P. De, Images débruitées par minimisation d'énergie. La colonne de gauche présente les résultats obtenus avec l'a priori J 2 Celle de droite présente les résultats obtenus avec une pénalisation TV. Les images montrées sont obtenues pour des valeurs de ? optimales en terme, p.53

.. Décomposition-d-'une-image-d-'empreinte-digitale, Première ligne : image originale Deuxième ligne : graphe non pondéré de 4- voisinage. Troisième ligne : graphe de 8-voisinage pondéré par poids gaussiens Quatrième ligne : 25-plus proches voisins avec poids gaussiens sur patchs 5 × 5, p.100

.. Décomposition-multi-Échelle-de, Barbara" : graphe en 8-voisinage, poids gaussiens, p.134

.. Décomposition-multi-Échelle-de, Barbara" : graphe des 7-plus proches voisins, poids gaussiens sur patchs 5 × 5 dans un voisinage 11 × 11, p.135

.. Décomposition-multi-Échelle-de, Man" : graphe des 7-plus proches voisins, poids gaussiens sur patchs 5 × 5 dans un voisinage 11 × 11, p.136

). Erreur, Transformées considérées : lifting sur graphe (4 et 8 voisinage, plus proches voisins), p.153

). Erreur, Transformées considérées : lifting sur graphe (4 et 8 voisinage, plus proches voisins), p.156

M. Hidane, O. Lezoray, V. Ta, and A. Elmoataz, Nonlocal Multiscale Hierarchical Decomposition on Graphs, European Conference on Computer Vision (ECCV), volume LNCS 6314, pp.638-650, 2010.
DOI : 10.1007/978-3-642-15561-1_46

URL : https://hal.archives-ouvertes.fr/hal-00521070

M. Hidane, O. Lézoray, and A. Elmoataz, Hierarchical Representation of Discrete Data on Graphs, International Conference on Computer Analysis of Images and Patterns (IAPR CAIP), volume LNCS 6854, pp.186-193, 2011.
DOI : 10.1007/978-3-642-23672-3_23

URL : https://hal.archives-ouvertes.fr/hal-00808924

M. Hidane, O. Lézoray, and A. Elmoataz, A scale-space based hierarchical representation of discrete data, 2011 18th IEEE International Conference on Image Processing, pp.285-288, 2011.
DOI : 10.1109/ICIP.2011.6116144

URL : https://hal.archives-ouvertes.fr/hal-00812281

M. Hidane, O. Lezoray, A. Elmoataz, and V. Ta, Représentation multiéchelle hiérarchique de données discrètes définies sur des graphes, 2011.

J. Aujol, G. Aubert, L. Blanc-féraud, A. Chambollead00, ]. F. Arandiga et al., Image Decomposition into a Bounded Variation Component and an Oscillating Component, Journal of Mathematical Imaging and Vision, vol.15, issue.3, pp.71-8885, 2000.
DOI : 10.1007/s10851-005-4783-8

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

J. Aujol, G. Gilboa, T. Chan, S. Osherak06, ]. G. Aubert et al., Structure-texture image decomposition?modeling, algorithms, and parameter selection Mathematical problems in image processing : partial differential equations and the calculus of variations Integro-differential equations based on (bv,l?1) image decomposition The laplacian pyramid as a compact image code, Bauschke and P.L. Combettes. Convex analysis and monotone operator theory in Hilbert spaces, pp.111-136300, 1983.

. [. Bibliographie, B. Buades, J. Coll, and . Morel, Image denoising methods. A new non-local principle, SIAM Review, vol.52, issue.1, pp.113-147, 2010.

