T. Trigano, E. Barat, T. Dautremer, and A. Souloumiac, Speech and Signal Processing, 2005 : cet article compare les performances de l'algorithme de désempilementdésempilementà temps discret introduit en Annexe A ` a l'algorithme dérivant de l'estimateur " na¨?fna¨?f, Pileup Correction Algorithms for Nuclear Spectrometry IEEE International Conference on Acoustics

T. Trigano, F. Roueff, E. Moulines, T. Montagu, and A. Souloumiac, Ce papier décrit des résultats sur données réelles obtenus en utilisant l'estimateur?mestimateur? estimateur?m, Analytical Energy Spectrum Reconstruction for HPGe Detectors in Gamma Spectrometry IEEE International Conference on Acoustics, Speech and Signal Processing Ces résultats sont redonnés au Chapitre 4, 2006.

G. F. Knoll, Radiation Detection and Measurement, 1989.

.. Inversion-théorique-de-la-transformée-de-laplace, 123 B.3.1 Inversion théorique de la transformée de Laplace d'une mesure

. Bibliographie, . Abate, ]. J. Whitt, W. Abate, and . Whitt, Laplace Transforms of Probability Density Functions with Series Representation, p.125, 1998.

W. Abate, W. Abate, and . Whitt, Computing Laplace Transforms for Numerical Inversion Via Continued Fractions, INFORMS Journal on Computing, vol.11, issue.4, pp.394-405, 1999.
DOI : 10.1287/ijoc.11.4.394

. Abate, Numerical inversion of multidimensional Laplace transforms by the Laguerre method, Performance Evaluation, vol.31, issue.3-4, p.125, 1996.
DOI : 10.1016/S0166-5316(97)00002-3

. Abate, On the Laguerre Method for Numerically Inverting Laplace Transforms, INFORMS Journal on Computing, vol.8, issue.4, pp.413-427, 1996.
DOI : 10.1287/ijoc.8.4.413

S. M. Abramowitz, I. A. Abramowitz, and . Stegun, Handbook of Mathematical Functions, American Journal of Physics, vol.34, issue.2, p.125, 1972.
DOI : 10.1119/1.1972842

A. , N. E. Albert, and L. Nelson, Contributions to the Statistical Theory of Counter Data, Annals of Mathmematical Statistics, vol.24, issue.1, pp.9-22, 1953.

J. Andai, R. Andai, and . Jedlovszky, Pile-up rejection live-time correction unit for precision ??-ray spectrometry, The International Journal of Applied Radiation and Isotopes, vol.34, issue.2, pp.501-507, 1983.
DOI : 10.1016/0020-708X(83)90269-7

. Ansi, American National Standard for Calibration and Use of Germanium Spectrometers for the Measurement of Gamma-Ray Emission Rates of Radionuclides. ANSI N42, pp.14-1999

. Baccelli, ]. F. Brémaud, P. Baccelli, and . Brémaud, Elements of Queueing Theory, p.135, 2002.
DOI : 10.1007/978-3-662-11657-9

. Bamford, Neutron, Proton and Gamma-Ray Event Identification with a HPGe Detector through Pulse Shape Analysis, IEEE Transactions on Nuclear Science, vol.37, issue.14, pp.200-208, 1991.

. Barat, . E. Dautremer, T. Barat, and . Dautremer, ADONIS : from Adaptive Filtering to Optimal Detection in Gamma Spectrometry, pp.81-84, 2002.

. Barat, . E. Dautremer, T. Barat, and . Dautremer, Algorithms Implementation in DSP for ADONIS, p.84, 2002.

M. Bayen, Bayen and C. Margaria. Distributions, Analyse de Fourier, Transformation de Laplace, Ellipses, vol.3, p.120, 1988.

P. H. Bingham, S. M. Bingham, M. Pitts, and . Queue, Non-parametric Estimation for the M/G/?? Queue, Annals of the Institute of Statistical Mathematics, vol.51, issue.1, pp.71-97, 1999.
DOI : 10.1023/A:1003831118254

. Bolotin, Simple technique for precise determinations of counting losses in nuclear pulse processing systems, Nuclear Instruments and Methods, vol.83, issue.1, pp.1-12, 1970.
DOI : 10.1016/0029-554X(70)90526-4

]. A. Boumenir, On The Numerical Inversion of the Laplace Transform by the Use of an Optimized Legendre Polynomials, Approx. Theory and Appl, vol.16, issue.4, pp.17-32, 2000.

