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

H. H. Bauschke and J. M. Borwein, On Projection Algorithms for Solving Convex Feasibility Problems, SIAM Review, vol.38, issue.3, pp.367-426, 1996.
DOI : 10.1137/S0036144593251710

H. H. Bauschke, P. L. Combettes, and S. G. Kruk, Extrapolation algorithm for affine-convex feasibility problems, Numerical Algorithms, pp.41-239, 2006.

H. Brézis, Analyse Fonctionnelle : Théorie et Applications, 1993.

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

C. Chaux, P. L. Combettes, J. Pesquet, and V. R. Wajs, A forwardbackward algorithm for image restoration with sparse representations, Proceedings of the International Conference on Signal Processing with Adaptative Sparse Structured Representations, pp.49-52, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00017658

C. Chaux, P. L. Combettes, J. Pesquet, and V. R. Wajs, Iterative image deconvolution using overcomplete representations, Proceedings of the 14th European Signal Processing Conference, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00621888

C. Chaux, P. L. Combettes, J. Pesquet, and V. R. Wajs, A variational formulation for frame-based inverse problems, Inverse Problems, vol.23, issue.4, pp.1495-1518, 2007.
DOI : 10.1088/0266-5611/23/4/008
URL : https://hal.archives-ouvertes.fr/hal-00621883

P. L. Combettes, The foundations of set theoretic estimation, Proceedings of the IEEE, pp.182-208, 1993.

P. L. Combettes, Inconsistent signal feasibility problems: least-squares solutions in a product space, IEEE Transactions on Signal Processing, vol.42, issue.11, pp.2955-2966, 1994.
DOI : 10.1109/78.330356

P. L. Combettes, Construction d'un point fixe communàcommunà une famille de contractions fermes, Comptes Rendus de l'Académie des Sciences de Paris, pp.320-1385, 1995.

P. L. Combettes, The convex feasibility problem in image recovery Advances in Imaging and Electron Physics, pp.155-270, 1996.

P. L. Combettes, Convex set theoretic image recovery by extrapolated iterations of parallel subgradient projections, IEEE Transactions on Image Processing, vol.6, issue.4, pp.493-506, 1997.
DOI : 10.1109/83.563316

P. L. Combettes, Quasi-Fejerian analysis of some optimization algorithms, in Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, pp.115-152, 2001.

P. L. Combettes, Solving monotone inclusions via compositions of nonexpansive averaged operators, Optimization, pp.53-475, 2004.

P. L. Combettes and P. Bondon, Hard-constrained inconsistent signal feasibility problems, IEEE Transactions on Signal Processing, vol.47, issue.9, pp.2460-2468, 1999.
DOI : 10.1109/78.782189

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 forwardbackward splitting, Multiscale Modeling and Simulation, pp.1168-1200, 2005.

J. M. Dye and S. Reich, Unrestricted iterations of nonexpansive mappings in Hilbert space, Nonlinear Analysis: Theory, Methods & Applications, vol.18, issue.2, pp.199-207, 1992.
DOI : 10.1016/0362-546X(92)90094-U

K. M. Furati, Z. Nashed, and A. H. Siddiqi, Mathematical Models and Methods for Real World Systems, 2005.

G. T. Herman, Image Reconstruction from Projections, the Fundamentals of, Computerized Tomography, 1980.

B. R. Hunt, The Application of Constrained Least Squares Estimation to Image Restoration by Digital Computer, IEEE Transactions on Computers, vol.22, issue.9, pp.805-812, 1973.
DOI : 10.1109/TC.1973.5009169

B. Lemaire, Which Fixed Point Does the Iteration Method Select?, Lecture Notes in Economics and Mathematical Systems, vol.452, pp.154-167, 1997.
DOI : 10.1007/978-3-642-59073-3_11

H. Ma??trema??tre, Le Traitement des Images, Hermès Science, 2003.

B. Mercier, Inéquations variationnelles de la mécanique, Publications Mathématiques d'Orsay, p.1, 1980.

Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations, 2001.
DOI : 10.1090/ulect/022

