C. Aguerrebere, A. Almansa, J. Delon, Y. Gousseau, and P. Musé, A Bayesian Hyperprior Approach for Joint Image Denoising and Interpolation, With an Application to HDR Imaging, IEEE Transactions on Computational Imaging, vol.3, issue.4, 2017.
DOI : 10.1109/TCI.2017.2704439

URL : https://hal.archives-ouvertes.fr/hal-01107519

P. Arias, V. Caselles, and G. Facciolo, Analysis of a Variational Framework for Exemplar-Based Image Inpainting, Multiscale Modeling & Simulation, vol.10, issue.2, pp.473-514, 2012.
DOI : 10.1137/110848281

S. Awate and R. Whitaker, Image denoising with unsupervised information-theoretic adaptive filtering, International Conference on Computer Vision and Pattern Recognition (CVPR 2005), pp.44-51, 2004.
DOI : 10.1109/cvpr.2005.176

URL : http://www.cs.utah.edu/projects/sci/publications/awate05/Awate_UINTA_CVPR.pdf

C. Barnes, E. Shechtman, A. Finkelstein, and D. Goldman, Patchmatch: A randomized correspondence algorithm for structural image editing, ACM Transactions on Graphics-TOG, vol.28, p.24, 2009.

L. Bergé, C. Bouveyron, and S. Girard, Package for Model-Based Clustering and Discriminant Analysis of High-Dimensional Data, Journal of Statistical Software, vol.46, issue.6, pp.46-47, 2012.
DOI : 10.18637/jss.v046.i06

C. Bouveyron and C. Brunet-saumard, Model-based clustering of high-dimensional data: A review, Computational Statistics & Data Analysis, vol.71, pp.71-52, 2014.
DOI : 10.1016/j.csda.2012.12.008

URL : https://hal.archives-ouvertes.fr/hal-00750909

C. Bouveyron, S. Girard, and C. Schmid, High-dimensional data clustering, Computational Statistics & Data Analysis, vol.52, issue.1, pp.502-519, 2007.
DOI : 10.1016/j.csda.2007.02.009

URL : https://hal.archives-ouvertes.fr/inria-00548573

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, 2006.
DOI : 10.1137/040616024

URL : https://hal.archives-ouvertes.fr/hal-00271141

A. Buades, B. Coll, J. Morel, and C. Sbert, Self-Similarity Driven Color Demosaicking, IEEE Transactions on Image Processing, vol.18, issue.6, pp.1192-202, 2009.
DOI : 10.1109/TIP.2009.2017171

URL : https://hal.archives-ouvertes.fr/hal-00449362

A. Criminisi, P. Pérez, 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

URL : http://www.csee.wvu.edu/~xinl/courses/ee565/image_inpainting.pdf

A. Criminisi, P. Pérez, and K. Toyama, Region filling and object removal by exemplar-based image inpainting, Image Process, IEEE Trans, vol.13, pp.1200-1212, 2004.
DOI : 10.1109/tip.2004.833105

URL : http://www.csee.wvu.edu/~xinl/courses/ee565/image_inpainting.pdf

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering, IEEE Transactions on Image Processing, vol.16, issue.8, pp.2080-2095, 2007.
DOI : 10.1109/TIP.2007.901238

URL : http://sp.cs.tut.fi/publications/archive/Dabov2007-Image.pdf

C. Deledalle, L. Denis, and F. Tupin, Iterative Weighted Maximum Likelihood Denoising With Probabilistic Patch-Based Weights, IEEE Transactions on Image Processing, vol.18, issue.12, pp.2661-72, 2009.
DOI : 10.1109/TIP.2009.2029593

URL : https://hal.archives-ouvertes.fr/ujm-00431266

C. Deledalle, S. Parameswaran, and T. Q. Nguyen, Image restoration with generalized gaussian mixture model patch priors, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01700082

C. Deledalle, F. Tupin, and L. Denis, Poisson NL means: Unsupervised non local means for Poisson noise, 2010 IEEE International Conference on Image Processing
DOI : 10.1109/ICIP.2010.5653394

URL : https://hal.archives-ouvertes.fr/hal-00957982

A. Efros and T. Leung, Texture synthesis by non-parametric sampling, Proceedings of the Seventh IEEE International Conference on Computer Vision, pp.1033-1038, 1999.
DOI : 10.1109/ICCV.1999.790383

URL : http://www.cs.berkeley.edu/~leungt/Research/ICCV99_synthesis.ps.gz

C. Fraley and A. Raftery, Model-Based Clustering, Discriminant Analysis, and Density Estimation, Journal of the American Statistical Association, vol.97, issue.458, pp.611-631, 2002.
DOI : 10.1198/016214502760047131

URL : http://www.csss.washington.edu/Papers/wp11.ps

O. Frigo, N. Sabater, J. Delon, and P. Hellier, Split and Match: Example-Based Adaptive Patch Sampling for Unsupervised Style Transfer, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp.553-561, 2016.
DOI : 10.1109/CVPR.2016.66

