A Statistical Framework for Modeling Paralyzable Pulse Pile-up Effects In Photon-Counting X-Ray Detectors
Abstract
Purpose
Photon-counting computed tomography (PCCT) is recognized as a revolutionary technology for next-generation spectral imaging. However, spectral distortion and count loss induced by pulse pile-up effects (PPEs) at high X-ray fluxes severely hinders its quantitative accuracy. While the deterministic effects of PPEs have been widely studied and modeled, the statistical properties associated with paralyzable mechanisms remain underexplored. Existing analytical approaches fail to provide a precise characterization of statistical properties—specifically variance and covariance—across multi-energy thresholds.
Methods
In this work, we propose a novel statistical framework to model paralyzable PPEs. Departing from traditional dead-time correction logic, our approach is grounded in the concept of the baseline probability density distribution. We model the detector output as a continuous-time stochastic process, where the instantaneous baseline is determined by the linear superposition of historical pulse shapes. By deriving the joint characteristic functions of baseline states and applying the Campbell-Bartlett theorem, we establish rigorous analytical expressions for the mean count rates, variances, and the covariance between arbitrary energy thresholds. This model explicitly captures the temporal correlations and statistical noise characteristics induced by pulse pile-up.
Results
Validation against Monte Carlo simulations demonstrated that the proposed model accurately predicted the noise covariance matrix, with a maximum Relative Frobenius Deviation (RFD) of less than 5% across various count rates.
Conclusion
This framework provides a theoretical basis for understanding the statistical behavior of paralyzable detectors. By offering a computationally efficient alternative to Monte Carlo simulations, this model facilitates precise performance analysis of PCCT spectral imaging and supports the development of advanced noise-reduction algorithms.