Lange K, Carson R
J Comput Assist Tomogr. 1984 Apr;8(2):306-16.
Two proposed likelihood models for emission and transmission image reconstruction accurately incorporate the Poisson nature of photon counting noise and a number of other relevant physical features. As in most algebraic schemes, the region to be reconstructed is divided into small pixels. For each pixel a concentration or attenuation coefficient must be estimated. In the maximum likelihood approach these parameters are estimated by maximizing the likelihood (probability of the observations). EM algorithms are iterative techniques for finding maximum likelihood estimates. In this paper we discuss the general principles behind all EM algorithms and derive in detail the specific algorithms for emission and transmission tomography. The virtues of the EM algorithms include (a) accurate incorporation of a good physical model, (b) automatic inclusion of non-negativity constraints on all parameters, (c) an excellent measure of the quality of a reconstruction, and (d) global convergence to a single vector of parameter estimates. We discuss the specification of necessary physical features such as source and detector geometries. Actual reconstructions are deferred to a later time.
两种用于发射和透射图像重建的似然模型准确地纳入了光子计数噪声的泊松特性以及许多其他相关物理特征。与大多数代数方法一样，待重建区域被划分为小像素。对于每个像素，必须估计浓度或衰减系数。在最大似然方法中，这些参数通过最大化似然性（观测值的概率）来估计。期望最大化（EM）算法是用于寻找最大似然估计的迭代技术。在本文中，我们讨论所有EM算法背后的一般原理，并详细推导发射和透射断层扫描的特定算法。EM算法的优点包括：（a）准确纳入良好的物理模型；（b）自动对所有参数施加非负性约束；（c）对重建质量的出色度量；以及（d）全局收敛到单个参数估计向量。我们讨论必要物理特征（如源和探测器几何形状）的规范。实际重建将留待以后进行。
