Glatting G, Wuchenauer M, Reske S N
Abteilung Nuklearmedizin, Universität Ulm, Germany.
Med Phys. 1999 Sep;26(9):1838-42. doi: 10.1118/1.598689.
The quality of the attenuation correction strongly influences the outcome of the reconstructed emission scan in positron emission tomography. The calculation of the attenuation correction factors must take into account the Poisson nature of the radioactive decay process, because-for a reasonable scan duration-the transmission measurements contain lines of response with low count numbers in the case of large attenuation factors. Our purpose in this study is to investigate a maximum likelihood estimator for attenuation correction factor calculation in positron emission tomography, which incorporates the Poisson nature of the radioactive decay into transmission and blank measurement. Therefore, the correct maximum likelihood function is used to derive two estimators for the calculation of the attenuation coefficient image and the corresponding attenuation correction factors depending on the measured blank and transmission data. Log likelihood convergence, mean differences, and the mean of squared differences for the attenuation correction factors of a mathematical thorax phantom were determined and compared. The algorithms yield adequate attenuation correction factors, however, the algorithm taking the noise in the blank scan into account can perform better for noisy blank scans. We conclude that maximum likelihood-including blank likelihood-is advantageous to reconstruct attenuation correction factors for low statistic blank and good statistic transmission data. For normal blank and transmission statistics the implementation of the statistical nature of the blank is not mandatory.
在正电子发射断层扫描中，衰减校正的质量对重建发射扫描的结果有很大影响。衰减校正因子的计算必须考虑放射性衰变过程的泊松特性，因为在合理的扫描持续时间内，对于较大的衰减因子，透射测量中包含计数较低的响应线。本研究的目的是研究一种用于正电子发射断层扫描中衰减校正因子计算的最大似然估计器，该估计器将放射性衰变的泊松特性纳入透射和空白测量中。因此，根据测量的空白和透射数据，使用正确的最大似然函数来推导两个用于计算衰减系数图像和相应衰减校正因子的估计器。确定并比较了数学胸部模型衰减校正因子的对数似然收敛、平均差异和平方差均值。这些算法能产生足够的衰减校正因子，然而，考虑空白扫描噪声的算法在处理有噪声的空白扫描时表现更好。我们得出结论，包括空白似然的最大似然法有利于重建低统计量空白和高统计量透射数据的衰减校正因子。对于正常的空白和透射统计量，考虑空白的统计特性并非必需。
