PENALIZED MAXIMUM-LIKELIHOOD IMAGE-RECONSTRUCTION USING SPACE-ALTERNATING GENERALIZED EM ALGORITHMS
PENALIZED MAXIMUM-LIKELIHOOD IMAGE-RECONSTRUCTION USING SPACE-ALTERNATING GENERALIZED EM ALGORITHMS
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DOI：
10.1109/83.465106
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发表时间：
1995-10-01
影响因子：
10.6
通讯作者：
HERO, AO
中科院分区：
文献类型：
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作者：
FESSLER, JA;HERO, AO
大多数用于惩罚最大似然图像重建的期望最大化 (EM) 类型算法收敛缓慢，特别是当其中包含附加背景效应（例如散射、随机巧合、暗电流或宇宙辐射）时。此外，正则化平滑度惩罚（或先验）会引入参数耦合，使大多数 EM 类型算法的 M 步变得棘手。本文提出了用于图像重建的空间交替广义 EM (SAGE) 算法，该算法使用序列按顺序更新参数小型“隐藏”数据空间，而不是同时使用一个大的完整数据空间，顺序更新解耦了 M 步，因此通常可以分析地执行最大化，我们引入了新的隐藏数据空间，其信息量比泊松数据的传统完整数据空间少，并且收敛速度显着提高，这种加速是由于统计考虑，而不是数值过度松弛方法，因此保证了目标函数的单调增加，我们为 SAGE 方法提供了通用的全局收敛证明具有非负约束。
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.