A. [. Baraniuk, R. Cohen, and . Wagner, Approximation and compression of scattered data by meshless multiscale decompositions, Applied and Computational Harmonic Analysis, vol.25, issue.2, pp.133-147, 2008.
DOI : 10.1016/j.acha.2007.10.003

A. [. Bougleux, M. Elmoataz, and . Melkemi, Discrete Regularization on Weighted Graphs for Image and Mesh Filtering
DOI : 10.1007/978-3-540-72823-8_12

URL : https://hal.archives-ouvertes.fr/hal-00333374

A. [. Bougleux, M. Elmoataz, and . Melkemi, Local and Nonlocal Discrete Regularization on Weighted Graphs for??Image and??Mesh??Processing, Scale Space and Variational Methods in Computer Vision, pp.128-139220, 2007.
DOI : 10.1007/s11263-008-0159-z

URL : https://hal.archives-ouvertes.fr/hal-00333329

]. J. Bes93 and . Besag, Towards bayesian image analysis*, Journal of Applied Statistics, vol.20, issue.5-6, pp.107-119, 1993.

V. [. Boykov and . Kolmogorov, An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol.26, issue.9, pp.1124-1137, 2004.

. Bkp-+-10-]-m, L. Botsch, M. Kobbelt, P. Pauly, B. Alliez et al., Polygon mesh processing, 2010.

M. Jonathan, . Borwein, S. Adrian, and . Lewis, Convex Analysis and Nonlinear Optimization : theory and examples, 2006.

T. [. Buades, J. M. Le, L. A. Morel, and . Vese, Fast Cartoon + Texture Image Filters, IEEE Transactions on Image Processing, vol.19, issue.8, pp.1978-1986, 2010.
DOI : 10.1109/TIP.2010.2046605

URL : https://hal.archives-ouvertes.fr/hal-00453255

S. [. Bae, F. Paris, and . Durand, Two-scale tone management for photographic look, ACM Transactions on Graphics, vol.25, issue.3, pp.637-645, 2006.
DOI : 10.1145/1141911.1141935

[. Bertalmio, G. Sapiro, V. Caselles, and C. Ballester, Image inpainting, Proceedings of the 27th annual conference on Computer graphics and interactive techniques , SIGGRAPH '00, pp.417-424, 2000.
DOI : 10.1145/344779.344972

URL : https://hal.archives-ouvertes.fr/hal-00522652

J. [. Bobin, J. Starck, Y. Fadili, and . Moudden, Morphological Diversity and Sparsity in Blind Source Separation, Image Processing IEEE Transactions on, vol.16, issue.11, pp.2662-2674, 2007.
DOI : 10.1007/978-3-540-74494-8_44

URL : https://hal.archives-ouvertes.fr/hal-00196328

J. [. Bresson, ]. A. Thiranbt09b, M. Beck, M. Teboulle, L. Bertalmio et al., Image segmentation model using active contour and image decomposition Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems A fast iterative shrinkagethresholding algorithm for linear inverse problems Simultaneous structure and texture image inpainting Fast approximate energy minimization via graph cuts. Pattern Analysis and Machine Intelligence An introduction to total variation for image analysis. Theoretical Foundations and Numerical Methods for Sparse Recovery, De Gruyter, Radon Series Comp Nonlinear wavelet transforms for image coding via lifting, Image Processing IEEE International Conference on Nonlinear wavelet image processing : variational problems, compression, and noise removal through wavelet shrinkage. IEEE Transactions on Image Processing, pp.1657-16602419, 1995.

F. Tony, S. Chan, and . Esedoglu, Aspects of total variation regularized l 1 function approximation An algorithm for total variation minimization and applications, SIAM J. Appl. Math Journal of Mathematical Imaging and Vision, vol.20, pp.89-97, 2004.

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

]. O. Chr08 and . Christensen, Frames and bases : An introductory course, Birkhäuser Boston, 2008.

]. F. Chu97 and . Chung, Spectral graph theory, 1997.

]. P. Cia88 and . Ciarlet, Introduction à l'analyse numérique matricielle et à l'optimisation, 1988.

