一种用于列表模式PET数据的快速全4D增量梯度重建算法。

A fast fully 4-D incremental gradient reconstruction algorithm for list mode PET data.

作者信息

Li Quanzheng, Asma Evren, Ahn Sangtae, Leahy Richard M

机构信息

Signal and Image Processing Institute, University of Southern California, Los Angeles, CA 90089, USA.

出版信息

IEEE Trans Med Imaging. 2007 Jan;26(1):58-67. doi: 10.1109/TMI.2006.884208.

DOI:10.1109/TMI.2006.884208

PMID:17243584

Abstract

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.

摘要

我们描述了一种快速且全局收敛的全四维增量梯度（4DIG）算法，用于从列表模式正电子发射断层扫描（PET）数据中估计连续时间示踪剂密度。将正电子 - 电子湮灭产生的511 keV光子对的检测建模为非齐次泊松过程，其速率函数使用三次B样条进行参数化。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。我们首先推导了最优时间基函数系数范数的可计算界。基于此界，我们构建并证明了一种增量梯度算法的收敛性。全四维模拟表明，4DIG算法相对于预处理共轭梯度算法具有显著更快的收敛行为。还包括真实数据的四维重建，以说明该方法的性能。