]. L. Brancik, Programs for Fast Numerical Inversion of Laplace Transforms in Matlab Language Environment, Sbornik 7. Proc. Matlab 99, pp.27-39, 1999.

]. Q. Bristow, Theoretical and experimental investigations of coincidences inPoisson distributed pulse trains and spectral distortion caused by pulse pileup, p.134, 1990.

N. Cisowski, M. Cisowski, and . Nieds´zwieckinieds´zwiecki, Adaptive scheme for elimination of broadband noise and impulsive disturbances from AR and ARMA signals, IEEE Transactions on Signal Processing, pp.44-3967, 1996.

]. P. Coates, Pile-up corrections in the measurement of lifetimes, Journal of Physics E: Scientific Instruments, vol.5, issue.2, pp.148-150, 1972.
DOI : 10.1088/0022-3735/5/2/018

]. P. Coates, Analytical corrections for dead time effects in the measurement of time???interval distributions, Review of Scientific Instruments, vol.63, issue.3, pp.2084-2088, 1992.
DOI : 10.1063/1.1143170

M. D. Amore, A. Amore, and . Murli, Regularization of a Fourier Series Method for the Laplace Transform Inversion with Real Data, Inverse Problems, vol.18, issue.4, pp.1185-1205, 2002.

. Amore, Algorithm 796: a Fortran software package for the numerical inversion of the Laplace transform based on a Fourier series method, ACM Transactions on Mathematical Software, vol.25, issue.3, pp.306-315, 1999.
DOI : 10.1145/326147.326149

M. Davies, B. Davies, and . Martin, Numerical inversion of the laplace transform: a survey and comparison of methods, Journal of Computational Physics, vol.33, issue.1, pp.1-32, 1979.
DOI : 10.1016/0021-9991(79)90025-1

K. C. Davis, T. A. Davis, and . King, Correction methods for photon pile-up in lifetime determination by single-photon counting, Journal of Physics A: General Physics, vol.3, issue.1, pp.101-109, 1970.
DOI : 10.1088/0305-4470/3/1/013

. Dempster, Maximum likelihood from incomplete data via the EM algorithm, J. Royal Stat. Soc. B, vol.39, issue.82, pp.1-38, 1977.

B. Devroye, A. Devroye, and . Berlinet, A Comparison of Kernel Density Estimates, Publications de l, p.75, 1994.

]. L. Devroye, Consistent deconvolution in density estimation, Canadian Journal of Statistics, vol.23, issue.404, pp.235-239, 1989.
DOI : 10.2307/3314852

]. G. Doetsch, Introduction to the Theory and the Application of the Laplace Transform, pp.74-144, 1974.

O. Dvurecenskij, G. A. Dvurecenskij, and . Ososkov, Note on Type II Counter Problem, Appl. Math. (Czech.), vol.29, pp.237-249, 1984.

O. Dvurecenskij, G. A. Dvurecenskij, and . Ososkoveglin, On a modified counter with prolonging dead time, IEEE Workshop on Statistical Signal Processing, pp.678-687, 1985.
DOI : 10.1017/S0021900200024530

]. R. Evans, Encyclopedia of Physics, chapter Corpuscules and Radiation in Matter, pp.218-197, 1958.

]. J. Fan, On the Optimal Rates of Convergence for Nonparametric Deconvolution Problems, The Annals of Statistics, vol.19, issue.3, 1991.
DOI : 10.1214/aos/1176348248

]. J. Feller, An Introduction to Probability Theory and its Applications, p.123, 1966.

K. Frolov, M. Y. Frolov, and . Kitaev, A problem of numerical inversion of implicitly defined Laplace transforms, Computers & Mathematics with Applications, vol.36, issue.5, pp.35-44, 1998.
DOI : 10.1016/S0898-1221(98)00148-5

]. W. Gautschi, Numerical Analysis : an Introduction. Birkhaüser, 1997.
DOI : 10.1007/978-0-8176-8259-0

. Gehrk, Method of Photon Spectral Analysis, p.14, 1993.

]. J. Gubner, Computation of Shot-Noise Probability Distributions and Densities, SIAM Journal on Scientific Computing, vol.17, issue.3, pp.750-761, 1996.
DOI : 10.1137/S1064827594268725

P. Hall, J. Hall, and . Park, Nonparametric inference about service time distribution from indirect measurements, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.53, issue.4, pp.861-875, 2004.
DOI : 10.1093/biomet/84.2.295

]. P. Hall, Introduction to the Theory of Coverage Processes, p.135, 1988.