E. [. Crovella and . Kolaczyk, Graph wavelets for spatial traffic analysis, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428), pp.1848-1857, 2003.
DOI : 10.1109/INFCOM.2003.1209207

[. 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

S. [. Chambolle, B. J. Levine, and . Lucier, An Upwind Finite-Difference Method for Total Variation???Based Image Smoothing, SIAM Journal on Imaging Sciences, vol.4, issue.1, pp.277-299, 2011.
DOI : 10.1137/090752754

C. [. Cormen, R. L. Leiserson, C. Rivest, and . Stein, Introduction to algorithms, 2001.

B. [. Cohen and . Matei, Compact representation of images by edge adapted multiscale transforms, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205), pp.8-11, 2001.
DOI : 10.1109/ICIP.2001.958938

M. [. Coifman and . Maggioni, Diffusion wavelets, Applied and Computational Harmonic Analysis, vol.21, issue.1, pp.53-94, 2006.
DOI : 10.1016/j.acha.2006.04.004

URL : http://doi.org/10.1016/j.acha.2006.04.004

A. Choudhury and G. G. Medioni, Perceptually motivated automatic sharpness enhancement using hierarchy of non-local means, 2011 IEEE International Conference on Computer Vision Workshops (ICCV Workshops), pp.730-737, 2011.
DOI : 10.1109/ICCVW.2011.6130325

S. [. Chan, J. Osher, and . Shen, The digital TV filter and nonlinear denoising, IEEE Transactions on Image Processing, vol.10, issue.2, pp.231-241, 2001.
DOI : 10.1109/83.902288

]. A. Cp11a, T. Chambolle, and . Pock, A first-order primal-dual algorithm for convex problems with applications to imaging, Journal of Mathematical Imaging and Vision, vol.40, issue.1, pp.120-145, 2011.

L. Patrick, J. Combettes, and . Pesquet, Proximal splitting methods in signal processing, Fixed-Point Algorithms for Inverse Problems in Science and Engineering, pp.185-212, 2011.

J. Chen, S. Paris, and F. Durand, Real-time edgeaware image processing with the bilateral grid, ACM Trans. Graph, vol.26, issue.3, 2007.

J. Chen, S. Paris, and F. Durand, Real-time edge-aware image processing with the bilateral grid, ACM Transactions on Graphics, vol.26, issue.3, p.103, 2007.
DOI : 10.1145/1276377.1276506

]. W. Casaca, A. Paiva, E. Gomez-nieto, P. Joia, and L. G. Nonato, Spectral Image Segmentation Using Image Decomposition and Inner Product-Based Metric, Journal of Mathematical Imaging and Vision, vol.19, issue.2, pp.1-12, 2012.
DOI : 10.1007/s10851-012-0359-6

J. Emmanuel, J. K. Candes, and . Romberg, Signal recovery from random projections, SPIE, vol.5674, pp.76-86, 2005.

B. [. Chapelle, A. Schölkopf, and . Zien, Semi-supervised learning
DOI : 10.7551/mitpress/9780262033589.001.0001

P. Choudhury and J. Tumblin, The trilateral filter for high contrast images and meshes, ACM SIGGRAPH 2005 Courses on , SIGGRAPH '05, pp.186-196, 2003.
DOI : 10.1145/1198555.1198565

Y. [. Choksi, A. Van-gennip, and . Oberman, Anisotropic total variation regularized l?1l?1-approximation and denoising/deblurring of 2d bar codes

L. Patrick, V. R. Combettes, and . Wajs, Signal recovery by proximal forward-backward splitting, Multiscale Modeling & Simulation, vol.4, issue.4, pp.1168-1200, 2005.

J. B. Cheng, S. Yang, Y. Yan, T. S. Fu, and . Huang, Learning with l1 graph for image analysis, IEEE Transactions on Image Processing, vol.19, issue.4, 2010.

J. [. Durand, . [. Dorsey, A. Dabov, V. Foi, K. Katkovnik et al., An iterative thresholding algorithm for linear inverse problems with a sparsity constraint Image denoising by sparse 3-d transform-domain collaborative filtering Accelerated projected gradient method for linear inverse problems with sparsity constraints Ideal spatial adaptation by wavelet shrinkage Fitting a graph to vector data Wavelet-based image codingan overview Applied and computational control, signals, and circuits De-noising by soft-thresholding. Information Theory Image restoration with discrete constrained total variation part i : Fast and exact optimization, ACM transactions on graphicsDFL08] Ingrid Daubechies, Massimo Fornasier, and Ignace Loris Proceedings of the 26th Annual International Conference on Machine LearningDS98] I. Daubechies and W. Sweldens. Factoring wavelet transforms into lifting stepsDSvS04] V. Delouille, J. Simoens, and R. von Sachs. Smooth designadapted wavelets for nonparametric stochastic regressionEA02] K. Egiazarian and J. Astola. Tree-structured haar transforms, pp.257-2661413, 1994.