J. Moreau, Fonctions convexes duales et points proximaux dans un espace hilbertien, Comptes-Rendus de l'Académie des Sciences, pp.255-2897, 1962.
DOI : 10.24033/bsmf.1625
URL : http://archive.numdam.org/article/BSMF_1965__93__273_0.pdf

J. Moreau, Propriétés des applications « prox ». Comptes-Rendus de l'Académie des Sciences, pp.1069-1071, 1963.

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

F. Natterer, The Mathematics of Computerized Tomography, SIAM, Second Edition, 2001.

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.259-268, 1992.
DOI : 10.1016/0167-2789(92)90242-F

H. Stark, Image Recovery : Theory and Application, 1987.

H. Stark and Y. Yang, Vector Space Projections : A Numerical Approach to Signal and Image Processing, Neural Nets, and Optics, 1998.

. Bibliographie, Alkin and H. Caglar, Design of efficient M-band coders with linear-phase and perfect-reconstruction properties, IEEE Transactions on Signal Processing, pp.43-1579, 1995.

H. Attouch and R. J. Wets, Epigraphical analysis, Analyse Non Linéaire, pp.73-100, 1989.

J. F. Bonnans, J. Ch, C. Gilbert, C. A. Lemaréchal, and . Sagastizábal, A family of variable metric proximal methods, Mathematical Programming, pp.68-83, 1995.
DOI : 10.1007/BF01585756
URL : https://hal.archives-ouvertes.fr/inria-00074821

J. M. Borwein and A. S. Lewis, Convex Analysis and Nonlinear Optimization . Theory and Examples, CMS Books in Mathematics, 2006.

J. M. Borwein and J. D. Vanderwerff, Convergence of Lipschitz Regularizations of Convex Functions, Journal of Functional Analysis, vol.128, issue.1, pp.139-162, 1995.
DOI : 10.1006/jfan.1995.1026

J. A. Cadzow and Y. Sun, Sequences with positive semidefinite Fourier transforms, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.34, issue.6, pp.1502-1510, 1986.
DOI : 10.1109/TASSP.1986.1164990

A. Chambolle, An algorithm for total variation minimization and applications, Journal of Mathematical Imaging and Vision, vol.20, pp.89-97, 2004.

P. L. Combettes, The convex feasibility problem in image recovery Advances in Imaging and Electron Physics, pp.155-270, 1996.

P. L. Combettes and J. Pesquet, Proximal Thresholding Algorithm for Minimization over Orthonormal Bases, SIAM Journal on Optimization, vol.18, issue.4
DOI : 10.1137/060669498
URL : https://hal.archives-ouvertes.fr/hal-00621819

P. J. Laurent, Approximation et Optimisation, 1972.

C. Lemaréchal and C. Sagastizábal, Variable metric bundle methods: From conceptual to implementable forms, Mathematical Programming, pp.393-410, 1997.
DOI : 10.1007/BF02614390

S. G. Mallat, A Wavelet Tour of Signal Processing, 1999.

J. Moreau, Propriétés des applications « prox ». Comptes-Rendus de l'Académie des Sciences, pp.1069-1071, 1963.

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

F. Riesz and B. S. Nagy, Functional Analysis, 1990.

R. T. Rockafellar, Convex Analysis, 1970.
DOI : 10.1515/9781400873173

H. Stark, Image Recovery : Theory and Application, 1987.

P. Steffen, P. Heller, R. A. Gopinath, and C. S. Burrus, Theory of regular M-band wavelet bases, IEEE Transactions on Signal Processing, vol.41, issue.12, pp.41-3497, 1993.
DOI : 10.1109/78.258088

D. C. Youla and H. Webb, Image Restoration by the Method of Convex Projections: Part 1ߞTheory, IEEE Transactions on Medical Imaging, vol.1, issue.2, pp.81-94, 1982.
DOI : 10.1109/TMI.1982.4307555

F. Acker and M. A. , Convergence d'un sch??ma de minimisation altern??e, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.2, issue.1, pp.1-9, 1980.
DOI : 10.5802/afst.541
URL : http://archive.numdam.org/article/AFST_1980_5_2_1_1_0.pdf

G. Aubert and L. Vese, A Variational Method in Image Recovery, SIAM Journal on Numerical Analysis, vol.34, issue.5, pp.1948-1979, 1997.
DOI : 10.1137/S003614299529230X

