Department of Radiology, University of Southern California, Los Angeles, CA 90033, USA.
Phys Med Biol. 2014 Feb 21;59(4):925-49. doi: 10.1088/0031-9155/59/4/925. Epub 2014 Feb 7.
Time-of-flight (TOF) information improves the signal-to-noise ratio in positron emission tomography (PET). The computation cost in processing TOF-PET sinograms is substantially higher than for nonTOF data because the data in each line of response is divided among multiple TOF bins. This additional cost has motivated research into methods for rebinning TOF data into lower dimensional representations that exploit redundancies inherent in TOF data. We have previously developed approximate Fourier methods that rebin TOF data into either three-dimensional (3D) nonTOF or 2D nonTOF formats. We refer to these methods respectively as FORET-3D and FORET-2D. Here we describe maximum a posteriori (MAP) estimators for use with FORET rebinned data. We first derive approximate expressions for the variance of the rebinned data. We then use these results to rescale the data so that the variance and mean are approximately equal allowing us to use the Poisson likelihood model for MAP reconstruction. MAP reconstruction from these rebinned data uses a system matrix in which the detector response model accounts for the effects of rebinning. Using these methods we compare the performance of FORET-2D and 3D with TOF and nonTOF reconstructions using phantom and clinical data. Our phantom results show a small loss in contrast recovery at matched noise levels using FORET compared to reconstruction from the original TOF data. Clinical examples show FORET images that are qualitatively similar to those obtained from the original TOF-PET data but with a small increase in variance at matched resolution. Reconstruction time is reduced by a factor of 5 and 30 using FORET3D+MAP and FORET2D+MAP respectively compared to 3D TOF MAP, which makes these methods attractive for clinical applications.
飞行时间（TOF）信息可提高正电子发射断层扫描（PET）中的信噪比。与非 TOF 数据相比，处理 TOF-PET 正弦图的计算成本要高得多，因为每条响应线的数据都分布在多个 TOF -bin 中。这种额外的成本促使研究人员开发了将 TOF 数据重新-bin 为利用 TOF 数据固有的冗余的低维表示形式的方法。我们之前已经开发了将 TOF 数据重新-bin 为三维（3D）非 TOF 或二维（2D）非 TOF 格式的近似傅里叶方法。我们分别将这些方法称为 FORET-3D 和 FORET-2D。在这里，我们描述了用于 FORET 重新-bin 数据的最大后验（MAP）估计器。我们首先推导出重新-bin 数据的方差的近似表达式。然后，我们使用这些结果对数据进行缩放，使得方差和均值大致相等，从而允许我们使用泊松似然模型进行 MAP 重建。使用这些重新-bin 数据的 MAP 重建使用了一个系统矩阵，其中探测器响应模型考虑了重新-bin 的影响。使用这些方法，我们使用 Phantom 和临床数据比较了 FORET-2D 和 3D 与 TOF 和非 TOF 重建的性能。我们的 Phantom 结果表明，与使用原始 TOF 数据重建相比，使用 FORET 重建时，在匹配噪声水平下对比度恢复略有损失。临床实例显示，FORET 图像在定性上与从原始 TOF-PET 数据获得的图像相似，但在匹配分辨率时方差略有增加。与 3D TOF MAP 相比，FORET3D+MAP 和 FORET2D+MAP 分别将重建时间减少了 5 倍和 30 倍，这使得这些方法在临床应用中具有吸引力。
