Roessl Ewald, Daerr Heiner, Proksa Roland
Philips GmbH Innovative Technologies, Philips Research Laboratories, Röntgenstrasse 24-26, D-22335 Hamburg, Germany.
Med Phys. 2016 Mar;43(3):1295-8. doi: 10.1118/1.4941743.
An analytic Fourier approach to predict the expected number of counts registered in a photon-counting detector subject to pulse pile-up for arbitrary photon flux, detector response function, and pulse-shape is presented. The analysis provides a complete forward model for energy-sensitive, photon-counting x-ray detectors for spectral computed tomography.
The formalism of the stochastic theory of the expected frequency of level crossings of shot noise processes is applied to the pulse pile-up effect and build on a recently published analytic Fourier representation of the level crossing frequency of shot noise processes with piece-wise continuous kernels with jumps.
The general analytic result is validated by a Monte Carlo simulation for pulses of the form g(t) = e(-t/τ) (t > 0) and a Gaussian detector response function. The Monte Carlo simulations are in excellent agreement with the analytic predictions of photon counts within the numerical accuracy of the calculations.
The phenomenon of pulse pile-up is identified with the level-crossing problem of shot noise processes and an exact, analytic formula for the expected number of counts in energy-sensitive, photon-counting x-ray detectors for arbitrary photon flux, response function, and pulse-shapes is derived. The framework serves as a theoretical foundation for future works on pulse pile-up.
提出一种解析傅里叶方法，用于预测在任意光子通量、探测器响应函数和脉冲形状下，受脉冲堆积影响的光子计数探测器中记录的预期计数数量。该分析为光谱计算机断层扫描的能量敏感型光子计数X射线探测器提供了一个完整的正向模型。
将散粒噪声过程电平交叉预期频率的随机理论形式应用于脉冲堆积效应，并基于最近发表的具有跳跃的分段连续核的散粒噪声过程电平交叉频率的解析傅里叶表示。
通过对形式为g(t) = e(-t/τ) （t > 0）的脉冲和高斯探测器响应函数进行蒙特卡罗模拟，验证了一般解析结果。蒙特卡罗模拟与计算数值精度内的光子计数解析预测结果非常吻合。
将脉冲堆积现象与散粒噪声过程的电平交叉问题联系起来，并推导了任意光子通量、响应函数和脉冲形状下能量敏感型光子计数X射线探测器预期计数数量的精确解析公式。该框架为未来关于脉冲堆积的研究奠定了理论基础。