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.67-111, 2006.
DOI : 10.1007/s11263-006-4331-z
URL : https://hal.archives-ouvertes.fr/hal-00201977

J. Baillon and G. Haddad, Quelques propri??t??s des op??rateurs angle-born??s etn-cycliquement monotones, Israel Journal of Mathematics, vol.17, issue.2, pp.137-150, 1977.
DOI : 10.1007/BF03007664

H. H. Bauschke, P. L. Combettes, and S. Reich, The asymptotic behavior of the composition of two resolvents, Nonlinear Anal, pp.283-301, 2005.

J. Bect, L. Blanc-féraud, G. Aubert, and A. Chambolle, A l 1-Unified Variational Framework for Image Restoration, Proc. Eighth Europ. Conf
DOI : 10.1007/978-3-540-24673-2_1
URL : https://hal.archives-ouvertes.fr/hal-00217251

J. Borwein, S. Reich, and I. Shafrir, Krasnosel'ski-Mann iterations in normed spaces, Bulletin canadien de math??matiques, vol.35, issue.1, pp.21-28, 1992.
DOI : 10.4153/CMB-1992-003-0

D. Butnariu, A. N. Iusem, and C. , On uniform convexity, total convexity and convergence of the proximal point and outer Bregman projection algorithms in Banach spaces, J. Convex Anal, vol.10, pp.35-61, 2003.

C. L. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Problems, vol.18, issue.2, pp.441-453, 2002.
DOI : 10.1088/0266-5611/18/2/310

Y. Censor and T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numerical Algorithms, vol.17, issue.2, pp.221-239, 1994.
DOI : 10.1007/BF02142692

Y. Censor and S. A. Zenios, Parallel Optimization : Theory, Algorithms and Applications, 1997.

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

A. Chambolle, R. A. Devore, N. Y. Lee, and B. J. Lucier, Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage, IEEE Transactions on Image Processing, vol.7, issue.3, pp.319-335, 1998.
DOI : 10.1109/83.661182
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.29.4107

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

A. Cohen, Wavelet methods in numerical analysis, 2003.
DOI : 10.1016/S1570-8659(00)07004-6

P. L. Combettes, The foundations of set theoretic estimation, Proc. IEEE, pp.182-208, 1993.

P. L. Combettes, The convex feasibility problem in image recovery, in Advances in Imaging and Electron Physics, pp.155-270, 1996.

P. L. Combettes, Convexité et signal, Actes du Congrès de Mathématiques Appliquées et Industrielles SMAI'01, pp.6-16, 2001.

P. L. Combettes, Solving monotone inclusions via compositions of nonexpansive averaged operators, Optimization, pp.53-475, 2004.

P. L. Combettes and P. Bondon, Hard-constrained inconsistent signal feasibility problems, IEEE Transactions on Signal Processing, vol.47, issue.9, pp.2460-2468, 1999.
DOI : 10.1109/78.782189

P. L. Combettes and S. A. Hirstoaga, Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal, vol.6, pp.117-136, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00017823

P. L. Combettes and J. Pesquet, Convex multiresolution analysis, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.20, issue.12, pp.1308-1318, 1998.
DOI : 10.1109/34.735804

P. L. Combettes and J. Pesquet, WAVELET-CONSTRAINED IMAGE RESTORATION, International Journal of Wavelets, Multiresolution and Information Processing, vol.02, issue.04, pp.371-389, 2004.
DOI : 10.1142/S0219691304000688
URL : https://hal.archives-ouvertes.fr/hal-00017834

I. Daubechies, M. Defrise, and C. Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Communications on Pure and Applied Mathematics, vol.58, issue.11, pp.1413-1457, 2004.
DOI : 10.1002/cpa.20042

C. De-mol and M. Defrise, A note on wavelet-based inversion algorithms, Contemp. Math, vol.313, pp.85-96, 2002.
DOI : 10.1090/conm/313/05370

D. Dobson and O. Scherzer, Analysis of regularized total variation penalty methods for denoising, Inverse Problems, vol.12, issue.5, pp.601-617, 1996.
DOI : 10.1088/0266-5611/12/5/005

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

D. L. Donoho, I. M. Johnstone, G. Kerkyacharian, and D. Picard, Wavelet shrinkage : Asymptopia ?, J. R. Statist. Soc. B, vol.57, pp.301-369, 1995.

