F. J. Anscombe, The transformation, of Poisson, binomial and negativebinomial data, Biometrika, vol.354, issue.3, pp.246-254, 1948.

J. M. Bardsley and J. Goldes, Regularization parameter selection methods for ill-posed Poisson maximum likelihood estimation, Inverse Problems, vol.25, issue.9, 2009.
DOI : 10.1088/0266-5611/25/9/095005

B. Colicchio, E. Maalouf, O. Haeberlé, and A. , Dieterlen Wavelet filtering applied to 3D wide field fluorescence microscopy deconvolution, Proceedings PSIP'07, 2007.

J. Boutet-de-monvel, S. L. Calvez, and M. , Image Restoration for Confocal Microscopy: Improving the Limits of Deconvolution, with Application to the Visualization of the Mammalian Hearing Organ, Biophysical Journal, vol.80, issue.5, pp.2455-2470, 2001.
DOI : 10.1016/S0006-3495(01)76214-5

A. Beck and M. Teboulle, A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems, SIAM Journal on Imaging Sciences, vol.2, issue.1, 2009.
DOI : 10.1137/080716542

E. Candès, L. Demanet, D. Donoho, and L. Ying, Fast Discrete Curvelet Transforms, Multiscale Modeling & Simulation, vol.5, issue.3, pp.861-899, 2006.
DOI : 10.1137/05064182X

M. Carlavan, P. Weiss, and L. Blanc-féraud, Régularité et parcimonie pour lesprobì emes inverses en imagerie : algorithmes et comparaisons, Traitement du Signal, vol.27, issue.2, pp.187-217, 2010.

M. Carlavan, P. Weiss, L. Blanc-féraud, and J. Zerubia, Complex wavelet regularization for solving inverse problems in remote sensing, 2009 IEEE International Geoscience and Remote Sensing Symposium, 2009.
DOI : 10.1109/IGARSS.2009.5417865
URL : https://hal.archives-ouvertes.fr/inria-00417708

A. Chambolle, An algorithm for total variation minimization and applications, J. Math. Imaging Vis, vol.20, issue.12, pp.89-97, 2004.

C. Chaux, L. Blanc-féraud, and J. Zerubia, Wavelet-based restoration methods: application to 3D confocal microscopy images, Wavelets XII, 2007.
DOI : 10.1117/12.731438
URL : https://hal.archives-ouvertes.fr/hal-00733457

C. Chaux, P. L. Combettes, J. Pesquet, and V. R. Wajs, A forwardbackward algorithm for image restoration with sparse representations, Signal Processing with Adaptative Sparse Structured Representations (SPARS'05), pp.49-52, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00017658

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

C. Chaux, J. Pesquet, and N. Pustelnik, Nested Iterative Algorithms for Convex Constrained Image Recovery Problems, SIAM Journal on Imaging Sciences, vol.2, issue.2, pp.730-762, 2009.
DOI : 10.1137/080727749
URL : https://hal.archives-ouvertes.fr/hal-00621932

P. L. Combettes and J. Pesquet, A proximal decomposition method for solving convex variational inverse problems, Inverse Problems, vol.24, issue.6, 2008.
DOI : 10.1088/0266-5611/24/6/065014
URL : https://hal.archives-ouvertes.fr/hal-00692901

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

N. Dey, L. Blanc-féraud, C. Zimmer, Z. Kam, P. Roux et al., Richardson???Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution, Microscopy Research and Technique, vol.59, issue.4, pp.260-266, 2006.
DOI : 10.1002/jemt.20294

F. Dupé, J. Fadili, and J. Starck, A Proximal Iteration for Deconvolving Poisson Noisy Images Using Sparse Representations, IEEE Transactions on Image Processing, vol.18, issue.2, pp.310-321, 2009.
DOI : 10.1109/TIP.2008.2008223

M. Elad, P. Milanfar, and R. Rubinstein, Analysis versus synthesis in signal priors, Inverse Problems, vol.23, issue.3, pp.947-968, 2007.
DOI : 10.1088/0266-5611/23/3/007

E. Esser, Applications of lagrangian-based alternating direction methods and connections to split bregman, UCLA Cam Report, 2009.

