Department of Medical Physics, Memorial Sloan Kettering Cancer Center, 1250 First Avenue, New York, NY, 10065, USA.
School of Mathematics, and Guangdong Provincial Key Lab of Computational Science, Sun Yat-sen University, No. 135, Xingang Xi Road, Guangzhou, 510275, P R China.
Med Phys. 2017 Aug;44(8):4083-4097. doi: 10.1002/mp.12292. Epub 2017 Jun 16.
Performance of the preconditioned alternating projection algorithm (PAPA) using relaxed ordered subsets (ROS) with a non-smooth penalty function was investigated in positron emission tomography (PET). A higher order total variation (HOTV) regularizer was applied and a method for unsupervised selection of penalty weights based on the measured data is introduced.
A ROS version of PAPA with HOTV penalty (ROS-HOTV-PAPA) for PET image reconstruction was developed and implemented. Two-dimensional PET data were simulated using two synthetic phantoms (geometric and brain) in geometry similar to GE D690/710 PET/CT with uniform attenuation, and realistic scatter (25%) and randoms (25%). Three count levels (high/medium/low) corresponding to mean information densities (ID¯s) of 125, 25, and 5 noise equivalent counts (NEC) per support voxel were reconstructed using ROS-HOTV-PAPA. The patients' brain and whole body PET data were acquired at similar ID¯s on GE D690 PET/CT with time-of-fight and were reconstructed using ROS-HOTV-PAPA and available clinical ordered-subset expectation-maximization (OSEM) algorithms. A power-law model of the penalty weights' dependence on ID¯ was semi-empirically derived. Its parameters were elucidated from the data and used for unsupervised selection of the penalty weights within a reduced search space. The resulting image quality was evaluated qualitatively, including reduction of staircase artifacts, image noise, spatial resolution and contrast, and quantitatively using root mean squared error (RMSE) as a global metric. The convergence rates were also investigated.
ROS-HOTV-PAPA converged rapidly, in comparison to non-ROS-HOTV-PAPA, with no evidence of limit cycle behavior. The reconstructed image quality was superior to optimally post-filtered OSEM reconstruction in terms of noise, spatial resolution, and contrast. Staircase artifacts were not observed. Images of the measured phantom reconstructed using ROS-HOTV-PAPA showed reductions in RMSE of 5%-44% as compared with optimized OSEM. The greatest improvement occurred in the lowest count images. Further, ROS-HOTV-PAPA reconstructions produced images with RMSE similar to images reconstructed using optimally post-filtered OSEM but at one-quarter the NEC.
Acceleration of HOTV-PAPA was achieved using ROS. This was accompanied by an improved RMSE metric and perceptual image quality that were both superior to that obtained with either clinical or optimized OSEM. This may allow up to a four-fold reduction of the radiation dose to the patients in a PET study, as compared with current clinical practice. The proposed unsupervised parameter selection method provided useful estimates of the penalty weights for the selected phantoms' and patients' PET studies. In sum, the outcomes of this research indicate that ROS-HOTV-PAPA is an appropriate candidate for clinical applications and warrants further research.
研究了使用非光滑惩罚函数的预条件交替投影算法（PAPA）在正电子发射断层扫描（PET）中的松弛有序子集（ROS）的性能。应用了高阶全变差（HOTV）正则化，并介绍了一种基于测量数据的无监督选择惩罚权重的方法。
开发并实现了用于 PET 图像重建的具有 HOTV 惩罚的 ROS-PAPA（ROS-HOTV-PAPA）。使用与 GE D690/710 PET/CT 相似的几何形状中的两个合成体模（几何和大脑）模拟二维 PET 数据，具有均匀衰减和真实散射（25%）和随机（25%）。使用 ROS-HOTV-PAPA 重建了与支持体素的平均信息密度（ID¯）为 125、25 和 5 个噪声等效计数（NEC）相对应的三个计数水平（高/中/低）。使用具有飞行时间的 GE D690 PET/CT 采集患者的大脑和全身 PET 数据，并使用 ROS-HOTV-PAPA 和可用的临床有序子集期望最大化（OSEM）算法进行重建。从数据中推导出惩罚权重与 ID¯依赖性的半经验幂律模型。从数据中阐明其参数，并在减少的搜索空间内用于无监督选择惩罚权重。使用均方根误差（RMSE）作为全局度量来定性评估图像质量，包括降低阶梯伪影、图像噪声、空间分辨率和对比度，并使用 RMSE 进行定量评估。还研究了收敛速度。
与非 ROS-HOTV-PAPA 相比，ROS-HOTV-PAPA 快速收敛，没有出现极限循环行为的迹象。与最佳后滤波 OSEM 重建相比，重建图像质量在噪声、空间分辨率和对比度方面均有所提高。未观察到阶梯伪影。使用 ROS-HOTV-PAPA 重建的测量体模图像显示，与优化的 OSEM 相比，RMSE 降低了 5%至 44%。在最低计数图像中，改善最大。此外，ROS-HOTV-PAPA 重建产生的图像的 RMSE 与使用最佳后滤波 OSEM 重建的图像相似，但 NEC 为四分之一。
使用 ROS 实现了 HOTV-PAPA 的加速。这伴随着 RMSE 度量和感知图像质量的提高，均优于临床或优化的 OSEM 获得的图像质量。与当前的临床实践相比，这可能使 PET 研究中的患者辐射剂量减少四分之一。所提出的无监督参数选择方法为所选体模和患者的 PET 研究提供了有用的惩罚权重估计。总的来说，这项研究的结果表明，ROS-HOTV-PAPA 是临床应用的合适候选者，值得进一步研究。