B. Eicke, Iteration methods for convexly constrained ill-posed problems in hilbert space, Numerical Functional Analysis and Optimization, vol.13, issue.5-6, pp.413-429, 1992.
DOI : 10.1016/0041-5553(88)90104-8

M. A. Figueiredo and R. D. Nowak, An EM algorithm for wavelet-based image restoration, IEEE Transactions on Image Processing, vol.12, issue.8, pp.906-916, 2003.
DOI : 10.1109/TIP.2003.814255

R. W. Gerchberg, Super-resolution through Error Energy Reduction, Optica Acta: International Journal of Optics, vol.19, issue.9, pp.709-720, 1974.
DOI : 10.1080/713818946

M. Goldburg, R. J. Marks, and I. , Signal synthesis in the presence of an inconsistent set of constraints, IEEE Transactions on Circuits and Systems, vol.32, issue.7, pp.647-663, 1985.
DOI : 10.1109/TCS.1985.1085777

G. T. Herman, Image Reconstruction from Projections, the Fundamentals of, Computerized Tomography, 1980.

U. Hermann and D. Noll, Adaptive Image Reconstruction Using Information Measures, SIAM Journal on Control and Optimization, vol.38, issue.4, pp.1223-1240, 2000.
DOI : 10.1137/S0363012997324338

H. S. Hundal, An alternating projection that does not converge in norm, Nonlinear Anal, pp.35-61, 2004.

B. R. Hunt, The inverse problem of radiography, Mathematical Biosciences, vol.8, issue.1-2, pp.161-179, 1970.
DOI : 10.1016/0025-5564(70)90148-3

B. R. Hunt, The Application of Constrained Least Squares Estimation to Image Restoration by Digital Computer, IEEE Transactions on Computers, vol.22, issue.9, pp.22-805, 1973.
DOI : 10.1109/TC.1973.5009169

N. Hurt, Phase Retrieval and Zero Crossings : Mathematical Methods in Image Reconstruction, 1989.
DOI : 10.1007/978-94-010-9608-9

S. L. Keeling, Total variation based convex filters for medical imaging, Applied Mathematics and Computation, vol.139, issue.1, pp.101-119, 2003.
DOI : 10.1016/S0096-3003(02)00171-6

A. Lannes, S. Roques, and M. J. Casanove, Stabilized Reconstruction in Signal and Image Processing, Journal of Modern Optics, vol.26, issue.2, pp.161-226, 1987.
DOI : 10.1137/0142067

E. S. Levitin and B. T. Polyak, Constrained minimization methods, USSR Computational Mathematics and Mathematical Physics, vol.6, issue.5, pp.1-50, 1966.
DOI : 10.1016/0041-5553(66)90114-5

A. J. Levy, A fast quadratic programming algorithm for positive signal restoration, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.31, issue.6, pp.31-1337, 1983.
DOI : 10.1109/TASSP.1983.1164246

S. G. Mallat, A Wavelet Tour of Signal Processing, 1999.

P. Maréchal, D. Togane, and A. Celler, A new reconstruction methodology for computerized tomography: FRECT (Fourier regularized computed tomography), 1999 IEEE Nuclear Science Symposium. Conference Record. 1999 Nuclear Science Symposium and Medical Imaging Conference (Cat. No.99CH37019), pp.47-1595, 2000.
DOI : 10.1109/NSSMIC.1999.842902

Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations, 2001.
DOI : 10.1090/ulect/022

J. Moreau, Décomposition orthogonale d'un espace hilbertien selon deux cônes mutuellement polaires, C. R. Acad. Sci. Paris Sér. A Math, vol.255, pp.238-240, 1962.
DOI : 10.24033/bsmf.1625
URL : http://archive.numdam.org/article/BSMF_1965__93__273_0.pdf

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, Propriétés des applications 'prox, C. R. Acad. Sci. Paris Sér. A Math, vol.256, pp.1069-1071, 1963.