M. Bibliographie, T. Eck, T. Derose, H. Duchamp, M. Hoppe et al., Multiresolution analysis of arbitrary meshes Texture synthesis by nonparametric sampling Sparse and redundant representations. From theory to applications in signal and image processing Nonlocal discrete regularization on weighted graphs : A framework for image and manifold processing Simultaneous cartoon and texture image inpainting using morphological component analysis (mca) Multiscale shape and detail enhancement from multi-light image collections Edgepreserving decompositions for multi-scale tone and detail manipulation An experimental assessment of a stochastic, anytime, decentralized, soft colourer for sparse graphs Total variation projection with first order schemes Image decomposition and separation using sparse representations : an overview, Proceedings of the 22nd annual conference on Computer graphics and interactive techniques Computer Vision The Proceedings of the Seventh IEEE International Conference onELB08] Abderrahim Elmoataz, Olivier Lézoray, and Sébastien Bougleux Stochastic Algorithms : Foundations and Applications Proceedings of the IEEEGem90] D. Geman. Random fields and inverse problems in imaging, pp.173-182, 1995.

D. [. Geman, . [. Geman, C. Geman, and . Graffigne, Stochastic relaxation, gibbs distributions, and the bayesian restoration of images. Pattern Analysis and Machine Intelligence Markov random field image models and their applications to computer vision, Proceedings of the International Congress of MathematiciansGil09] J. Gilles. Image decomposition : Theory, numerical schemes, and performance evaluation. Advances in Imaging and Electron Physics, pp.721-74189, 1984.

R. R. Nadler, . [. Coifman, S. Gilboa, . [. Osher, S. Gilboa et al., Multiscale wavelets on trees, graphs and high dimensional data : Theory and applications to semi supervised learning Nonlocal linear image regularization and supervised segmentation Nonlocal operators with applications to image processing Domain transform for edgeaware image and video processing Discrete Calculus : Applied Analysis on Graphs for Computational Science Exact maximum a posteriori estimation for binary images Discrete multi-resolution analysis and generalized wavelets, Vese. Image decompositions using bounded variation and generalized homogeneous besov spaces. Applied and Computational Harmonic Analysis Proc. International Conference on Machine LearningGW99] C. Gasquet and P. Witomski. Fourier analysis and applications : filtering, numerical computation, wavelets. Texts in applied mathematics, pp.25-56595, 1989.

]. A. Bibliographie-[-har96 and . Harten, Multiresolution representation of data : A general framework, SIAM Journal on Numerical Analysis, vol.33, issue.3, pp.1205-1256, 1996.

T. [. Huang and . Jebara, Loopy belief propagation for bipartite maximum weight b-matching, Artificial Intelligence and Statistics, 2007.

L. [. Hammond, P. Jacques, and . Vandergheynst, Image Processing and Analysis with Graphs : Theory and Practice, chapter 1, 2012.

]. M. Hle11a, O. Hidane, A. Lézoray, M. Elmoataz, O. Hidane et al., Hierarchical representation of discrete data on graphs A scale-space based hierarchical representation of discrete data, Computer Analysis of Images and Patterns Image Processing (ICIP) 18th IEEE International Conference on, pp.186-193, 2011.

O. [. Hidane, A. Lézoray, . Elmoatazhpfs11-]-l, L. Holmström, R. Pasanen et al., Nonlinear multilayered representation of graph-signals Scale space multiresolution analysis of random signals, Journal of Mathematical Imaging and Vision Computational Statistics & Data Analysis, issue.10, pp.1-24, 2011.

