圖形處理器(Graphic Processing Unit, GPU)是一種專門處理影像運算工作的微處理器，近年來也被廣泛用於科學數值運算中，可以分擔中央處理器(Central Processing unit, CPU)的數值運算工作量，提供了另一種高速運算的選擇。
在電腦斷層掃瞄(Computed Tomography, CT)中，需計算X-ray射線通過物體的路徑上與不同體素(voxel)的作用長度，評估射線的衰減狀況。而Siddon提出的射線追蹤演算法，除了解決CT的問題外，也可藉由此交會長模擬光子偵收機率值，計算正向與反向的投影資料，應用在正子斷層掃描(Positron emission tomography, PET)與單光子發射斷層掃描(Single Photon Emission Computed Tomography, SPECT)的影像重建法之中。
本研究主要是利用GPU並搭配統一計算架構(Compute Unified Device Architecture, CUDA)這項整合技術來加速射線追蹤演算法，應用在模擬偵測機率值，並計算正向與反向的投影資料。會比較CPU與GPU的多執行緒程式，探討計算此類問題的效能差異。實驗部分包含PET、SPECT與CT三種類型的醫學成像原理。
本研究的實驗結果，在投影資料計算的正確性及效率上來看，GPU執行結果是正確的，與CPU四個執行緒搭配OpenMP做平行處理相比，GPU效率約提升1.2 ~ 1.8倍。GPU的效率在工作量平均且資料彼此獨立的狀況下，有較佳的表現。

1.R. L. Siddon. “ Fast calculation of the exact radiological path for a three-dimensional CT array”. Medical Physics,12-2, p.252-255 ,1985.
2.Turkington TG. Introduction to PET instrumentation. Journal of Nuclear Medicine Technology 29: 4-11, 2001.
3.Steven R. Meikle, Mark F. Smith, Anatoly B. Rosenfeld, "A Prototype Coded Aperture Detector for Small Animal SPECT" , IEEE Transctions on Nuclear Sciencs, Vol. 49, No. 5, October 2002.
4.Ollinger J. and Fessler J. Positron Emission Tomography. IEEE Signal Processing Magazine 14(1): 43–55, 1997.
5.David R. Butenhoh, “Programming with POSIX Threads”, Addision-Wesley, 1997.
6.NVIDIA CUDA Compute Unified Device Architecture Programming
Guide, NVIDIA Corporation, 2.1 edition 2008.
7.M. de Greef, J. Crezee, J. C. van Eijk, R. Pool, and A. Bel, “Accelerated Ray Tracing for Radiotherapy Dose Calculations on a GPU.” Medical Physics, Vol 36, Issue 9. 2009.
8.A. Grama, A. Gupta, G. Karypis, V. Kumar, “Introduction to Parallel Computing” 2nd Edition, Addison Wesley, 2003.
9. OpenMP, “http://openmp.org/wp/”
10.國研院國網中心, “http://www.nchc.org.tw/tw/”
11.陳乙菩, 平行處理應用簡介,“http://www.cc.ntu.edu.tw/chinese/
epaper/0012/20100320_1208.htm”
12.OpenMP與MPI的差別,"http://kewang.pixnet.net/blog/post/2959
194”
13.Michael J. Qinn, “Parallel programming in C with MPI and OpenMP”, 2004 McGraw Hill
14.Siemens, “http://www.medical.siemens.com”
15.Chien-Min Kao, Yun Dong, Qingguo Xie and Chin-Tu Chen, “Accurate Image Reconstruction with Computed System Response Matrix for a High-Sensitivity Dual-Head PET Scanner”, IEEE Transactions on Nuclear Science, 2009
16.D.Paix “pinhole imaging of Gamma Rays” Phys. Med Biol., Vol. 12, No. 4, 1967.
17.Scott D. Metzler, “Feasibility of whole-body functional mouse imaging using helical pinhole SPECT”, Molecular Imaging and Biology , Vol. 12, No. 1 February 2010.
18.PW Henson, RA Fox , “The electron density of bone for inhomogeneity correction in radiotherapy planning using CT numbers” , Physics in Medicine and Biology, 1984.