D. Noll, Reconstruction with Noisy Data: An Approach via Eigenvalue Optimization, SIAM Journal on Optimization, vol.8, issue.1, pp.82-104, 1998.
DOI : 10.1137/S105262349629856X

A. Papoulis, A new algorithm in spectral analysis and band-limited extrapolation, IEEE Transactions on Circuits and Systems, vol.22, issue.9, pp.735-742, 1975.
DOI : 10.1109/TCS.1975.1084118

J. Pesquet and P. L. Combettes, Wavelet synthesis by alternating projections, IEEE Transactions on Signal Processing, vol.44, issue.3, pp.728-732, 1996.
DOI : 10.1109/78.489050

R. T. Rockafellar, Monotone Operators and the Proximal Point Algorithm, SIAM Journal on Control and Optimization, vol.14, issue.5, pp.877-898, 1976.
DOI : 10.1137/0314056

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.259-268, 1992.
DOI : 10.1016/0167-2789(92)90242-F

A. Sabharwal and L. C. Potter, Convexly constrained linear inverse problems: iterative least-squares and regularization, IEEE Transactions on Signal Processing, vol.46, issue.9, pp.2345-2352, 1998.
DOI : 10.1109/78.709518

J. Starck, D. L. Donoho, and E. J. Candès, Astronomical image representation by the curvelet transform, Astronom. and Astrophys, pp.398-785, 2003.

J. Starck, M. K. Nguyen, and F. Murtagh, Wavelets and curvelets for image deconvolution : A combined approach, Signal Process, pp.2279-2283, 2003.

H. Stark, Image Recovery : Theory and Application, 1987.

H. Stark and Y. Yang, Vector Space Projections : A Numerical Approach to Signal and Image Processing, Neural Nets, and Optics, 1998.

A. M. Thompson and J. Kay, On some Bayesian choices of regularization parameter in image restoration, Inverse Problems, vol.9, issue.6, pp.749-761, 1993.
DOI : 10.1088/0266-5611/9/6/011

D. M. Titterington, General structure of regularization procedures in image reconstruction, Astronom. and Astrophys, vol.144, pp.381-387, 1985.

S. Twomey, The application of numerical filtering to the solution of integral equations encountered in indirect sensing measurements, Journal of the Franklin Institute, vol.279, issue.2, pp.95-109, 1965.
DOI : 10.1016/0016-0032(65)90209-7

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

L. A. Vese and S. J. Osher, Image Denoising and Decomposition with Total Variation Minimization and Oscillatory Functions, Journal of Mathematical Imaging and Vision, vol.20, issue.1/2, pp.7-18, 2004.
DOI : 10.1023/B:JMIV.0000011316.54027.6a

D. C. Youla, Generalized Image Restoration by the Method of Alternating Orthogonal Projections, IEEE Transactions on Circuits and Systems, vol.25, issue.9, pp.694-702, 1978.
DOI : 10.1109/TCS.1978.1084541

D. C. Youla and H. Webb, Image Restoration by the Method of Convex Projections: Part 1ߞTheory, IEEE Transactions on Medical Imaging, vol.1, issue.2, pp.81-94, 1982.
DOI : 10.1109/TMI.1982.4307555

E. Zeidler, Nonlinear Functional Analysis and Its Applications I : Fixed-Point Theorems, 1993.

O. Alkin and H. Caglar, Design of efficient M-band coders with linear-phase and perfect-reconstruction properties, IEEE Transactions on Signal Processing, vol.43, issue.7, pp.1579-1590, 1995.
DOI : 10.1109/78.398719

M. Antonini, M. Barlaud, P. Mathieu, and I. Daubechies, Image coding using wavelet transform, IEEE Transactions on Image Processing, vol.1, issue.2, pp.205-220, 1992.
DOI : 10.1109/83.136597
URL : https://hal.archives-ouvertes.fr/hal-01322224

J. M. Bioucas-dias, Bayesian wavelet-based image deconvolution: a GEM algorithm exploiting a class of heavy-tailed priors, IEEE Transactions on Image Processing, vol.15, issue.4, pp.937-951, 2006.
DOI : 10.1109/TIP.2005.863972

