Count statistics and pileup correction for nonparalyzable photon counting detectors with finite pulse length

Abstract

Photon counting detectors are expected to be the next big step in the development of medical computed tomography. Accurate modeling of the behavior of photon counting detectors in the high count rate regime is therefore important for detector performance evaluations and the development of accurate image reconstruction methods. The commonly used ideal nonparalyzable detector model is based on the assumption that photon interactions are converted to pulses with zero extent in time, which is too simplistic to accurately predict the behavior of photon counting detectors in both low and high count rate regimes. In this work we develop a statistical count model for a nonparalyzable detector with finite pulse length and use it to derive the asymptotic mean and variance of the output count distribution using tools from renewal theory. We use the statistical moments of the distribution to construct an estimator of the true number of counts for pileup correction. We confirm the accuracy of the model and evaluate the pileup correction using Monte Carlo simulations. The results show that image quality is preserved for surprisingly high count rates.