L. Alvarez, P. Lions, and J. Morel, Image Selective Smoothing and Edge Detection by Nonlinear Diffusion. II, SIAM Journal on Numerical Analysis, vol.29, issue.3, pp.29-845, 1992.
DOI : 10.1137/0729052

J. F. Aujol, G. Aubert, and L. , Blanc-Fraud, and A. Chambolle, Decomposing an image: Application to textured images and sar images, INRIA Research Report, vol.4704, 2003.

S. A. Awate and R. T. Whitaker, Image denoising with unsupervised, information-theoretic, adaptive filtering, UUCS, 2004.

T. Buades, B. Coll, and J. Morel, Procédé de traitement de données d'image, par réduction de bruit d'image, et caméra intégrant des moyens de mise en oeuvre du procédé (image data process by image noise reduction and camera integrating the means for implementing this process) European patent pending, 2004.

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.1845-1909, 1995.
DOI : 10.1137/0732085

A. Chambolle and P. L. 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. F. Chan and H. M. Zhou, Total variation improved wavelet thresholding in image compression, Proceedings 2000 International Conference on Image Processing (Cat. No.00CH37101), pp.391-394, 2000.
DOI : 10.1109/ICIP.2000.899404

D. Donoho, De-noising by soft-thresholding, IEEE Transactions on Information Theory, vol.41, issue.3, pp.613-627, 1995.
DOI : 10.1109/18.382009

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

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, Restoration of wavelet coefficients by minimizing a specially designed objective function, Proc. of IEEE Workshop on Variational and Level Set Methods in Computer Vision, 2003.

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

F. Guichard, J. Morel, and R. Ryan, Image analysis and p.d.e.'s

E. Levina, Statistical Issues in Texture Analysis, 2002.

M. Lindenbaum, M. Fischer, and A. M. Bruckstein, On Gabor's contribution to image enhancement, Pattern Recognition, vol.27, issue.1, pp.1-8, 1994.
DOI : 10.1016/0031-3203(94)90013-2

S. Lintner and F. Malgouyres, constraints, Inverse Problems, vol.20, issue.3, 2003.
DOI : 10.1088/0266-5611/20/3/010

L. Yaroslavsky, K. Egiazarian, and J. Astola, <title>Transform domain image restoration methods: review, comparison, and interpretation</title>, Nonlinear Image Processing and Pattern Analysis XII, 2001.
DOI : 10.1117/12.424970

F. Malgouyres, A noise selection approach of image restoration, Applications in signal and image processing IX, pp.34-41, 2001.

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

B. Merriman, J. Bence, and S. Osher, Diffusion generated motion by mean curvature, Proceedings of the Geometry Center Workshop, 1992.

Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations, 2002.
DOI : 10.1090/ulect/022

E. A. Nadaraya, On estimating regression, Theory of Probability and its Applications, pp.186-190, 1964.

E. Ordentlich, G. Seroussi, M. Weinberger, S. Verdú, 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

S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, Using geometry and iterated refinement for inverse problems (1): Total variation based image restoration, pp.4-13, 2004.

E. , L. Pennec, and S. Mallat, Geometrical image compression with bandelets, Proceedings of the SPIE 2003, pp.1273-1286, 2003.

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

G. Roussas, Nonparametric regression estimation under mixing conditions, Stochastic processes and their applications, pp.36-107, 1990.
DOI : 10.1016/0304-4149(90)90045-t
URL : http://doi.org/10.1016/0304-4149(90)90045-t

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

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

C. Shannon and W. Weaver, The mathematical theory of communication, 1998.

A. Sharf, M. Alexa, and D. Cohen-or, Context-based surface completion, Proceedings of the 2004 SIGGRAPH Conference, pp.878-887, 2004.

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

J. Starck, E. Cands, and D. Donoho, The curvelet transform for image denoising, IEEE Transactions on Image Processing, vol.11, issue.6, pp.670-684, 2000.
DOI : 10.1109/TIP.2002.1014998

E. Tadmor, S. Nezzar, and L. Vese, A multiscale image representation using hierarchical (bv, l2) decompositions, Multiscale Modeling and Simulation, pp.553-572, 2004.

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

G. S. Watson, Smooth regression analysis, The Indian Journal of Statistics, vol.26, pp.359-372, 1964.

T. Weissman, E. Ordentlich, G. Seroussi, S. Verdu, and M. Weinberger, Universal discrete denoising: Known channel
DOI : 10.1109/isit.2003.1228098
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.58.3305

L. P. Yaroslavsky, Digital Picture Processing -An Introduction, 1985.

L. Yaroslavsky, <title>Local adaptive image restoration and enhancement with the use of DFT and DCT in a running window</title>, Wavelet Applications in Signal and Image Processing IV, pp.1-13, 1996.
DOI : 10.1117/12.255218