基于部分系统矩阵的快速三维正电子对寿命估计的共轭贝叶斯框架
A Conjugate Bayesian Framework for Fast 3D Positronium Lifetime Estimation with a Partial System Matrix
AI总结：
本文提出一种共轭贝叶斯框架，通过限制系统矩阵到观测探测器时间通道，实现快速三维正电子对寿命估计，结合后验事件到体素加权和共轭Gamma-指数更新，提升计算效率和稳定性。
摘要：
背景：正电子对寿命成像通过利用正电子发射与湮灭之间的时间间隔作为额外对比机制扩展了常规正电子发射计算机断层扫描。在完全三维设置中，体素级寿命估计计算困难，因为可行的探测器时间通道数量迅速增加，而实际观察到的仅是小部分。我们开发了一种可扩展的统计框架，基于时间飞行意识的部分系统矩阵，限制到观测探测器时间通道，结合后验事件到体素加权和共轭Gamma-指数更新，实现闭形式体素级有效率估计。结果：限制前向模型到观测探测器时间通道减少了内存和计算需求，同时保留了保留的三重巧合检测的泊松数据模型。在模拟数据中，4056个体素的分析贝叶斯估计器需要2.76秒，而10次L-BFGS-B迭代在同一CPU上需要74.46秒，准确恢复有效率图。在使用J-PET原型扫描仪和NEMA图像质量幻影获取的三重巧合数据集中，约3.64×10^5个保留事件从约234 375个体素估计出有效率图，约3秒内完成。结论：限制系统矩阵到观测探测器时间通道使稀疏三重巧合数据的完全三维正电子对寿命估计计算变得可行。所提出的后验加权共轭更新为大规模三维正电子对寿命成像提供了快速且稳定的单组件替代估计器，用于体素级有效寿命估计。
英文摘要：
Background: Positronium lifetime imaging extends conventional positron emission tomography by using the time interval between positron emission and annihilation as an additional contrast mechanism. Voxel-wise lifetime estimation in fully three-dimensional settings is computationally difficult because the number of feasible detector-time channels grows rapidly, whereas only a small subset is observed in practice. We developed a scalable statistical framework for three-dimensional positronium lifetime estimation based on a time-of-flight-aware partial system matrix restricted to observed detector-time channels, combined with posterior event-to-voxel weighting and a conjugate Gamma--Exponential update for closed-form voxel-wise effective-rate estimation. Results: Restricting the forward model to observed detector-time channels reduced memory and computational requirements while preserving the Poisson data model for retained detected triple coincidences. In simulated data with 4056 voxels, the analytic Bayesian estimator required 2.76 s versus 74.46 s for 10 L-BFGS-B iterations on the same CPU while accurately recovering the effective-rate map. In a triple-coincidence dataset acquired with a J-PET prototype scanner and a NEMA image-quality phantom, a 234 375-voxel effective-rate map was estimated in approximately 3 s from about $3.64\times10^5$ retained events. Conclusions: Restricting the system matrix to observed detector-time channels makes fully three-dimensional positronium lifetime estimation computationally practical for sparse triple-coincidence data. The proposed posterior-weighted conjugate update provides a fast and stable single-component surrogate estimator of voxel-wise effective lifetime for large-scale three-dimensional positronium lifetime imaging.
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