[1]

S. Ahn and J. Fessler, Globally convergent image reconstruc tion for emission tomography using relaxed ordered subsets algorithms, IEEE Trans. Med. Imag., 22 (2003), 613626.

[2]

S. Alenius and U. Ruotsalainen, Bayesian image reconstruction for emission tomography based on median root prior, Europ. J. of Nucl. Med. and Molec. Im., 24 (1998), 258265.

[3]

F. J. Andscombe, The transformation of Poisson, binomial and non negativebinomial data, Biometrika, 35 (1948), 246254.

[4]

A. Beck and M. Teboulle, Fast gradientbased algorithms for constrained total variation image denoising and deblurring problems, IEEE TIP, 18 (2009), 24192434.

[5]

A. Beck and M. Teboulle, A fast iterative shrinkagethresholding algorithm for linear inverse problems, SIAM J. on Imag. Sci., 2 (2009), 183202.

[6]

M. Bertero, P. Boccacci, G. Talenti, R. Zanella and L. Zanni, A discrepancy principle for Poisson data, Inverse Problems, 26 (2010), 105004, 20 pp.

[7]

S. Bonettini and V. Ruggiero, An alternating extragradient method for total variationbased image restoration from Poisson data, Inverse Problems, 27 (2011), 095001, 26 pp.

[8]

L. M. BriceñoArias and P. L. Combettes, Convex variational formulation with smooth coupling for multicomponent signal decomposition and recovery, Numerical Mathematics: Theory, Methods, and Applications, 2 (2009), 485508.

[9]

F. C. Brunner, J.C. Clemens, C. Hemmer and C. Morel, Imaging performance of the hybrid pixel detectors xpad3s, Physics in Medicine and Biology, 54 (2009), 17731789.

[10]

A. Chambolle, An algorithm for total variation minimization and applications, JMIV, 20 (2004), 8997.

[11]

A. Chambolle and T. Pock, A firstorder primaldual algorithm for convex problems with applications to imaging, JMIV, 40 (2011), 120145.

[12]

G. Chen and M. Teboulle, A proximalbased decomposition method for convex minimization problems, Mathematical Programming, 64 (1994), 81101.

[13]

P. L. Combettes and V. Wajs, Signal recovery by proximal forwardbackward splitting, Multi. Model. and Simu., 4 (2005), 11681200.

[14]

I. Daubechies, M. Defrise and C. De Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Com. P. & A. Math., 57 (2004), 14131457.

[15]

A. Dempster, N. M. Laird and D. B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, J. of the Roy. Stat. Soc. Ser. B, 39 (1977), 138.

[16]

Y. K. Dewaraja, K. F. Koral and J. A. Fessler, Regularized reconstruction in quantitative spect using CT side information from hybrid imaging, Phys. Med. Biol., 55 (2010), 25232539.

[17]

F.X. Dupé, J. Fadili and J.L. Starck, A proximal iteration for deconvolving Poisson noisy images using sparse representations, IEEE TIP, 18 (2009), 310321.

[18]

H. Erdoğan and J. Fessler, Monotonic algorithms for transmission tomography, IEEE TMI, 18 (1999), 801814.

[19]

L. Feldkamp, L. Davis and J. Kress, Practical conebeam algorithm, J. Opt. Soc. Am. A., 1 (1984), 612619.

[20]

M. Figueiredo and J. BioucasDias, Restoration of Poissonian images using alternating direction optimization, IEEE Transactions on Image Processing, 19 (2010), 31333145.

[21]

M. Fisz, The limiting distribution of a function of two independant random variables and its statistical application, Colloquium Mathematicum, 3 (1955), 138146.

[22]

Kenneth M. Hanson and George W. Wecksung, Local basisfunction approach to computed tomography, Appl. Opt., 24 (1985), 40284039.

[23]

Z. Harmany, R. Marcia and R. Willett, This is SPIRALTAP: Sparse Poisson intensity Reconstruction ALgorithms Theory and Practice, IEEE Trans. Image Process., 21 (2010), 10841096.

[24]

S. Helgason, "Groups and Geometric Analysis. Integral Geometry, Invariant Differential Operators, and Spherical Functions," Pure and Applied Mathematics, 113, Academic Press, Orlando, FL, 1984.

[25]

Julia Herzen, Tilman Donath, Franz Pfeiffer, Oliver Bunk, Celestiste, Felix Beckmann, Andreas Schreyer and Christian David, Quantitative phasecontrast tomography of a liquid phantom using a conventional xray tube source, Opt. Express, 17 (2009), 1001010018.

[26]

H. M. Hudson and R. S. Larkin, Accelerated image reconstruction using ordered subsets of projection data, IEEE Trans. Med. Imag., 13 (1994), 601609.