B. [. Heijmans, G. Pesquet-popescu, and . Piella, Building nonredundant adaptive wavelets by update lifting, Applied and Computational Harmonic Analysis, vol.18, issue.3, pp.252-281, 2005.
DOI : 10.1016/j.acha.2004.11.006

URL : http://doi.org/10.1016/j.acha.2004.11.006

]. C. Hsu83 and . Hsu, Minimum-via topological routing. Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on, vol.2, issue.4, pp.235-246, 1983.

R. [. Hastie, J. Tibshirani, and . Friedman, The elements of statistical learning : data mining, inference, and prediction, 2001.

P. [. Hammond, R. Vandergheynst, and . Gribonval, Wavelets on graphs via spectral graph theory, Applied and Computational Harmonic Analysis, vol.30, issue.2, pp.129-150, 2011.
DOI : 10.1016/j.acha.2010.04.005

URL : https://hal.archives-ouvertes.fr/inria-00541855

]. H. Bibliographie-[-ish03 and . Ishikawa, Exact optimization for markov random fields with convex priors. Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol.25, issue.10, pp.1333-1336, 2003.

L. [. Jacques, C. Duval, G. Chaux, and . Peyré, A panorama on multiscale geometric representations, intertwining spatial, directional and frequency selectivity, Proc. SPIE, pp.2699-2730, 2001.
DOI : 10.1016/j.sigpro.2011.04.025

URL : https://hal.archives-ouvertes.fr/hal-01330604

G. [. Jansen, B. Nason, and . Silverman, Multiscale methods for data on graphs and irregular multidimensional situations, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.82, issue.1, pp.97-125, 2009.
DOI : 10.1111/j.1467-9868.2008.00672.x

J. [. Jebara, S. F. Wang, and . Chang, -matching for semi-supervised learning, Proceedings of the 26th Annual International Conference on Machine Learning, ICML '09, pp.441-448, 2009.
DOI : 10.1145/1553374.1553432

URL : https://hal.archives-ouvertes.fr/hal-00741688

M. Kaaniche, B. Pesquet-popescu, A. Benazza-benyahia, and J. C. Pesquet, Adaptive lifting scheme with sparse criteria for image coding EURASIP Journal on Advances in Signal Processing : Special Issue on New Image and Video Representations Based on Sparsity Image-based material editing What energy functions can be minimized via graph cuts ? Pattern Analysis and Machine Intelligence, In ACM Transactions on Graphics IEEE Transactions on, vol.2012, issue.262, pp.22-654, 2004.

A. [. Lezoray, S. Elmoataz, and . Bougleux, Graph regularization for color image processing, Computer Vision and Image Understanding, vol.107, issue.1-2, pp.38-55, 2007.
DOI : 10.1016/j.cviu.2006.11.015

URL : https://hal.archives-ouvertes.fr/hal-00255996

L. [. Lezoray and . Grady, Image Processing and Analysis With Graphs : Theory and Practice, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00813324

]. T. Lin93 and . Lindeberg, Scale-space theory in computer vision, 1993.

. [. Bibliographie, B. Lee, L. Nadler, and . Wasserman, Treelets?an adaptive multi-scale basis for sparse unordered data, The Annals of Applied Statistics, vol.2, issue.2, pp.435-471, 2008.

[. Lézoray, V. Ta, and A. Elmoataz, Partial differences as tools for filtering data on graphs, Pattern Recognition Letters, vol.31, issue.14, pp.312201-2213, 2010.
DOI : 10.1016/j.patrec.2010.03.022

D. [. Leonardi and . Van-de-ville, Wavelet frames on graphs defined by fMRI functional connectivity, 2011 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, pp.2136-2139, 2011.
DOI : 10.1109/ISBI.2011.5872835

]. S. Mal89 and . Mallat, A theory for multiresolution signal decomposition : the wavelet representation. Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol.11, issue.7, pp.674-693, 1989.

]. S. Mal09 and . Mallat, A Wavelet Tour of Signal Rrocessing, the Sparse way, 2009.

]. S. Mas02 and . Masnou, Disocclusion : a variational approach using level lines, Image Processing IEEE Transactions on, vol.11, issue.2, pp.68-76, 2002.

