The main objective of spectrometry is to characterize the radioactive elements of an unknown source by studying the energy of the emitted gamma photons. When a photon interacts with a detector,its photonic energy is converted into an electrical pulse, whose integral energy is measured. The histogram obtained by collecting the energies can be used to identify radioactive elements andmeasure their activity.However, at high counting rates, perturbations which are due to the stochastic aspect of the temporal signal can cripple the identification of the radioactive elements. More specifically, since the detector has a finite resolution, close arrival times of photons which can be modeled as an homogeneous Poisson process cause pileups of individual pulses. This phenomenon distorts energy spectra by introducing multiple fake spikes and prolonging artificially the Compton continuum, which can mask spikes of lowintensity.The objective of this thesis is to correct the distortion caused by the pileup phenomenon in the energy spectra. Since the shape of photonic pulses depends on many physical parameters, we considerthis problem in a nonparametric framework. By introducing an adapted model based on two marked point processes, we establish a nonlinear relation between the probability measure associated to the observations and the probability density function we wish to estimate. This relation is derived both for continuous and for discrete time signals, and therefore can be used on a large set of detectors and from an analogical or digital point of view. It also provides a framework to this problem, which can be considered as a problem of nonlinear density deconvolution and nonparametric density estimation from indirect measurements.Using these considerations, we propose an estimator obtained by direct inversion. We show that this estimator is consistent and almost achieves the usual rate of convergence obtained in classicalnonparametric density estimation in the L2 sense. We illustrate these theoretical aspects of our study with numerical results obtained both on simulations and on energy spectra associated to real-world data from the ADONIS intrumentation systemdeveloped by the CEA Saclay. We show that the distortions caused by the pileup phenomenon are well corrected by the algorithms derived from our estimators.
