Lougovski A, Hofheinz F, Maus J, Schramm G, Will E, van den Hoff J
PET Center, Institute of Radiopharmaceutical Cancer Research, Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, D-01328 Dresden, Germany.
Phys Med Biol. 2014 Feb 7;59(3):561-77. doi: 10.1088/0031-9155/59/3/561. Epub 2014 Jan 17.
The aim of this study is the evaluation of on-the-fly volume of intersection computation for system's geometry modelling in 3D PET image reconstruction. For this purpose we propose a simple geometrical model in which the cubic image voxels on the given Cartesian grid are approximated with spheres and the rectangular tubes of response (ToRs) are approximated with cylinders. The model was integrated into a fully 3D list-mode PET reconstruction for performance evaluation. In our model the volume of intersection between a voxel and the ToR is only a function of the impact parameter (the distance between voxel centre to ToR axis) but is independent of the relative orientation of voxel and ToR. This substantially reduces the computational complexity of the system matrix calculation. Based on phantom measurements it was determined that adjusting the diameters of the spherical voxel size and the ToR in such a way that the actual voxel and ToR volumes are conserved leads to the best compromise between high spatial resolution, low noise, and suppression of Gibbs artefacts in the reconstructed images. Phantom as well as clinical datasets from two different PET systems (Siemens ECAT HR(+) and Philips Ingenuity-TF PET/MR) were processed using the developed and the respective vendor-provided (line of intersection related) reconstruction algorithms. A comparison of the reconstructed images demonstrated very good performance of the new approach. The evaluation showed the respective vendor-provided reconstruction algorithms to possess 34-41% lower resolution compared to the developed one while exhibiting comparable noise levels. Contrary to explicit point spread function modelling our model has a simple straight-forward implementation and it should be easy to integrate into existing reconstruction software, making it competitive to other existing resolution recovery techniques.
本研究的目的是评估在三维正电子发射断层显像（PET）图像重建中用于系统几何建模的实时交集体积计算。为此，我们提出了一个简单的几何模型，其中给定笛卡尔网格上的立方图像体素用球体近似，响应矩形管（ToR）用圆柱体近似。该模型被集成到一个全三维列表模式PET重建中进行性能评估。在我们的模型中，体素与ToR之间的交集体积仅是碰撞参数（体素中心到ToR轴的距离）的函数，而与体素和ToR的相对方向无关。这大大降低了系统矩阵计算的计算复杂度。基于体模测量确定，以保持实际体素和ToR体积的方式调整球形体素大小和ToR的直径，可在重建图像的高空间分辨率、低噪声和抑制吉布斯伪影之间实现最佳折衷。使用开发的算法以及各供应商提供的（与相交线相关的）重建算法对来自两个不同PET系统（西门子ECAT HR(+)和飞利浦Ingenuity-TF PET/MR）的体模以及临床数据集进行了处理。对重建图像的比较表明新方法具有非常好的性能。评估显示，与开发的算法相比，各供应商提供的重建算法分辨率低34-41%，同时噪声水平相当。与显式点扩散函数建模不同，我们的模型具有简单直接的实现方式，并且应该易于集成到现有的重建软件中，使其与其他现有的分辨率恢复技术具有竞争力。
