Analytical model for pulse pileup in photon counting detectors with seminonparalyzable behavior

Photon counting x-ray detectors (PCDs) with energy discrimination capabilities provide spectral information, can eliminate electronic and Swank noise, and image multiple contrast agents simultaneously with high resolution. However, with high flux on the detectors, pulse pileup leads to count loss and spectral distortion. Accurate description of the output count rate and spectrum behavior of a PCD is crucial to the development of further applications, e.g., material decomposition. In this work, a fully analytical model of the pulse pileup spectrum and count statistics for a nonparalyzable detector with nonzero pulse length is proposed, which accounts for seminonparalyzable behavior, i.e., retriggering of counts by pulses incident during the dead time. We use a triangle to approximate a realistic pulse shape and recursively compute the output spectrum of different pulse pileup orders. A count-rate and spectrum dependent expression of count statistics is further derived based on renewal theory. Our analytical model can then be used to predict material decomposition noise using the Cramer-Rao lower bound (CRLB). We compared our model predictions with Monte Carlo simulations. The results show that our model can accurately predict the count loss and spectral distortion resulting from pulse pileup and can be used in predicting material decomposition noise over a large range of count rates.