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

C. L. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Problems, vol.20, issue.1, pp.103-120, 2004.
DOI : 10.1088/0266-5611/20/1/006

E. J. Candès and D. L. Donoho, Recovering edges in ill-posed inverse problems: optimality of curvelet frames, The Annals of Statistics, vol.30, issue.3, pp.784-842, 2002.
DOI : 10.1214/aos/1028674842

C. Chaux, L. Duval, and J. Pesquet, Image analysis using a dual-tree M-band wavelet transform, IEEE Transactions on Image Processing, vol.15, issue.8, pp.2397-2412, 2006.
DOI : 10.1109/TIP.2006.875178
URL : https://hal.archives-ouvertes.fr/hal-01330599

A. Cohen, Wavelet methods in numerical analysis, 2003.
DOI : 10.1016/S1570-8659(00)07004-6

A. Cohen, I. Daubechies, and J. Feauveau, Biorthogonal bases of compactly supported wavelets, Communications on Pure and Applied Mathematics, vol.10, issue.5, pp.485-560, 1992.
DOI : 10.1002/cpa.3160450502

P. L. Combettes, The foundations of set theoretic estimation, Proc. IEEE, pp.182-208, 1993.

P. L. Combettes, A block-iterative surrogate constraint splitting method for quadratic signal recovery, IEEE Transactions on Signal Processing, vol.51, issue.7, pp.1771-1782, 2003.
DOI : 10.1109/TSP.2003.812846

P. L. Combettes, Solving monotone inclusions via compositions of nonexpansive averaged operators, Optimization, pp.475-504, 2004.

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

I. Daubechies, A. Grossmann, and Y. Meyer, Painless nonorthogonal expansions, Journal of Mathematical Physics, vol.27, issue.5, pp.1271-1283, 1986.
DOI : 10.1063/1.527388

C. De-mol and M. Defrise, A note on wavelet-based inversion algorithms, Contemp. Math, vol.313, pp.85-96, 2002.
DOI : 10.1090/conm/313/05370

L. Devroye, Non-Uniform Random Variate Generation, 1986.
DOI : 10.1007/978-1-4613-8643-8
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.333.8896

M. N. Do and M. Vetterli, The contourlet transform: an efficient directional multiresolution image representation, IEEE Transactions on Image Processing, vol.14, issue.12, pp.2091-2106, 2005.
DOI : 10.1109/TIP.2005.859376

R. J. Duffin and A. C. Schaeffer, A class of nonharmonic Fourier series, Transactions of the American Mathematical Society, vol.72, issue.2, pp.341-366, 1952.
DOI : 10.1090/S0002-9947-1952-0047179-6

M. Elad and A. Feuer, Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images, IEEE Transactions on Image Processing, vol.6, issue.12, pp.1646-1658, 1997.
DOI : 10.1109/83.650118

O. D. Escoda, L. Granai, and P. Vandergheynst, On the use of a priori information for sparse signal approximations, IEEE Transactions on Signal Processing, vol.54, issue.9, pp.3468-3482, 2006.
DOI : 10.1109/TSP.2006.879306

H. G. Feichtinger and T. Strohmer, Gabor Analysis and Algorithms, 1998.
DOI : 10.1007/978-3-540-70529-1_354

D. Gabor, Theory of communication, Journal of the Institution of Electrical Engineers - Part I: General, vol.94, issue.73, pp.429-457, 1946.
DOI : 10.1049/ji-1.1947.0015

D. Han and D. R. Larson, Frames, bases and group representations, Memoirs of the American Mathematical Society, vol.147, issue.697, 2000.
DOI : 10.1090/memo/0697

J. N. Kapur and H. K. Kesevan, Entropy Optimization Principles and Their Applications, 1992.
DOI : 10.1007/978-94-011-2430-0_1

E. , L. Pennec, and S. G. Mallat, Sparse geometric image representations with bandelets, IEEE Trans. Image Process, vol.14, pp.423-438, 2005.

S. G. Mallat, A Wavelet Tour of Signal Processing, 1999.

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.

