Hudson H M, Ma J, Green P
Department of Statistics, Macquarie University, NSW, Australia.
Stat Methods Med Res. 1994;3(1):41-61. doi: 10.1177/096228029400300104.
Many algorithms for medical image reconstruction adopt versions of the expectation-maximization (EM) algorithm. In this approach, parameter estimates are obtained which maximize a complete data likelihood or penalized likelihood, in each iteration. Implicitly (and sometimes explicitly) penalized algorithms require smoothing of the current reconstruction in the image domain as part of their iteration scheme. In this paper, we discuss alternatives to EM which adapt Fisher's method of scoring (FS) and other methods for direct maximization of the incomplete data likelihood. Jacobi and Gauss-Seidel methods for non-linear optimization provide efficient algorithms applying FS in tomography. One approach uses smoothed projection data in its iterations. We investigate the convergence of Jacobi and Gauss-Seidel algorithms with clinical tomographic projection data.
许多医学图像重建算法都采用了期望最大化（EM）算法的变体。在这种方法中，每次迭代都会获得使完整数据似然或惩罚似然最大化的参数估计。隐式（有时显式）惩罚算法在其迭代方案中需要对图像域中的当前重建进行平滑处理。在本文中，我们讨论了EM的替代方法，这些方法采用了费舍尔评分法（FS）以及其他直接最大化不完全数据似然的方法。用于非线性优化的雅可比和高斯 - 赛德尔方法为在断层扫描中应用FS提供了高效算法。一种方法在其迭代中使用平滑投影数据。我们研究了雅可比和高斯 - 赛德尔算法与临床断层扫描投影数据的收敛性。
