Accelerating the EMML algorithm and related iterative algorithms by rescaled block-iterative methods
Accelerating the EMML algorithm and related iterative algorithms by rescaled block-iterative methods
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DOI：
10.1109/83.650854
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发表时间：
1998-01-01
影响因子：
10.6
通讯作者：
Byrne, CL
中科院分区：
文献类型：
--
作者：
Byrne, CL
代数重建技术（ART）的收敛性分析表明，它倾向于收敛到一个解决方案比同时的方法，如Cimmino-Landweber型，期望最大化最大似然方法的泊松模型（EMML），和同时乘法ART（SMART），其中使用所有的数据在每一步，尽管数据排序和松弛参数的选择很重要，但正如赫尔曼和迈耶所表明的那样，它们并不是全部。类似的乘法ART（MART）只适用于y > 0的系统y = Pr，P大于或等于0并且寻求非负解，也是顺序的（或“行作用”），而不是同时的，但通常不会表现出与其同时版本SMART相同的加速收敛。通过将每个方程除以P的相应行的最大值，我们发现，当解存在时，这种重新缩放的MART（RMART）确实收敛得更快，在行最大值基本上小于1的情况下，这种情况在层析成像中经常出现，并且当P的列已经被归一化为具有总和1时。在同时方法之间，在每个步骤使用所有数据，和顺序（或行操作）方法，在每一步仅使用单个数据值，还有块迭代（或有序子集）方法，其中在每一步处理单个块或数据子集。哈德逊等人的有序子集EM（OSEM）比EMML快得多，但常常不能收敛。“重缩放块迭代”EMML（RBI-EMML）是EMML的加速块迭代版本，在一致的情况下，对于任何子集的选择，它收敛到一个解;当限制性的“子集平衡”条件成立时，它简化为OSEM。
Analysis of convergence of the algebraic reconstruction technique (ART) shows it to be predisposed to converge to a solution faster than simultaneous methods, such as those of the Cimmino-Landweber type, the expectation maximization maximum likelihood method for the Poisson model (EMML), and the simultaneous multiplicative ART (SMART), which use all the data at each step, Although choice of ordering of the data and of relaxation parameters are important, as Herman and Meyer have shown, they are not the full story, The analogous multiplicative ART (MART), which applies only to systems y = Pr in which y > 0, P greater than or equal to 0 and a nonnegative solution is sought, is also sequential (or "row-action"), rather than simultaneous, but does not generally exhibit the same accelerated convergence relative to its simultaneous version, SMART. By dividing each equation by the maximum of the corresponding row of P, we find that this rescaled MART (RMART) does converge faster, when solutions exist, significantly so in cases in which the row maxima are substantially less than one, Such cases arise frequently in tomography and when the columns of P have been normalized to have sum one.Between simultaneous methods, which use all the data at each step, and sequential (or row-action) methods, which use only a single data value at each step, there are the block-iterative (or ordered subset) methods, in which a single block or subset of the data is processed at each step. The ordered subset EM (OSEM) of Hudson et al, is significantly faster than the EMML, but often fails to converge. The "rescaled block-iterative" EMML RBI-EMML) is an accelerated block-iterative version of EMML that converges, in the consistent case, to a solution, for any choice of subsets; it reduces to OSEM when the restrictive "subset balanced" condition holds, Rescaled block-iterative versions of SMART and MART also exhibit accelerated convergence.