/biomet/83.1.95

URL : http://biomet.oxfordjournals.org/cgi/content/short/83/1/95

M. C. Robini, A. Lachal, and I. E. Magnin, A Stochastic Continuation Approach to Piecewise Constant Reconstruction, IEEE Transactions on Image Processing, vol.16, issue.10, pp.2576-2589, 2007.
DOI : 10.1109/TIP.2007.904975

URL : https://hal.archives-ouvertes.fr/hal-00443442

G. G. Roussas, Nonparametric regression estimation under mixing conditions. Stochastic Process, Appl, vol.36, issue.1, pp.107-116, 1990.
DOI : 10.1016/0304-4149(90)90045-t

URL : http://doi.org/10.1016/0304-4149(90)90045-t

P. Rousseeuw and A. Leroy, Robust regression and outlier detection, 1987.
DOI : 10.1002/0471725382

D. Ruderman, The statistics of natural images, Network: Computation in Neural Systems, vol.5, issue.4, pp.517-548, 1994.
DOI : 10.1088/0954-898X_5_4_006

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.1-4259, 1992.
DOI : 10.1016/0167-2789(92)90242-F

H. Rue, New Loss Functions in Bayesian Imaging, Journal of the American Statistical Association, vol.82, issue.431, pp.900-908, 1995.
DOI : 10.1080/01621459.1995.10476589

H. Rue and M. Hurn, A Loss Function Model for the Restoration of Grey Level Images, Scandinavian Journal of Statistics, vol.24, issue.1, pp.103-114, 1997.
DOI : 10.1111/1467-9469.t01-1-00051

J. Savage and K. Chen, On multigrids for solving a class of improved total variation based PDE models, Proceedings of the 1st International Conference PDE-based Image Processing and Related Inverse Problems, 2006.

E. Simoncelli, Bayesian Denoising of Visual Images in the Wavelet Domain, Lecture Notes in Statistics, p.41, 1999.
DOI : 10.1007/978-1-4612-0567-8_18

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

A. Srivastava, A. B. Lee, E. P. Simoncelli, and S. Zhu, On advances in statistical modeling of natural images, Special issue on imaging science, pp.17-33, 2002.
DOI : 10.1023/A:1021889010444

G. Steidl, J. Weickert, T. Brox, P. Mrázek, and M. Welk, On the Equivalence of Soft Wavelet Shrinkage, Total Variation Diffusion, Total Variation Regularization, and SIDEs, SIAM Journal on Numerical Analysis, vol.42, issue.2, pp.686-713, 2004.
DOI : 10.1137/S0036142903422429

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

D. Strong and T. Chan, Edge-preserving and scale-dependent properties of total variation regularization, Inverse Problems, vol.19, issue.6, pp.165-187, 2003.
DOI : 10.1088/0266-5611/19/6/059

D. M. Strong, P. Blomgren, C. , and T. F. , <title>Spatially adaptive local-feature-driven total variation minimizing image restoration</title>, Statistical and Stochastic Methods in Image Processing II, pp.222-233, 1997.
DOI : 10.1117/12.279642

L. Tierney, Markov Chains for Exploring Posterior Distributions, The Annals of Statistics, vol.22, issue.4, pp.1701-1762, 1994.
DOI : 10.1214/aos/1176325750

J. A. Tropp, Just relax: convex programming methods for identifying sparse signals in noise, IEEE Transactions on Information Theory, vol.52, issue.3, pp.1030-1051, 2006.
DOI : 10.1109/TIT.2005.864420

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

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, Image Quality Assessment: From Error Visibility to Structural Similarity, IEEE Transactions on Image Processing, vol.13, issue.4, pp.600-612, 2004.
DOI : 10.1109/TIP.2003.819861

L. Yaroslavsky and M. Eden, Fundamentals of Digital Optics, 1996.
DOI : 10.1007/978-1-4612-0845-7

S. C. Zhu and D. Mumford, Prior learning and Gibbs reaction-diffusion, IEEE Trans. on Pattern Anal. Mach. Intell, vol.19, issue.11, pp.1236-1250, 1997.

S. C. Zhu, Y. Wu, and D. Mumford, Filters, random fields and maximum entropy (FRAME): Towards a unified theory for texture modeling, Int. J. Comput. Vision, issue.2, pp.27107-126, 1998.