A fast fully 4-d incremental gradient reconstruction algorithm for list mode PET data
A fast fully 4-d incremental gradient reconstruction algorithm for list mode PET data
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DOI：
10.1109/tmi.2006.884208
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发表时间：
2007-01-01
影响因子：
10.6
通讯作者：
Leahy, Richard M.
中科院分区：
文献类型：
--
作者：
Li, Quanzheng;Asma, Evren;Leahy, Richard M.
我们描述了一个快速和全局收敛的全四维增量梯度（4DIG）算法来估计连续时间示踪剂密度从列表模式正电子发射断层扫描（PET）数据。正电子-电子湮灭产生的511 keV光子对的检测被建模为一个非齐次泊松过程，其速率函数使用三次B样条参数化。通过最小化由到达时间的负对数似然、空间和时间粗糙度惩罚以及负性惩罚之和形成的成本函数来估计速率函数。首先，我们推导出一个可计算的最佳时间基函数系数的范数界。在此基础上，构造并证明了一个增量梯度算法的收敛性.全4-D模拟表明，相对于预处理共轭梯度的4DIG算法的收敛行为快得多。通过对真实的数据的四维重建，验证了该方法的有效性。
We describe a fast and globally convergent fully four-dimensional incremental gradient (4DIG) algorithm to estimate the continuous-time tracer density from list mode positron emission tomography (PET) data. Detection of 511-keV photon pairs produced by positron-electron annihilation is modeled as an inhomogeneous Poisson process whose rate function is parameterized using cubic B-splines. The rate functions are estimated by minimizing the cost function formed by the sum of the negative log-likelihood of arrival times, spatial and temporal roughness penalties, and a negativity penalty. We first derive a computable bound for the norm of the optimal temporal basis function coefficients. Based on this bound we then construct and prove convergence of an incremental gradient algorithm. Fully 4-D simulations demonstrate the substantially faster convergence behavior of the 4DIG algorithm relative to preconditioned conjugate gradient. Four-dimensional reconstructions of real data are also included to illustrate the performance of this method.