The Maximum Likelihood Estimator Method of Image Reconstruction: Its Fundamental Characteristics and their Origin
The Maximum Likelihood Estimator Method of Image Reconstruction: Its Fundamental Characteristics and their Origin
复制标题
图像重建的最大似然估计方法：其基本特征及其起源
DOI：
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发表时间：
1988
期刊：
影响因子：
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通讯作者：
E. Veklerov
中科院分区：
文献类型：
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作者：
J. Llacer;E. Veklerov
在本文中，我们回顾了我们最近在表征MLE算法的图像重建特性方面的工作。我们研究了它的收敛性，并证实了图像劣化的开始，这是源中计数数的函数。通过调整在重建过程中给予具有高计数的投影管相对于具有低计数的投影管的权重，我们已经确认图像恶化是由于算法试图将具有高计数的投影数据管与迭代图像投影过于接近。我们还为算法开发了一个停止规则，该规则测试了重建图像可以以与泊松分布变量的基本假设一致的方式给出初始投影数据的假设。该规则已成功应用于两个数学生成的幻影和第三个具有“精确”（无统计波动）投影数据的幻影，其结果证实了我们对迭代图像重建基本过程的理解。我们得出结论，在迭代格式中寻求极值的目标函数的行为在重建的早期阶段比在后期阶段更重要，当极值接近但结果与测量的泊松性质相矛盾时。
In this paper we review our recent work in characterizing the image reconstruction properties of the MLE algorithm. We have studied its convergence properties and confirmed the onset of image deterioration, which is a function of the number of counts in the source. By modulating the weight given to projection tubes with high numbers of counts with respect to those with low numbers of counts in the reconstruction process, we have confirmed that image deterioration is due to an attempt by the algorithm to match projection data tubes with high numbers of counts too closely to the iterative image projections. We have also developed a stopping rule for the algorithm that tests the hypothesis that a reconstructed image could have given the initial projection data in a manner consistent with the underlying assumption of Poisson distributed variables. The rule has been applied to two mathematically generated phantoms with success and to a third phantom with “exact” (no statistical fluctuations) projection data with results which confirm our understanding of the fundamental process of iterative image reconstruction. We conclude that the behavior of the target functions whose extrema are sought in iterative schemes is more important in the early stages of the reconstruction than in the later stages, when the extrema are being approached but the results are in contradiction with the Poisson nature of the measurement.