URL : https://hal.archives-ouvertes.fr/hal-01280818

A. Hertzmann, C. E. Jacobs, N. Oliver, B. Curless, and D. H. Salesin, Image analogies, Proceedings of the 28th annual conference on Computer graphics and interactive techniques , SIGGRAPH '01, pp.327-340, 2001.
DOI : 10.1145/383259.383295

A. Houdard, C. Bouveyron, and J. Delon, Clustering en haute dimensions pour le débruitage d'image, inXXVIì eme colloque GRETSI

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

URL : http://www.irisa.fr/vista/Papers/2006_ip_kervrann.pdf

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, 2007.
DOI : 10.1007/978-1-4612-0845-7

V. Kwatra, I. Essa, A. Bobick, and N. Kwatra, Texture optimization for example-based synthesis, ACM Transactions on Graphics, pp.24-795, 2005.
DOI : 10.1145/1186822.1073263

M. Lebrun, An Analysis and Implementation of the BM3D Image Denoising Method, Image Processing On Line, pp.175-213, 2012.

M. Lebrun, A. Buades, and J. M. , A Nonlocal Bayesian Image Denoising Algorithm, SIAM Journal on Imaging Sciences, vol.6, issue.3, pp.1665-1688, 2013.
DOI : 10.1137/120874989

M. Lebrun, A. Buades, and J. Morel, Implementation of the "Non-Local Bayes" (NL-Bayes) Image Denoising Algorithm, Image Processing On Line, vol.3, pp.1-42, 2013.
DOI : 10.5201/ipol.2013.16

E. Luo, S. H. Chan, and T. Q. Nguyen, Adaptive Image Denoising by Mixture Adaptation, IEEE Transactions on Image Processing, vol.25, issue.10, pp.4489-4503, 2016.
DOI : 10.1109/TIP.2016.2590318

URL : http://arxiv.org/pdf/1601.04770

G. Mclachlan and T. Krishnan, The EM Algorithm and Extensions, 1997.

G. Mclachlan and D. Peel, Finite mixture models, 2000.
DOI : 10.1002/0471721182

A. Newson, A. Almansa, M. Fradet, Y. Gousseau, and P. Pérez, Video Inpainting of Complex Scenes, SIAM Journal on Imaging Sciences, vol.7, issue.4, pp.1993-2019, 2014.
DOI : 10.1137/140954933

URL : https://hal.archives-ouvertes.fr/hal-00937795

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

G. Peyré, S. Bougleux, and L. Cohen, Non-local Regularization of Inverse Problems, pp.57-68, 2008.
DOI : 10.1109/TIT.2006.871582

G. Schwarz, Estimating the dimension of a model, The annals of statistics, pp.461-464, 1978.

M. Tipping and C. Bishop, Mixtures of Probabilistic Principal Component Analyzers, Neural Computation, vol.2, issue.1, pp.443-482, 1999.
DOI : 10.1007/BF00162527

Y. Wang, The Implementation of SURE Guided Piecewise Linear Image Denoising, Image Processing On Line, vol.3, pp.43-67, 2013.
DOI : 10.5201/ipol.2013.52

Y. Wang and J. Morel, SURE Guided Gaussian Mixture Image Denoising, SIAM Journal on Imaging Sciences, vol.6, issue.2, pp.999-1034, 2013.
DOI : 10.1137/120901131

URL : https://hal.archives-ouvertes.fr/hal-00785334

T. Weissman, E. Ordentlich, G. Seroussi, S. Verdú, and M. J. Weinberger, Universal discrete denoising: Known channel, IEEE Transactions on Information Theory, pp.51-56, 2005.
DOI : 10.1109/isit.2003.1228098

Y. Wexler, E. Shechtman, and M. Irani, Space-time completion of video, IEEE Transactions on pattern analysis and machine intelligence, p.29, 2007.

C. Wu, On the convergence properties of the EM algorithm, The Annals of Statistics, pp.95-103, 1983.

J. Yang, X. Liao, X. Yuan, P. Llull, D. J. Brady et al., Compressive Sensing by Learning a Gaussian Mixture Model From Measurements, IEEE Transactions on Image Processing, vol.24, issue.1, pp.106-119, 2015.
DOI : 10.1109/TIP.2014.2365720

G. Yu, G. Sapiro, and S. Mallat, Solving inverse problems with piecewise linear estimators: from gaussian mixture models to structured sparsity, IEEE Trans. Image Process, vol.21, pp.2481-99, 2012.
DOI : 10.21236/ADA540722

D. Zoran and Y. Weiss, From learning models of natural image patches to whole image restoration, 2011 International Conference on Computer Vision, pp.479-486, 2011.
DOI : 10.1109/ICCV.2011.6126278