Dept. of Electr. Eng. and Comput. Sci., Michigan Univ., Ann Arbor, MI.
IEEE Trans Image Process. 1995;4(10):1417-29. doi: 10.1109/83.465106.
Most expectation-maximization (EM) type algorithms for penalized maximum-likelihood image reconstruction converge slowly, particularly when one incorporates additive background effects such as scatter, random coincidences, dark current, or cosmic radiation. In addition, regularizing smoothness penalties (or priors) introduce parameter coupling, rendering intractable the M-steps of most EM-type algorithms. This paper presents space-alternating generalized EM (SAGE) algorithms for image reconstruction, which update the parameters sequentially using a sequence of small "hidden" data spaces, rather than simultaneously using one large complete-data space. The sequential update decouples the M-step, so the maximization can typically be performed analytically. We introduce new hidden-data spaces that are less informative than the conventional complete-data space for Poisson data and that yield significant improvements in convergence rate. This acceleration is due to statistical considerations, not numerical overrelaxation methods, so monotonic increases in the objective function are guaranteed. We provide a general global convergence proof for SAGE methods with nonnegativity constraints.
大多数惩罚最大似然图像重建的期望最大化 (EM) 类型算法收敛速度较慢，特别是当添加散射、随机符合、暗电流或宇宙辐射等附加背景效应时。此外，正则化平滑惩罚（或先验）会引入参数耦合，使得大多数 EM 类型算法的 M 步变得难以处理。本文提出了用于图像重建的空间交替广义 EM (SAGE) 算法，该算法使用一系列小的“隐藏”数据空间顺序更新参数，而不是同时使用一个大型完整数据空间。顺序更新解耦了 M 步，因此通常可以进行解析最大化。我们引入了新的隐藏数据空间，对于泊松数据来说，这些数据空间的信息量比传统的完整数据空间要少，并且在收敛速度方面有显著的提高。这种加速是由于统计考虑，而不是数值过松弛方法，因此保证了目标函数的单调递增。我们为具有非负约束的 SAGE 方法提供了一般的全局收敛性证明。