]. E. Meddmo11, E. Martinez-enriquez, A. Diaz-de-maria, and . Ortega, Video encoder based on lifting transforms on graphs, Image Processing (ICIP) 18th IEEE International Conference on, pp.3509-3512, 2011.

A. [. Martínez-enríquez and . Ortega, Lifting Transforms on Graphs for Video Coding, 2011 Data Compression Conference, pp.73-82, 2011.
DOI : 10.1109/DCC.2011.15

Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations : The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures, 2001.
DOI : 10.1090/ulect/022

]. P. Mil11 and . Milanfar, A tour of modern image filtering, IEEE Signal Processing Magazine, vol.2, 2011.

]. F. Ml12a, N. Malgouyres, and . Lermé, Non-heuristic reduction of the graph in graph-cut optimization, Journal of Physics : Conference Series, p.12002, 2012.

F. Malgouyres and N. Lermé, A Non-Heuristic Reduction Method For Graph Cut Optimization, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00692464

B. Mohar, The laplacian spectrum of graphs. Graph theory combinatorics and applications, pp.871-898, 1991.

]. B. Moh97 and . Mohar, Some applications of laplace eigenvalues of graphs. Graph symmetry : Algebraic methods and applications, p.227, 1997.

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. [. Mumford and . Shah, Optimal approximations by piecewise smooth functions and associated variational problems, Communications on Pure and Applied Mathematics, vol.3, issue.5, pp.577-685, 1989.
DOI : 10.1002/cpa.3160420503

]. F. Mur07 and . Murtagh, The haar wavelet transform of a dendrogram, Journal of Classification, vol.24, issue.1, pp.3-32, 2007.

]. E. Nad64 and . Nadaraya, On estimating regression. Theory of Probability & Its Applications, pp.141-142, 1964.

]. Y. Nes03 and . Nesterov, Introductory lectures on convex optimization : A basic course, 2003.

A. [. Narang and . Ortega, Lifting based wavelet transforms on graphs, Proceedings : APSIPA ASC 2009 : Asia-Pacific Signal and Information Processing Association Annual Summit and Conference Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, International Organizing Committee, pp.441-444, 2009.

A. [. Narang and . Ortega, Perfect Reconstruction Two-Channel Wavelet Filter Banks for Graph Structured Data, IEEE Transactions on Signal Processing, vol.60, issue.6, pp.2786-2799, 2012.
DOI : 10.1109/TSP.2012.2188718

M. Stanley-osher, D. Burger, J. Goldfarb, W. Xu, and . Yin, An Iterative Regularization Method for Total Variation-Based Image Restoration, Multiscale Modeling & Simulation, vol.4, issue.2, pp.460-489, 2005.
DOI : 10.1137/040605412

M. [. Oh, J. Chen, F. Dorsey, and . Durand, Image-based modeling and photo editing, Proceedings of the 28th annual conference on Computer graphics and interactive techniques , SIGGRAPH '01, pp.433-442, 2001.
DOI : 10.1145/383259.383310

[. Peyré, S. Bougleux, and L. Cohen, Nonlocal regularization of inverse problems, Computer Vision ECCV 2008, pp.57-68, 2008.

J. [. Pattanaik, M. D. Ferwerda, D. P. Fairchild, and . Greenberg, A multiscale model of adaptation and spatial vision for realistic image display, Proceedings of the 25th annual conference on Computer graphics and interactive techniques , SIGGRAPH '98, pp.287-298, 1998.
DOI : 10.1145/280814.280922

. Pfs-+-07-]-g, J. Peyré, J. L. Fadili, and . Starck, Learning adapted dictionaries for geometry and texture separation, Proceedings of SPIE, Wavelets XII, 2007.