M. Nikolova and M. K. Ng, Analysis of Half-Quadratic Minimization Methods for Signal and Image Recovery, SIAM Journal on Scientific Computing, vol.27, issue.3, pp.937-966, 2005.
DOI : 10.1137/030600862

I. W. Selesnick, R. G. Baraniuk, and N. C. Kingsbury, The dual-tree complex wavelet transform, IEEE Signal Processing Magazine, vol.22, issue.6, pp.123-151, 2005.
DOI : 10.1109/MSP.2005.1550194

H. Stark, Image Recovery : Theory and Application, 1987.

A. M. Thompson and J. Kay, On some Bayesian choices of regularization parameter in image restoration, Inverse Problems, vol.9, issue.6, pp.749-761, 1993.
DOI : 10.1088/0266-5611/9/6/011

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

@. Le-point-de-vue-applicatif, Il restè a faire, d'une part, uné etude plus approfondie des propriétés de chaque composante de la décomposition proximale de l'image analysée, ainsi dégagées au Chapitre 2 ` a partir du choix des fonctionnelles. D'autre part, il serait intéressant d'appliquer la théoriethéorié elaborée dans cette thèse en utilisant d'autres techniques spécifiques au traitement de l'image. Les applications pourraient, de plus, s'´ elargiràelargirà d'autres signaux que les images, et même

]. H. Bibliographie1, R. J. Attouch, and . Wets, Epigraphical analysis, Analyse Non Linéaire, pp.73-100, 1989.

J. M. Borwein, A. S. Lewis, and D. Noll, Maximum Entropy Reconstruction Using Derivative Information, Part 1: Fisher Information and Convex Duality, Mathematics of Operations Research, vol.21, issue.2, pp.442-468, 1996.
DOI : 10.1287/moor.21.2.442
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.3544

J. M. Borwein, A. S. Lewis, M. N. Limber, and D. Noll, Maximum entropy reconstruction using derivative information part 2: computational results, Numerische Mathematik, vol.69, issue.3, pp.69-243, 1995.
DOI : 10.1007/s002110050090

G. H. Chen and R. T. Rockafellar, Convergence Rates in Forward--Backward Splitting, SIAM Journal on Optimization, vol.7, issue.2, pp.421-444, 1997.
DOI : 10.1137/S1052623495290179

P. L. Combettes and S. A. Hirstoaga, Equilibrium programming in Hilbert spaces, Journal of Nonlinear and Convex Analysis, vol.6, pp.117-136, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00017823

Y. Fang and N. Huang, H-Monotone operator and resolvent operator technique for variational inclusions, Applied Mathematics and Computation, vol.145, issue.2-3, pp.795-803, 2003.
DOI : 10.1016/S0096-3003(03)00275-3

U. Hermann and D. Noll, Adaptive Image Reconstruction Using Information Measures, SIAM Journal on Control and Optimization, vol.38, issue.4, pp.1223-1240, 2000.
DOI : 10.1137/S0363012997324338

C. Lemaréchal and C. Sagastizábal, Variable metric bundle methods: From conceptual to implementable forms, Mathematical Programming, pp.393-410, 1997.
DOI : 10.1007/BF02614390

D. Noll, Reconstruction with Noisy Data: An Approach via Eigenvalue Optimization, SIAM Journal on Optimization, vol.8, issue.1, pp.82-104, 1998.
DOI : 10.1137/S105262349629856X

R. T. Rockafellar, Integrals which are convex functionals, Pacific Journal of Mathematics, vol.24, issue.3, pp.525-539, 1968.
DOI : 10.2140/pjm.1968.24.525

R. T. Rockafellar, Integrals which are convex functionals. II, Pacific Journal of Mathematics, vol.39, issue.2, pp.439-469, 1971.
DOI : 10.2140/pjm.1971.39.439

J. Serra, Image Analysis and Mathematical Morphology I, 1982.

J. Serra, Image Analysis and Mathematical Morphology II : Theoretical Advances, 1988.

L. A. Vese and S. J. Osher, -Harmonic Flows and Applications to Image Processing, SIAM Journal on Numerical Analysis, vol.40, issue.6, pp.2085-2104, 2002.
DOI : 10.1137/S0036142901396715
URL : https://hal.archives-ouvertes.fr/inria-00590199