Pile-up correction algorithms for nuclear spectrometry

This article presents a problem encountered in nuclear physics, queuing theory and point processes. The studied signal consists of pulses of random length and energy, possibly sampled, whose time occurrences are points of an homogenous Poisson process. Incoming pulses can combine into pile-ups, which results in a biased estimation of the density of lengths and energies. We introduce a model based on two marked point processes and derive an analytical relation between the probability density function (pdf) of the observed pile-ups and the pdf of the pulses, that leads to an algorithm for pile-up correction, in both continuous time and discrete time signals. Simulations show cancellation of the pile-up effect and prove efficiency of the algorithms in gamma spectrometry.