[. Pauly, M. Gross, and L. P. Kobbelt, Efficient simplification of point-sampled surfaces, IEEE Visualization, 2002. VIS 2002., pp.163-170, 2002.
DOI : 10.1109/VISUAL.2002.1183771

H. [. Piella and . Heijmans, Adaptive lifting schemes with perfect reconstruction, IEEE Transactions on Signal Processing, vol.50, issue.7, pp.1620-1630, 2002.
DOI : 10.1109/TSP.2002.1011203

[. Pauly, L. P. Kobbelt, and M. Gross, Point-based multiscale surface representation, ACM Transactions on Graphics, vol.25, issue.2, pp.177-193, 2006.
DOI : 10.1145/1138450.1138451

]. G. Plo09 and . Plonka, The easy path wavelet transform : A new adaptive wavelet transform for sparse representation of two-dimensional data, Multiscale Modeling & Simulation, vol.7, issue.3, pp.1474-1496, 2009.

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

M. [. Ram, I. Elad, and . Cohen, Generalized Tree-Based Wavelet Transform, IEEE Transactions on Signal Processing, vol.59, issue.9, pp.4199-4209, 2011.
DOI : 10.1109/TSP.2011.2158428

URL : https://hal.archives-ouvertes.fr/hal-00705951

M. [. Ram, I. Elad, and . Cohen, Redundant Wavelets on Graphs and High Dimensional Data Clouds, IEEE Signal Processing Letters, vol.19, issue.5, pp.291-294, 2012.
DOI : 10.1109/LSP.2012.2190983

URL : https://hal.archives-ouvertes.fr/hal-00705953

D. [. Rahman and G. A. Jobson, Multi-scale retinex for color image enhancement, Proceedings of 3rd IEEE International Conference on Image Processing, pp.1003-1006, 1996.
DOI : 10.1109/ICIP.1996.560995

]. R. Bibliographie-[-roc96 and . Rockafellar, Convex analysis, 1996.

S. [. Rudin, E. Osher, and . 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

L. [. Roweis and . Saul, Nonlinear Dimensionality Reduction by Locally Linear Embedding, Science, vol.290, issue.5500, pp.2323-2326, 2000.
DOI : 10.1126/science.290.5500.2323

URL : http://astro.temple.edu/~msobel/courses_files/saulmds.pdf

D. M. Strong, J. Aujol, and T. F. Chan, Scale Recognition, Regularization Parameter Selection, and Meyer's G Norm in Total Variation Regularization, Multiscale Modeling & Simulation, vol.5, issue.1, pp.273-303, 2006.
DOI : 10.1137/040621624

J. [. Smith and . 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

M. [. Starck, D. Elad, . [. Donoho, M. Starck, D. L. Elad et al., Redundant multiscale transforms and their application for morphological component separation Advances in Imaging and Electron Physics Image decomposition via the combination of sparse representations and a variational approach, Image Processing IEEE Transactions, vol.132, issue.10, pp.287-348, 2004.

C. [. Scherzer and . Groetsch, Inverse scale space theory for inverse problems. Scale-Space and Morphology in Computer Vision, pp.317-325, 2006.

]. A. Sha08 and . Shamir, A survey on mesh segmentation techniques, Computer graphics forum, pp.1539-1556, 2008.

]. J. She05 and . Shen, Piecewise h-1+ h0+ h1 images and the mumfordshah-sobolevmodel for segmented image decomposition, Applied Mathematics Research Express, issue.4, pp.143-167, 2005.

. [. Bibliographie, J. Shi, and . Malik, Normalized cuts and image segmentation. Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol.22, issue.8, pp.888-905, 2000.

F. [. Starck, J. M. Murtagh, and . Fadili, Sparse image and signal processing : wavelets, curvelets, morphological diversity, 2010.
DOI : 10.1017/CBO9780511730344

URL : https://hal.archives-ouvertes.fr/hal-01132685

D. I. Shuman, S. K. Narang, P. Frossard, A. Ortega, and P. Vandergheynst, Signal processing on graphs : Extending high-dimensional data analysis to networks and other irregular data domains, 1211.

A. [. Shen and . Ortega, Optimized distributed 2D transforms for irregularly sampled sensor network grids using wavelet lifting, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, pp.2513-2516, 2008.
DOI : 10.1109/ICASSP.2008.4518159

]. D. Spi07 and . Spielman, Spectral graph theory and its applications, FOCS'07. 48th Annual IEEE Symposium on, pp.29-38, 2007.

