Department of Radiology, University of British Columbia, Vancouver V5Z 1M9, Canada.
Med Phys. 2011 Jan;38(1):429-38. doi: 10.1118/1.3528170.
Compton camera has been proposed as a potential imaging tool in astronomy, industry, homeland security, and medical diagnostics. Due to the inherent geometrical complexity of Compton camera data, image reconstruction of distributed sources can be ineffective and/or time-consuming when using standard techniques such as filtered backprojection or maximum likelihood-expectation maximization (ML-EM). In this article, the authors demonstrate a fast reconstruction of Compton camera data using a novel stochastic origin ensembles (SOE) approach based on Markov chains.
During image reconstruction, the origins of the measured events are randomly assigned to locations on conical surfaces, which are the Compton camera analogs of lines-of-responses in PET. Therefore, the image is defined as an ensemble of origin locations of all possible event origins. During the course of reconstruction, the origins of events are stochastically moved and the acceptance of the new event origin is determined by the predefined acceptance probability, which is proportional to the change in event density. For example, if the event density at the new location is higher than in the previous location, the new position is always accepted. After several iterations, the reconstructed distribution of origins converges to a quasistationary state which can be voxelized and displayed.
Comparison with the list-mode ML-EM reveals that the postfiltered SOE algorithm has similar performance in terms of image quality while clearly outperforming ML-EM in relation to reconstruction time.
In this study, the authors have implemented and tested a new image reconstruction algorithm for the Compton camera based on the stochastic origin ensembles with Markov chains. The algorithm uses list-mode data, is parallelizable, and can be used for any Compton camera geometry. SOE algorithm clearly outperforms list-mode ML-EM for simple Compton camera geometry in terms of reconstruction time. The difference in computational time will be much larger when full Compton camera system model, including resolution recovery, is implemented and realistic Compton camera geometries are used. It was also shown in this article that while correctly reconstructing the relative distribution of the activity in the object, the SOE algorithm tends to underestimate the intensity values and increase variance in the images; improvements to the SOE reconstruction algorithm will be considered in future work.
康普顿相机已被提议作为天文学、工业、国土安全和医学诊断领域的潜在成像工具。由于康普顿相机数据固有的几何复杂性，使用滤波反投影或最大似然-期望最大化（ML-EM）等标准技术对分布式源进行图像重建可能效率低下和/或耗时。在本文中，作者展示了一种使用基于马尔可夫链的新颖随机起源集合（SOE）方法对康普顿相机数据进行快速重建的方法。
在图像重建过程中，测量事件的起源被随机分配到圆锥曲面上的位置，圆锥曲面是正电子发射断层扫描（PET）中响应线的康普顿相机模拟。因此，图像被定义为所有可能事件起源的起源位置的集合。在重建过程中，事件的起源被随机移动，新事件起源的接受由预定义的接受概率决定，该概率与事件密度的变化成正比。例如，如果新位置的事件密度高于前一个位置，则新位置始终被接受。经过几次迭代，起源的重建分布收敛到一个准静态状态，该状态可以进行体素化和显示。
与列表模式 ML-EM 的比较表明，在图像质量方面，后滤波 SOE 算法的性能相似，而在重建时间方面明显优于 ML-EM。
在这项研究中，作者实现并测试了一种基于具有马尔可夫链的随机起源集合的康普顿相机新图像重建算法。该算法使用列表模式数据，可并行化，可用于任何康普顿相机几何形状。在简单的康普顿相机几何形状方面，SOE 算法在重建时间方面明显优于列表模式 ML-EM。当实现完整的康普顿相机系统模型，包括分辨率恢复，并使用现实的康普顿相机几何形状时，计算时间的差异会更大。本文还表明，虽然 SOE 算法正确重建了物体中活性的相对分布，但它倾向于低估图像中的强度值并增加方差；未来的工作将考虑对 SOE 重建算法进行改进。