M. A. Figueiredo and J. M. Bioucas-dias, Restoration of Poissonian Images Using Alternating Direction Optimization, IEEE Transactions on Image Processing, vol.19, issue.12, 2010.
DOI : 10.1109/TIP.2010.2053941

R. Glowinski, Numerical Methods for Nonlinear variation al Problems, 1984.

G. H. Golub, M. Heath, and G. Wahba, Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter, Technometrics, vol.5, issue.2, pp.215-223, 1979.
DOI : 10.1080/03610927508827223

A. Grinvald and I. Z. Steinberg, On the analysis of fluorescence decay kinetics by the method of least-squares, Analytical Biochemistry, vol.59, issue.2, pp.583-598, 1974.
DOI : 10.1016/0003-2697(74)90312-1

L. B. Lucy, An iterative technique for the rectification of observed distributions, The Astronomical Journal, vol.79, issue.6, pp.745-765, 1974.
DOI : 10.1086/111605

S. Mallat, A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way, 2008.

M. Minsky, Memoir on inventing the confocal scanning microscope, Scanning, vol.10, issue.4, pp.128-138, 1988.
DOI : 10.1002/sca.4950100403

V. A. Morozov, Regularization Methods for Ill-Posed Problems, 1993.

Y. Nesterov, Gradient methods for minimizing composite objective function. CORE Discussion Paper, 2007.

M. Ng, P. Weiss, and X. M. Yuan, Solving Constrained Total-variation Image Restoration and Reconstruction Problems via Alternating Direction Methods, SIAM Journal on Scientific Computing, vol.32, issue.5, 2009.
DOI : 10.1137/090774823

G. P. Bernad, L. Blanc-féraud, and J. Zerubia, A Restoration Method for Confocal Microscopy Using Complex Wavelet Transform, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005., 2005.
DOI : 10.1109/ICASSP.2005.1415481

N. Pustelnik, C. Chaux, J. Pesquet, S. Ramani, T. Blu et al., Hybrid regularization for data restoration in the presence of Poisson noise Monte-Carlo SURE: A Black- Box Optimization of Regularization Parameters for General Denoising Algorithms, 17th European Signal Processing Conference, pp.1540-1554, 2008.

S. Ramani, C. Vonesch, and M. Unser, Deconvolution of 3D fluorescence micrographs with automatic risk minimization, 2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, pp.732-735, 2008.
DOI : 10.1109/ISBI.2008.4541100

W. H. Richardson, Bayesian-Based Iterative Method of Image Restoration*, Journal of the Optical Society of America, vol.62, issue.1, pp.55-59, 1972.
DOI : 10.1364/JOSA.62.000055

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

I. W. Selesnick, R. G. Baraniuk, and N. G. 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

I. W. Selesnick and M. A. Figueiredo, Signal restoration with overcomplete wavelet transforms: comparison of analysis and synthesis priors, Wavelets XIII, 2009.
DOI : 10.1117/12.826663

S. Setzer, G. Steidl, and T. Teuber, Deblurring Poissonian images by split Bregman techniques, Journal of Visual Communication and Image Representation, vol.21, issue.3, pp.193-199, 2010.
DOI : 10.1016/j.jvcir.2009.10.006

C. J. Sheppard and C. J. , Three-dimensional image formation in confocal microscopy, Journal of Microscopy, vol.1, issue.2, pp.179-194, 1990.
DOI : 10.1111/j.1365-2818.1990.tb04774.x

G. M. Van-kempen, Image Restoration in Fluorescence Microscopy, 1999.

G. M. Van-kempen, L. J. Van, and . Vliet, The influence of the regularization parameter and the first estimate on the performance of Tikhonov regularized non-linear image restoration algorithms, Journal of Microscopy, vol.198, issue.1, pp.63-75, 2000.
DOI : 10.1046/j.1365-2818.2000.00671.x

G. M. Van-kempen, L. J. Van-vliet, P. J. Verveer, H. T. Van-der, and . Voort, A quantitative comparison of image restoration methods for confocal microscopy, Journal of Microscopy, vol.185, issue.3, pp.354-365, 1997.
DOI : 10.1046/j.1365-2818.1997.d01-629.x

R. Zanella, P. Boccacci, L. Zanni, and M. Bertero, Efficient gradient projection methods for edge-preserving removal of poisson noise, Inverse Problems, vol.25, issue.4, 2009.

M. N. Do and M. Vetterli, Framing pyramids, IEEE Transactions on Signal Processing, vol.51, issue.9, pp.2329-2342, 2003.
DOI : 10.1109/TSP.2003.815389