G. K. Hartwell, S. G. Hartwell, and . Goodwin, Pulser injection with subsequent removal-implementation and applications, IEEE Transactions on Nuclear Science, vol.36, issue.1, pp.36801-809, 1989.
DOI : 10.1109/23.34553

]. S. Haykin, Adaptive Filter Theory, p.79, 1995.

]. R. Helmer, Efficiency Calibration of a Ge Detector for 30-2800 keV Gamma-Rays. Nuclear Instruments and Methods, pp.87-90, 1982.

]. W. Hoeffding, Probability Inequalities for Sums of Bounded Random Variables, Journal of the American Statistical Association, vol.1, issue.301, pp.13-30, 1963.
DOI : 10.1214/aoms/1177730491

. Johnson, Utilization of Concurrently Gathered Pulser Data for Complete Spectral Validation of Gamma-Ray Spectra from Germanium Detectors, IEEE Transactions on Nuclear Science, vol.28, issue.1, pp.28638-28653, 1981.
DOI : 10.1109/TNS.1981.4331255

. Johnstone, Wavelet deconvolution in a periodic setting, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.11, issue.3, pp.547-573, 2004.
DOI : 10.1081/NFA-120003678
URL : https://hal.archives-ouvertes.fr/hal-00102266

. Jorion, ]. B. Stoller, C. Jorion, and . Stoller, Method for Pulse Shaping Regulation and Discrimination in a Nuclear Spectroscopy System, p.16, 1999.

]. G. Knoll, Radiation Detection and Measurement, p.133, 1989.

]. J. Lacroix, Cha??nesCha??nes de Markov et Processus de Poisson, p.120, 2000.

. Lee, ]. D. Seung, H. S. Lee, and . Seung, Algorithms for Nonnegative Matrix Factorization, Adv. in Neural and Inform. Process. Syst, pp.556-562, 2001.

R. William and . Leo, Techniques for Nuclear and Particle Physics Experiments : A How-To Approach, p.133, 1994.

B. Logothetis, ]. A. Krishnamurthy, V. Logothetis, and . Krishnamurthy, Expectation maximization algorithms for MAP estimation of jump Markov linear systems, IEEE Transactions on Signal Processing, vol.47, issue.8, pp.2139-2156, 1999.
DOI : 10.1109/78.774753

T. D. Martin, R. J. Martin, and . Thomson, Robust-resistant spectrum estimation, Proceedings of the IEEE, pp.1097-1115, 1982.
DOI : 10.1109/PROC.1982.12434

]. C. Masreliez, Approximate non-Gaussian filtering with linear state and observation relations, IEEE Transactions on Automatic Control, vol.20, issue.1, pp.107-110, 1975.
DOI : 10.1109/TAC.1975.1100882

. Montémont, Arqù es, and A. Mohammad-Djafari. A Bayesian Method for Pulse Shape and Energy Estimation for Gamma Spectrometry Measurements using Semiconductor Detectors, Proc. 20th int. workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, p.15, 2000.

. Mott, Highly Sensitive Nuclear Spectrometer Apparatus and Method, p.14, 1994.

]. C. Cinneide and . O-'cinneide, Euler summation for fourier series and laplace transform inversion, Communications in Statistics. Stochastic Models, vol.24, issue.2, pp.315-337, 1997.
DOI : 10.1016/0010-4809(72)90039-0

]. E. Parzen, On Estimation of a Probability Density Function and Mode, The Annals of Mathematical Statistics, vol.33, issue.3, pp.1065-1076, 1962.
DOI : 10.1214/aoms/1177704472

. Pensky, ]. M. Vidakovic, B. Pensky, and . Vidakovic, Adaptive Wavelet Estimator for Nonparametric Density Estimation, Ann. Statist, vol.27, issue.90, pp.2033-2053, 1999.

. Pommé, Accuracy and precision of loss-free counting in ??-ray spectrometry, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol.422, issue.1-3, pp.388-394, 1999.
DOI : 10.1016/S0168-9002(98)00989-9

. Pommé, Influence of Pileup Rejection on Nuclear Counting, Viewed from the Time-Domain Perspective. Nuclear Instruments and Methods in, Physics Research, vol.426, issue.2, pp.564-582, 1999.

