Mean and variance of single photon counting with deadtime.
Mean and variance of single photon counting with deadtime.
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DOI：
10.1088/0031-9155/45/7/324
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发表时间：
2000-07
影响因子：
3.5
通讯作者：
D. F. Yu;J. Fessler
中科院分区：
文献类型：
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作者：
D. F. Yu;J. Fessler
受死区时间影响的系统的光子计数统计对于统计图像重建方法可能很重要。我们提出了一种新方法来分析受 PET 和 SPECT 成像相关的各种死区时间模型影响的计数器系统的计数过程时刻。我们推导出各种模型下记录事件数的一阶矩和二阶矩的简单而精确的表达式。根据 SPECT 死区时间模型的平均表达式，我们得出了底层泊松过程实际强度的简单估计量；模拟表明，即使对于极高的计数率，我们的估计器也是无偏的。通过此分析，我们研究了大多数统计图像重建算法中假设的泊松统计模型的适用性。对于包含具有多个探测器元件的“模块”的系统，其中每个元件都会导致整个模块的死区时间损失，例如块 PET 探测器或 Anger 相机，即使存在死区时间损失，泊松统计模型似乎也足够了。
The statistics of photon counting by systems affected by deadtime are potentially important for statistical image reconstruction methods. We present a new way of analysing the moments of the counting process for a counter system affected by various models of deadtime related to PET and SPECT imaging. We derive simple and exact expressions for the first and second moments of the number of recorded events under various models. From our mean expression for a SPECT deadtime model, we derive a simple estimator for the actual intensity of the underlying Poisson process; simulations show that our estimator is unbiased even for extremely high count rates. From this analysis, we study the suitability of the Poisson statistical model assumed in most statistical image reconstruction algorithms. For systems containing 'modules' with several detector elements, where each element can cause deadtime losses for the entire module, such as block PET detectors or Anger cameras, the Poisson statistical model appears to be adequate even in the presence of deadtime losses.