[27]

P. J. Huber, "Robust Statistics," Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, 1981.

[28]

J.J.Moreau, Proximité et dualité dans un espace hilbertien, Bulletin Soc. Math. France, 93 (1965), 273299.

[29]

R. Khoury, A. Bonissent, J.C. Clémens, C. Meessen, E. Vigeolas, M. Billault and C. Morel, A geometrical calibration method for the PIXSCAN microCT scanner, Journal of Instrumentation, 4 (2009), P07016.

[30]

K. Lange and R. Carson, EM reconstruction algorithms for emission and transmission tomography, J. Comput. Assist. Tomo., 8 (1984), 306316.

[31]

C. Lartizien, N. Costes, A. Reilhac, M. Janier and D. SappeyMarinier, The clearPET project: Development of a 2nd generation highperformance small animal PET scanner, in "Second AMI Meeting," Madrid, Spain, Sept., 2003.

[32]

J.B. Mosset, O. Devroede, M. Krieguer, M. Rey, J.M. Vieira, J. H. Jung, C. Kuntner, M. Streun, K. Ziemons, E. Auffray, P. SempereRoldan, P. Lecoq, P. Bruyndonckx, J.F. Loude, S. Tavernier and C. Morel, Development of an optimized LSO/LuYAP phoswich detector head for the Lausanne ClearPET demonstrator, Nuclear Science, IEEE Transactions on, 53 (2006), 2529.

[33]

Yu. Nesterov, "Introductory Lectures on Convex Optimization: A Basic Course," Optimization, 87, Kluwer Ac. Pub., Boston, MA, 2004.

[34]

Yu. Nesterov, Smooth minimization of nonsmooth functions, Math. Progr., 103 (2005), 127152.

[35]

Y. Nesterov, Gradient methods for minimizing composite objective function, Ecore discussion paper, 2007.

[36]

S. Nicol, S. Karkar, C. Hemmer, A. Dawiec, D. Benoit, P. Breugnon, B. Dinkespiler, F. Riviere, J.P. Logier, M. Niclas, J. Royon, C. Meessen, F. Cassol, J.C. Clemens, A. Bonissent, F. Debarbieux, E. Vigeolas, P. Delpierre and C. Morel, Design and construction of the ClearPET/XPAD small animal PET/CT scanner, Nuclear Science Symposium Conference Record (NSS/MIC), 2009 IEEE, Oct. 24 2009Nov. 1 2009, 33113314.

[37]

P. Pangaud, S. Basolo, N. Boudet, J.F. Berar, B. Chantepie, P. Delpierre, B. Dinkespiler, S. Hustache, M. Menouni and C. Morel, XPAD3: A new photon counting chip for Xray CTscanner, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 571 (2007), 321324; Proceedings of the 1st International Conference on Molecular Imaging Technology  EuroMedIm, 2006.

[38]

A. R. De Pierro, A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography, IEEE TMI, 14 (1995), 132137.

[39]

N. Pustelnik, C. Chaux and J.C. Pesquet, Parallel proximal algorithm for image restoration using hybrid regularization, IEEE TIP, 20 (2011), 24502462.

[40]

N. Pustelnik, C. Chaux, J.C. Pesquet and C. Comtat, Parallel algorithm and hybrid regularization for dynamic PET reconstruction, in "IEEE Med. Im. Conf.," Knoxville, TN, 2010.

[41]

M. Rey, S. Jan, J.M. Vieira, J.B. Mosset, M. Krieguer, C. Comtat and C. Morel, Count rate performance study of the Lausanne ClearPET scanner demonstrator, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 571 (2007), 207210; Proceedings of the 1st International Conference on Molecular Imaging Technology  EuroMedIm, 2006.

[42]

T. Rockafellar, "Convex Analysis," Princeton Mathematical Series, No. 28, Princeton University Press, Princeton, NJ, 1970.

[43]

L. A. Shepp and Y. Vardi, Maximum likelihood reconstruction in positron emission tomography, IEEE TMI, 1 (1982), 113122.

[44]

E. Y. Sidky and X. Pan, Image reconstruction in circular conebeam computed tomography by constrained, totalvariation minimization, Phys. Med. Biol., 53 (2008), 47774807.

[45]

Z. Wang, A. Bovik, H. Sheikh and E. Simoncelli, Image quality assessment: From error visibility to structural similarity, IEEE TIP, 13 (2004), 600612.

[46]

P. Weiss, G. Aubert and L. BlancFéraud, Efficient schemes for total variation minimization under constraints in image processing, SIAM J. on Sci. Comp., 31 (2009), 20472080.