]. S. Pommé, Time distortion of a Poisson process and its effect on experimental uncertainty, Applied Radiation and Isotopes, vol.49, issue.9-11, pp.9-111213, 1998.
DOI : 10.1016/S0969-8043(97)10048-3

]. S. Pommé, How Pileup Rejection Affects the Precision of Loss-Free Counting. Nuclear Instruments and Methods in Physics Research, pp.456-470, 1999.

]. S. Pommé, Time-Interval Distributions and Counting Statistics with a Non- Paralysable Spectrometer. Nuclear Instruments and Methods in Physics Research, pp.481-489, 1999.

]. R. Pyke, On Renewal Processes Related to Type I and Type II Counter Models, The Annals of Mathematical Statistics, vol.29, issue.3, pp.737-754, 1958.
DOI : 10.1214/aoms/1177706533

]. S. Resnick, Adventures in Stochastic Processes, pp.29-38, 1992.
DOI : 10.1007/978-1-4612-0387-2

R. , C. Robert, and G. Casella, Monte Carlo Statistical Methods, p.128, 2004.

]. M. Rosenblatt, Remarks on Some Nonparametric Estimates of a Density Function, The Annals of Mathematical Statistics, vol.27, issue.3, pp.832-837, 1956.
DOI : 10.1214/aoms/1177728190

]. W. Rudin, Real and Complex Analysis, p.120, 1987.

. Saul, Statistical Signal Processing with Nonnegativity Constraints, Europ. Conf. on Speech Process, pp.1001-1004, 2003.

B. Seeman, N. Seeman, and . Bronislaw, Nuclear Spectroscopy Method and Apparatus for Digital Pulse Height Analysis, p.14, 1991.

. Sha, Multiplicative Updates for Large Margin Classifiers Random Point Processes Numerical Inversion of the Laplace Transform on the Real Line from Expected Values On a Probability Problem in the Theory of Counters, Montagu, E. Moulines, F. Roueff, and A. Souloumiac. Analytical Pileup Correction Method for HPGe Detectors. soumisàsoumisà IEEE Transactions on Signal Processing, pp.188-202, 1958.

]. N. Tsoulfanidis, Measurement and Detection of Radiation. Taylor and Francis, 1995.

]. P. Valko and J. Abate, Comparison of sequence accelerators forthe Gaver method of numerical Laplace transform inversion, Computers & Mathematics with Applications, vol.48, issue.3-4, p.126, 2003.
DOI : 10.1016/j.camwa.2002.10.017

V. Valko, S. Valko, and . Vajda, Inversion of Noise-Free Laplace Transforms: Towards a Standardized Set of Test Problems, Inverse Problems in Engineering, vol.2, issue.5, pp.467-483, 2002.
DOI : 10.1016/S0378-3758(98)00096-2

D. Waart, ]. A. Wellner, J. A. Van-der-waart, and . Wellner, Weak Convergence and Empirical Processes with Applications to Statistics, pp.58-59, 1996.

H. K. Warburton, B. Warburton, . K. Hubbard-]-w, Z. Warburton, and . Zhou, Method and Apparatus for Digitally Based High-Speed X-ray Spectrometer Method and Apparatus for Combinatorial Logic Signal Processor in a Digitally Based High-Speed X-ray Spectrometer, pp.14-14, 1997.

]. W. Warburton, Method and Apparatus for Digitally Based High-Speed X-ray Spectrometer for Direct Coupled Use with Continuous Discharge Preamplifiers, p.14, 1998.

. Westphal, Adaptive digital filter for high-rate high-resolution gamma spectrometry, IEEE Transactions on Nuclear Science, vol.48, issue.3, pp.461-465, 2001.
DOI : 10.1109/23.940100

]. G. Westphal, Real-time correction of counting losses in nuclear pulse spectroscopy, Journal of Radioanalytical Chemistry, vol.61, issue.1-2, pp.387-397, 1982.
DOI : 10.1007/BF02516125

]. G. Westphal-]-w and . Whitt, Application of the Virtual Pulse Generator Method to Real-Time Correction of Counting Losses in High-Rate Gamma Ray Spectroscopy Infinite-Series Representations of Laplace Transforms of Probability Density Functions for Numerical Inversion [Wiernik, 1971] M. Wiernik. Normal and Random Pulse Generators for the Correction of Dead-Time Losses in Nuclear Spectrometry, ] C. H. Zhang. Fourier Methods for Estimating Mixing Densities and Distributions, pp.411-417, 1971.