Brain Imaging Centre, Montreal Neurological Institute, McGill University, Montreal, Canada.
Phys Med Biol. 2010 Nov 21;55(22):6739-57. doi: 10.1088/0031-9155/55/22/009. Epub 2010 Oct 28.
The non-negativity constraint inherently present in OSEM reconstruction successfully reduces the standard deviation in cold regions but at the cost of introducing a positive bias, especially at low iteration numbers. For low-count data, as often encountered in short-duration frames in dynamic imaging protocols, it has been shown that it can be advantageous (in terms of bias in the reconstructed image) to remove the non-negativity constraint. In this work two competing algorithms that do not impose non-negativity in the reconstructed image are investigated: NEG-ML and AB-OSEM. It was found that the AB-OSEM reconstruction outperformed the NEG-ML reconstruction. The AB-OSEM algorithm was then further developed to allow a forward model that includes randoms and scatter background terms. In addition to static reconstruction the current analysis was extended to consider the important case of kinetic parameter estimation from dynamic PET data. Simulation studies (comparing OSEM, FBP and AB-OSEM) showed that the positive bias obtained with OSEM reconstruction can be avoided in both static and parametric imaging through use of a negative lower bound in AB-OSEM reconstruction (i.e. by lifting the implicit non-negativity constraint of OSEM). When quantification tasks are considered, the overall error in the estimates (composed of both bias and standard deviation) is often of primary concern. An important finding of this work is that in most cases the activity concentration and the kinetic parameters obtained from images reconstructed using AB-OSEM showed a lower overall root mean squared error compared to the popular choices of either OSEM or FBP reconstruction for both cold and warm regions. As such, AB-OSEM should be preferred instead of the standard OSEM and FBP reconstructions when kinetic parameter estimation is considered. Finally, this work shows example parametric images from the high-resolution research tomograph obtained using the different reconstruction methods.
在 OSEM 重建中，固有的非负约束成功地降低了冷区的标准差，但代价是引入了正偏差，尤其是在迭代次数较低的情况下。对于低计数数据，如动态成像协议中短时间帧中经常遇到的情况，已经表明去除非负约束在重建图像的偏差方面可能是有利的。在这项工作中，研究了两种不强制在重建图像中进行非负约束的竞争算法：NEG-ML 和 AB-OSEM。结果发现，AB-OSEM 重建的效果优于 NEG-ML 重建。然后，进一步开发了 AB-OSEM 算法，以允许包含随机和散射背景项的正向模型。除了静态重建，当前的分析还扩展到考虑从动态 PET 数据进行动力学参数估计的重要情况。模拟研究（比较 OSEM、FBP 和 AB-OSEM）表明，通过在 AB-OSEM 重建中使用负下限（即通过提升 OSEM 重建的隐式非负约束），可以避免 OSEM 重建中获得的正偏差，无论是在静态还是参数成像中。当考虑量化任务时，估计值的整体误差（由偏差和标准差组成）通常是主要关注点。这项工作的一个重要发现是，在大多数情况下，使用 AB-OSEM 重建的图像获得的活性浓度和动力学参数的整体均方根误差低于 OSEM 或 FBP 重建的常见选择，无论是冷区还是暖区。因此，在考虑动力学参数估计时，应该优先选择 AB-OSEM 而不是标准的 OSEM 和 FBP 重建。最后，这项工作展示了使用不同重建方法从高分辨率研究断层扫描仪获得的示例参数图像。
