Time-of-flight (TOF) positron emission tomography (PET) scanners can provide significant benefits by improving the noise properties of reconstructed images. In order to achieve this, the timing response of the scanner needs to be modelled as part of the reconstruction process. This is currently achieved using Gaussian TOF kernels. However, the timing measurements do not necessarily follow a Gaussian distribution. In ultra-fast timing resolutions, the depth of interaction of the γ-photon and the photon travel spread (PTS) in the crystal volume become increasingly significant factors for the timing performance. The PTS of a single photon can be approximated better by a truncated exponential distribution. Therefore, we computed the corresponding TOF kernel as a modified Laplace distribution for long crystals. The obtained (CTR) kernels could be more appropriate to model the joint probability of the two in-coincidenceγ-photons. In this paper, we investigate the impact of using a CTR kernel vs. Gaussian kernels in TOF reconstruction using Monte Carlo generated data. The geometry and physics of a PET scanner with two timing configurations, (a) idealised timing resolution, in which only the PTS contributed in the CTR, and (b) with a range of ultra-fast timings, were simulated. In order to assess the role of the crystal thickness, different crystal lengths were considered. The evaluation took place in terms of Kullback–Leibler (K-L) distance between the proposed model and the simulated timing response, contrast recovery (CRC) and spatial resolution. The reconstructions were performed using STIR image reconstruction toolbox. Results for the idealised scanner showed that the CTR kernel was in excellent agreement with the simulated time differences. In terms of K-L distance outperformed the a fitted normal distribution for all tested crystal sizes. In the case of the ultra-fast configurations, a convolution kernel between the CTR and a Gaussian showed the best agreement with the simulated data below 40 ps timing resolution. In terms of CRC, the CTR kernel demonstrated improvements, with values that ranged up to 3.8% better CRC for the thickest crystal. In terms of spatial resolution, evaluated at the 60th iteration, the use of CTR kernel showed a modest improvement of the peek-to-valley ratios up to 1% for the 10-mm crystal, while for larger crystals, a clear trend was not observed. In addition, we showed that edge artefacts can appear in the reconstructed images when the timing kernel used for the reconstruction is not carefully optimised. Further iterations, can help improve the edge artefacts.

中文翻译：

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使用非高斯飞行时间内核对超快速 PET 扫描仪的蒙特卡罗模拟数据进行图像重建。

飞行时间 (TOF) 正电子发射断层扫描 (PET) 扫描仪可以通过改善重建图像的噪声特性来提供显着的好处。为了实现这一点，扫描仪的时序响应需要作为重建过程的一部分进行建模。目前这是使用高斯 TOF 内核实现的。然而，时序测量不一定遵循高斯分布。在超快时序分辨率中，γ-光子的相互作用深度和晶体体积中的光子传播扩展（PTS）成为时序性能的越来越重要的因素。单个光子的 PTS 可以通过截断指数分布更好地近似。因此，我们将相应的 TOF 核计算为长晶体的修正拉普拉斯分布。获得的（CTR）内核可能更适合模拟两个重合γ-光子的联合概率。在本文中，我们使用 Monte Carlo 生成的数据研究了在 TOF 重建中使用 CTR 内核与高斯内核的影响。具有两种定时配置的 PET 扫描仪的几何形状和物理特性，(a) 理想化的定时分辨率，其中只有 PTS 对 CTR 有贡献，以及 (b) 具有一系列超快速定时，都进行了模拟。为了评估晶体厚度的作用，考虑了不同的晶体长度。评估是根据所提出模型与模拟时序响应、对比度恢复 (CRC) 和空间分辨率之间的 Kullback-Leibler (KL) 距离进行的。使用 STIR 图像重建工具箱进行重建。理想化扫描仪的结果表明，CTR 内核与模拟的时间差非常一致。就 KL 距离而言，所有测试晶体尺寸的拟合正态分布均优于拟合正态分布。在超快速配置的情况下，CTR 和高斯之间的卷积核与低于 40 ps 时序分辨率的模拟数据表现出最佳一致性。在 CRC 方面，CTR 内核表现出改进，对于最厚的晶体，CRC 值提高了 3.8%。在第 60 次迭代评估的空间分辨率方面，CTR 内核的使用显示出 10 毫米晶体的峰谷比适度改善高达 1%，而对于较大的晶体，明显的趋势不是观察到的。此外，我们表明，当用于重建的时序内核没有经过仔细优化时，重建图像中可能会出现边缘伪影。进一步的迭代，可以帮助改善边缘伪影。