Yavuz M, Fessler J A
GE Research and Development Center, Niskayuna, NY 12309, USA.
IEEE Trans Med Imaging. 1999 Aug;18(8):665-74. doi: 10.1109/42.796280.
This paper analyzes and compares image reconstruction methods based on practical approximations to the exact log likelihood of randoms-precorrected positron emission tomography (PET) measurements. The methods apply to both emission and transmission tomography, however, in this paper we focus on transmission tomography. The results of experimental PET transmission scans and variance approximations demonstrate that the shifted Poisson (SP) method avoids the systematic bias of the conventional data-weighted least squares (WLS) method and leads to significantly lower variance than conventional statistical methods based on the log likelihood of the ordinary Poisson (OP) model. We develop covariance approximations to analyze the propagation of noise from attenuation maps into emission images via the attenuation correction factors (ACF's). Empirical pixel and region variances from real transmission data agree closely with the analytical predictions. Both the approximations and the empirical results show that the performance differences between the OP model and SP model are even larger, when considering noise propagation from the transmission images into the final emission images, than the differences in the attenuation maps themselves.
本文基于对随机预校正正电子发射断层扫描（PET）测量精确对数似然的实际近似，分析并比较了图像重建方法。这些方法适用于发射断层扫描和透射断层扫描，不过在本文中我们聚焦于透射断层扫描。PET透射扫描实验结果和方差近似表明，移位泊松（SP）方法避免了传统数据加权最小二乘法（WLS）的系统偏差，并且与基于普通泊松（OP）模型对数似然的传统统计方法相比，方差显著更低。我们开发了协方差近似，以分析噪声从衰减图通过衰减校正因子（ACF）传播到发射图像中的情况。来自实际透射数据的经验像素和区域方差与分析预测结果非常吻合。近似结果和经验结果均表明，当考虑噪声从透射图像传播到最终发射图像时，OP模型和SP模型之间的性能差异比衰减图本身的差异更大。
