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Statistical image reconstruction and performance analysis for dynamic positron emission tomography.

机译：动态正电子发射断层扫描的统计图像重建和性能分析。

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We developed dynamic PET image reconstruction algorithms for the penalized likelihood estimation of voxelwise time activity curves directly from list-mode data. We used an efficient format for the spatiotemporal data in which we augmented the sinogram with an associated list of event arrival times indexed by the sinogram entries. We combined our accurate system model developed for static PET with an accurate statistical model that models the emission from each voxel as an inhomogeneous Poisson process to reconstruct dynamic images with high spatial and temporal resolution.; We derived computationally efficient methods for the estimation of the mean and variance properties of penalized likelihood dynamic PET images. This allowed us to predict the accuracy of reconstructed activity estimates and to compare reconstruction algorithms theoretically. We combined a bin-mode approach in which data is modeled as a collection of independent Poisson random variables at each spatiotemporal bin with the space-time separabilities in the imaging equation and penalties to derive rapidly computable analytic mean and variance approximations. We used these approximations to show that our dynamic PET image reconstruction algorithm has superior bias/variance properties over multiframe static PET reconstructions.; We also studied the spatial and temporal resolution properties of penalized likelihood dynamic PET images and showed that approximately uniform spatial resolution over time could be achieved by applying spatiotemporally varying smoothing. The degree of smoothing at each voxel is determined by the corresponding diagonal entry of the dynamic Fisher Information Matrix. We also showed that by performing the reconstruction in a transformed time domain, we could also make the spatial resolution not only uniform in space but also approximately constant over time.; In order to take advantage of the full spatiotemporal content of list-mode data, we proved the convergence of a globally convergent, fully four-dimensional, incremental gradient dynamic PET image reconstruction algorithm and demonstrated its feasibility by reconstructing simulated four-dimensional PET data from a small-animal scanner.; We also developed an efficient algorithm to compress large dynamic PET datasets that provided an additional 35--40% compression over standard compression software for datasets with more than 60 frames.
机译：我们开发了动态PET图像重建算法，用于直接从列表模式数据对voxelwise时间活动曲线进行惩罚似然估计。我们为时空数据使用了一种有效的格式，其中我们用正弦图条目索引的事件到达时间的相关列表来扩充正弦图。我们将为静态PET开发的精确系统模型与为每个体素的发射建模为不均匀的Poisson过程的精确统计模型相结合，以重建具有高时空分辨率的动态图像。我们推导了计算有效的方法来估计受罚似然动态PET图像的均值和方差属性。这使我们能够预测重建活动估计的准确性，并从理论上比较重建算法。我们结合了bin模式方法，其中数据被建模为每个时空bin处独立的Poisson随机变量的集合，以及成像方程中的时空可分离性和惩罚，以得出可快速计算的分析均值和方差近似值。我们使用这些近似值来表明我们的动态PET图像重建算法比多帧静态PET重建具有更好的偏差/方差属性。我们还研究了惩罚似然动态PET图像的空间和时间分辨率特性，并表明，通过应用时空变化的平滑度，可以实现随时间变化的近似均匀的空间分辨率。每个体素的平滑度取决于动态Fisher信息矩阵的对角线条目。我们还表明，通过在变换的时域中执行重构，我们还可以使空间分辨率不仅在空间上均匀，而且在时间上近似恒定。为了利用列表模式数据的全部时空内容，我们证明了全局收敛的全四维增量梯度动态PET图像重建算法的收敛性，并通过从中重建模拟的四维PET数据证明了其可行性。小动物扫描仪。我们还开发了一种高效的算法来压缩大型动态PET数据集，该算法比标准压缩软件为60帧以上的数据集提供了额外的35--40％的压缩率。

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