Washington Univ., St. Louis, MO.
IEEE Trans Med Imaging. 1994;13(1):89-101. doi: 10.1109/42.276147.
The expectation-maximization (EM) algorithm for computing maximum-likelihood estimates of transmission images in positron-emission tomography (PET) (see K. Lange and R. Carson, J. Comput. Assist. Tomogr., vol.8, no.2, p.306-16, 1984) is extended to include measurement error, accidental coincidences and Compton scatter. A method for accomplishing the maximization step using one step of Newton's method is proposed. The algorithm is regularized with the method of sieves. Evaluations using both Monte Carlo simulations and phantom studies on the Siemens 953B scanner suggest that the algorithm yields unbiased images with significantly lower variances than filtered-backprojection when the images are reconstructed to the intrinsic resolution. Large features in the images converge in under 200 iterations while the smallest features required up to 2,000 iterations. All but the smallest features in typical transmission scans converge in approximately 250 iterations. The initial implementation of the algorithm requires 50 sec per iteration on a DECStation 5000.
正电子发射断层成像术（PET）中用于计算传输图像最大似然估计的期望最大化（EM）算法（参见 K. Lange 和 R. Carson，《计算机辅助层析成像学报》，第 8 卷，第 2 期，第 306-316 页，1984 年）扩展到包括测量误差、偶然符合和康普顿散射。提出了一种使用牛顿法的一步来完成最大化步骤的方法。该算法使用筛法进行正则化。在西门子 953B 扫描仪上进行的蒙特卡罗模拟和体模研究评估表明，当图像重建到固有分辨率时，与滤波反投影相比，该算法产生的图像具有无偏性，且方差显著降低。图像中的大特征在 200 次迭代以下收敛，而最小特征则需要 2000 次迭代。在典型的透射扫描中，除了最小的特征之外，所有特征都在大约 250 次迭代中收敛。该算法的初始实现需要在 DECStation 5000 上每次迭代 50 秒。
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