Varnyú Dóra, Paczári Krisztián, Szirmay-Kalos László
Mediso Medical Imaging Systems, Laborc u. 3., Budapest, 1037, Hungary.
Department of Control Engineering and Information Technology, Budapest University of Technology and Economics, Műegyetem rkp. 3., Budapest, 1111, Hungary.
EJNMMI Phys. 2024 Dec 26;11(1):106. doi: 10.1186/s40658-024-00710-7.
In the back projection step of the 3D PET reconstruction, all Lines of Responses (LORs) that go through a given voxel need to be identified and included in an integral. The standard Monte Carlo solution to this task samples stochastically the surfaces of the detector crystals and the volume of the voxel to search for valid LORs. To get a low noise Monte Carlo estimate, the number of samples needs to be very high, making the computational cost of the projection significant. In this paper, a novel deterministic projection algorithm called trapezoidal back projection (TBP) is proposed that replaces the extensive Monte Carlo sampling. Its goal is to determine all LORs that contribute to a given voxel together with their exact contribution weights. This is achieved by trapezoidal rasterization and a pre-computed look-up table.
The precision and speed of the proposed TBP algorithm were compared to that of the Monte Carlo back projection of 1000, 10,000 and 100,000 samples. Measurements were run on a National Electrical Manufacturers Association (NEMA) NU 4-2008 image quality phantom as well as on a mouse acquisition. Results show that the TBP algorithm achieves the same low noise level (2.5 Uniformity %STD) as the Monte Carlo method with the highest sample number, but 13 times faster-the highest-precision Monte Carlo back projection takes 31.3 s, while TBP takes only 2.3 s on the NEMA NU 4-2008 image quality phantom of voxels.
The proposed deterministic TBP algorithm achieves a low noise level in a short runtime, thus it can be a promising solution for the back projection of the 3D PET reconstruction. Its performance advantage could be used to reduce either the reconstruction time, the data acquisition time, or the noise level of the image.
在三维正电子发射断层扫描（PET）重建的反投影步骤中，需要识别并将穿过给定体素的所有响应线（LOR）纳入积分。解决此任务的标准蒙特卡罗方法是随机对探测器晶体表面和体素体积进行采样，以搜索有效的LOR。为获得低噪声的蒙特卡罗估计，采样数量需非常高，这使得投影的计算成本很高。本文提出一种名为梯形反投影（TBP）的新型确定性投影算法，以取代大量的蒙特卡罗采样。其目标是确定对给定体素有贡献的所有LOR及其精确的贡献权重。这通过梯形光栅化和预先计算的查找表来实现。
将所提出的TBP算法的精度和速度与1000、10000和100000个样本的蒙特卡罗反投影的精度和速度进行了比较。在国家电气制造商协会（NEMA）NU 4 - 2008图像质量体模以及小鼠采集上进行了测量。结果表明，TBP算法实现了与最高样本数的蒙特卡罗方法相同的低噪声水平（2.5%标准差均匀性），但速度快13倍——在NEMA NU 4 - 2008图像质量体模上，最高精度的蒙特卡罗反投影需要31.3秒，而TBP仅需2.3秒。
所提出的确定性TBP算法在短运行时间内实现了低噪声水平，因此它可能是三维PET重建反投影的一个有前景的解决方案。其性能优势可用于减少重建时间、数据采集时间或图像的噪声水平。