B. [. Shuman, P. Ricaud, and . Vandergheynst, A windowed graph fourier transform Spherical wavelets : Efficiently representing functions on the sphere, Statistical Signal Processing Workshop (SSP), 2012 IEEE Proceedings of the 22nd annual conference on Computer graphics and interactive techniques, pp.133-136, 1995.

[. Subr, C. Soler, and F. Durand, Edge-preserving multiscale image decomposition based on local extrema, ACM Trans. Graph, vol.28, issue.5, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00461396

. A. Ssn09, Y. Singer, B. Shkolnisky, and . Nadler, Diffusion interpretation of nonlocal neighborhood filters for signal denoising, SIAM Journal on Imaging Sciences, vol.2, issue.1, pp.118-139, 2009.

. J. Swac12, R. Salmon, E. Willett, and . Arias-castro, A two-stage denoising filter : the preprocessed yaroslavsky filter. arXiv preprint arXiv :1208, 2012.

]. W. Swe96 and . Sweldens, The lifting scheme : A custom-design construction of biorthogonal wavelets, Applied and Computational Harmonic Analysis, vol.3, issue.2, p.186, 1996.

]. W. Bibliographie-[-swe98 and . Sweldens, The lifting scheme : A construction of second generation wavelets, SIAM Journal on Mathematical Analysis, vol.29, issue.2, pp.511-546, 1998.

[. Tikhonov, V. Y. Arseninta09-]-e, P. Tadmor, and . Athavale, Solutions of ill-posed problems Multiscale image representation using novel integro-differential equations, Inverse problems and imaging, vol.35, issue.4, p.693, 1977.

R. [. Tomasi and . 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

S. [. Tadmor, L. Nezzar, and . Vese, A multiscale image representation using hierarchical

]. D. Tsc06 and . Tschumperlé, Fast anisotropic smoothing of multi-valued images using curvature-preserving pde's, International Journal of Computer Vision, vol.68, issue.1, pp.65-82, 2006.

G. [. Tumblin and . Turk, LCIS, Proceedings of the 26th annual conference on Computer graphics and interactive techniques , SIGGRAPH '99, pp.83-90, 1999.
DOI : 10.1145/311535.311544

]. O. Vek99 and . Veksler, Efficient graph-based energy minimization methods in computer vision, 1999.

J. [. Vetterli and . Kova?evi?, Wavelets and subband coding, 1995.

L. Ulrike-von, A tutorial on spectral clustering, Statistics and Computing, vol.17, pp.395-416, 2007.

H. [. Wagner, R. Choi, V. Baraniuk, and . Delouille, Distributed wavelet transform for irregular sensor network grids, IEEE/SP 13th Workshop on Statistical Signal Processing, 2005, pp.1196-1201, 2005.
DOI : 10.1109/SSP.2005.1628777

]. P. Wei08 and . Weiss, Algorithmes rapides d'optimisation convexe

L. Applications-À, Scale-space filtering : A new approach to multi-scale description, Acoustics, Speech, and Signal Processing, IEEE Bibliographie International Conference on ICASSP'84, pp.150-153, 1984.

B. [. Wang, . [. Lucier, S. Wagner, R. Sarvotham, and . Baraniuk, Error Bounds for Finite-Difference Methods for Rudin???Osher???Fatemi Image Smoothing, Acoustics, Speech, and Signal Processing, 2005. Proceedings.(ICASSP'05), pp.845-868, 2011.
DOI : 10.1137/090769594

M. [. Yaroslavsky and . Eden, Fundamentals of Digital Optics : Digital Signal Processing in Optics and Holography, 1996.
DOI : 10.1007/978-1-4612-0845-7

D. Zhou, O. Bousquet, T. N. Lal, J. Weston, and B. Schölkopf, Learning with local and global consistency Advances in neural information processing systems, pp.321-328, 2004.

B. [. Zhou and . Schölkopf, A regularization framework for learning from graph data, 2004.

[. Zhou and B. Schölkopf, Regularization on Discrete Spaces, Pattern Recognition, pp.361-368, 2005.
DOI : 10.1007/11550518_45