Li Quanzheng, Leahy Richard M
Signal and Image Processing Institute, University of Southern California, Los Angeles, CA 90089 USA.
IEEE Trans Med Imaging. 2006 Dec;25(12):1565-72. doi: 10.1109/tmi.2006.884193.
Randoms precorrected positron emission tomography (PET) data is formed as the difference of two Poisson random variables. Its exact probability mass function (PMF) is inconvenient for use in likelihood-based iterative image reconstruction as it contains an infinite summation. The shifted Poisson model is a tractable approximation to this PMF but requires that negative values are truncated, resulting in positively biased reconstructions in low count studies. Here we analyze the properties of the exact PMF and propose a simple but accurate approximation that allows negative valued data. We investigate the properties of this approximation and demonstrate its application to penalized maximum likelihood image reconstruction.
随机预校正正电子发射断层扫描（PET）数据是由两个泊松随机变量的差值形成的。其精确的概率质量函数（PMF）在基于似然的迭代图像重建中使用不便，因为它包含一个无穷求和。移位泊松模型是对该PMF的一种易于处理的近似，但要求截断负值，这在低计数研究中会导致重建结果出现正偏差。在此，我们分析精确PMF的性质，并提出一种简单而准确的近似方法，该方法允许出现负值数据。我们研究了这种近似方法的性质，并展示了其在惩罚最大似然图像重建中的应用。
