面回訊頻譜影像是一項創新而且快速的磁振頻譜影像技術。為了讓頻譜影像在LCModel上對代謝物做定量分析，必須要有一套自動化的頻譜影像重建系統，而影像重建是為了要得到乾淨的頻譜，即頻譜有良好的信雜比。最近，愈來愈多研究利用圖形處理器來加速影像重建，而統一計算架構是以C語言為基礎來開發的，使得程式設計者可以容易地去撰寫平行運算處理的程式。

面回訊頻譜影像資料包括水抑制和非水抑制掃描，每種掃描都包含ODD跟EVEN資料，而這兩組資料需要分開執行影像重建，而重建的步驟大致上分為K空間濾波、時域濾波、三維快速傅立葉轉換、相位校正和合併ODD跟EVEN資料。我們利用三種程式語言，包括MATLAB、C++、還有平行運算處理來實作面回訊頻譜影像重建，而平行運算處理是利用NVIDIA所提出的統一計算架構。

在我們的研究中，所撰寫的三種程式語言其執行結果，即平均的水抑制和非水抑制面回訊頻譜影像差異極小。在我們的資料量下，平行運算處理的執行時間比MATLAB和C++來得快，尤其是在快速傅立葉轉換的步驟。因此，我們會針對快速傅立葉轉換進行討論，模擬並比較一維至三維快速傅立葉轉換的效能。

根據我們模擬的一維至三維快速傅立葉轉換效能比較，和不同資料量下單一線圈面回訊頻譜影像重建時間比較，顯示利用圖形處理器來做平行運算處理的加速效能與資料量的多寡有關。當資料量約大於65536的時候，如同我們的實驗設計，圖形處理器加速的效能才會明顯優於中央處理器。

Proton echo planar spectroscopic imaging(PEPSI) is a novel and rapid technique of magnetic resonance spectroscopic imaging(MRSI). To analyze the metabolite in PEPSI by using LCModel, an automatic reconstruction system is necessary. Recently, many researches use graphic processing unit(GPU) to accelerate imaging reconstruction, and Compute Unified Device Architecture(CUDA) is developed by C language, so the programmers can write the program in parallel computing easily.

PEPSI data acquisition includes non water suppression and water suppression scans, each scan contains odd and even echoes, these two data are reconstructed separately. The image reconstruction contains k-space filter, time-domain filter, three-dimension fast Fourier transform(FFT), phase correction and combine odd and even data. We use MATLAB, C++ and parallel computing to implement PEPSI reconstruction, and parallel computing applied CUDA which proposed by NVIDIA.

In our study, the averaged non water suppression spectroscopic imaging executed by three different programming language are almost the same. In our data scale, the execution time of parallel computing is faster than MATLAB and C++, especially in the FFT step. Therefore, we simulated and compared the performance of one- to three-dimension FFT.

Our result shows that accelerating performance of GPU depends on the number of data points according to the performance of FFT and the execution time of single coil PEPSI reconstruction. While the amount of data points is larger than 65536, as demonstrated in our study, parallel computing contribute in terms of computational acceleration.

致謝i
摘要ii
Abstract iii
1 緒論1
1.1 前言. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 文獻回顧. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 大綱. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 工具與方法8
2.1 面回訊頻譜影像資料擷取. . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 面回訊頻譜影像重建流程. . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 K空間濾波. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.2 時域濾波. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.3 快速傅立葉轉換. . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.4 相位校正. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.5 合併資料. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 統一計算架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.1 圖形處理器. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.2 統一計算架構簡介. . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.3 統一計算架構編譯器. . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.4 計算能力版本. . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3 實驗環境與結果29
3.1 實驗環境. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 實驗結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4 討論與結論35
4.1 討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
參考文獻43

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