Bias reduction for low-statistics PET: maximum likelihood reconstruction with a modified Poisson distribution.
Bias reduction for low-statistics PET: maximum likelihood reconstruction with a modified Poisson distribution.
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DOI：
10.1109/tmi.2014.2347810
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发表时间：
2015-01
影响因子：
10.6
通讯作者：
Nuyts J
中科院分区：
文献类型：
--
作者：
Van Slambrouck K;Stute S;Comtat C;Sibomana M;van Velden FH;Boellaard R;Nuyts J
正电子发射断层扫描数据通常用最大似然期望最大化（MLEM）重建。然而，由于非负约束，MLEM遭受正偏置。这对于示踪剂动力学建模是特别成问题的。两种重建方法的偏差减少属性，不使用严格的泊松优化，并相互比较，过滤反投影（FBP），和MLEM。第一种方法是NEGML的扩展，其中对于低计数数据点，泊松分布被高斯分布取代。高斯和泊松状态之间的过渡点是模型的参数。第二种方法是ABML的简化。ABML具有重建图像的下限和上限，而AML具有设置为无穷大的上限。AML使用负下限来获得偏倚减少属性。研究了下界的不同选择。这两种算法的参数决定了偏差减少的有效性，并且应该选择足够大的参数以确保无偏差图像。这意味着这两种算法变得更类似于最小二乘算法，这被证明是获得无偏差重建所必需的。这是以增加差异为代价的。然而，NEGML和AML的方差低于FBP。此外，随机处理对偏倚有很大影响。与使用未平滑的随机数或随机数预校正数据的重建相比，使用平滑的随机数的重建导致更低的偏差。然而，NEGML和AML对于它们的参数的大值都产生无偏置图像。
Positron emission tomography data are typically reconstructed with maximum likelihood expectation maximization (MLEM). However, MLEM suffers from positive bias due to the non-negativity constraint. This is particularly problematic for tracer kinetic modeling. Two reconstruction methods with bias reduction properties that do not use strict Poisson optimization are presented and compared to each other, to filtered backprojection (FBP), and to MLEM. The first method is an extension of NEGML, where the Poisson distribution is replaced by a Gaussian distribution for low count data points. The transition point between the Gaussian and the Poisson regime is a parameter of the model. The second method is a simplification of ABML. ABML has a lower and upper bound for the reconstructed image whereas AML has the upper bound set to infinity. AML uses a negative lower bound to obtain bias reduction properties. Different choices of the lower bound are studied. The parameter of both algorithms determines the effectiveness of the bias reduction and should be chosen large enough to ensure bias-free images. This means that both algorithms become more similar to least squares algorithms, which turned out to be necessary to obtain bias-free reconstructions. This comes at the cost of increased variance. Nevertheless, NEGML and AML have lower variance than FBP. Furthermore, randoms handling has a large influence on the bias. Reconstruction with smoothed randoms results in lower bias compared to reconstruction with unsmoothed randoms or randoms precorrected data. However, NEGML and AML yield both bias-free images for large values of their parameter.