Ahmed Abdella M, Kikuchi Yohei, Matsuyama Shigeo, Terakawa Atsuki, Takyu Sodai, Sugai Hiroyuki, Ishii Keizo
Department of Quantum Science and Energy Engineering, Tohoku University, Aramaki-Aza-Aoba 6-6-01-2, Aoba-ku, Sendai, Miyagi, Japan,
Radiol Phys Technol. 2015 Jan;8(1):88-96. doi: 10.1007/s12194-014-0293-y. Epub 2014 Sep 26.
A system matrix (SM) is the basic component of iterative image reconstruction algorithms. Calculation of the SM needs a considerable amount of time due to an enormous number of lines of response (LORs) being modeled. In this study, we developed a technique based on a piece-wise calculation method in which symmetry and further division of the voxels are applied. The detector response function for all detectable pairs of photons along certain LORs originating from each voxel is calculated analytically. The total number of LORs in 300 × 300 × 120 voxels (with 2 × 2 × 2 mm(3)) is ~44 billion, and the SM was calculated by the use of three different computers independently; the calculation time was 5 h. The SM took 5 days when calculated by the use of the conventional method (where symmetry and the piece-wise method are not used). The sensitivity correction factor was stored; it had a size of 42 MB in a four-byte computer memory.
系统矩阵（SM）是迭代图像重建算法的基本组成部分。由于要对大量的响应线（LOR）进行建模，SM的计算需要相当长的时间。在本研究中，我们开发了一种基于逐段计算方法的技术，该方法应用了体素的对称性和进一步划分。对于源自每个体素的沿特定LOR的所有可检测光子对的探测器响应函数进行解析计算。在300×300×120体素（2×2×2mm³）中的LOR总数约为440亿条，并且使用三台不同的计算机独立计算SM；计算时间为5小时。使用传统方法（未使用对称性和逐段方法）计算时，SM需要5天时间。存储了灵敏度校正因子；在四字节计算机内存中其大小为42MB。
