腦電波儀(EEG)是常常用來進行腦功能研究的工具之一，因為它具有相當高的取樣頻率以及低廉的價位，本論文中，我們將開發出一套系統，把EEG獲得的頭皮電位資料，經過電腦處理，來估測目標腦波訊號源的位置，本研究所採用的方法，包括了簡單的頭模型(球模型)，正向模型的計算，以及最後逆向問題計算。其正向模型是假設腦電波訊號源的位置和方向是已知的，然後推導出頭皮的電位。逆向問題則是由已知的頭皮電極點電位資料求出腦電波訊號源的位置及方向；最後以臨床實驗:左右手分別出力握拳，來檢驗我們系統所計算的位置是否正確。實驗結果顯示，我們所開發系統的正確率可達56%，已具有初步的實用性。

Electroencephalogram (EEG) is one of the tools widely used in functional brain studies due to its high sampling rate (temporal resolution) and low cost. In this thesis, our team proposes a system, which uses the scalp potential data recorded by EEG to predict the location of the target brain source through the process of computer. The measurement that we use in this experiment includes the simple head model, the calculation of the forward model and the resolution to the inverse problem. The forward model is based on the hypothesis that both the brain source location and the orientation are known, which can be used to infer and predict the scalp potential. As for the inverse problem, the location and the orientation of brain source can be measured from the known scalp electrode data. Through the clinical trial, we may examine the system to see whether the location is shown in the motor area of brain by using two hands to hold firmly. The result indicates that the accuracy rate of this system can be up to 56%, which has a preliminary practicality.

摘要 i
Abstract ii
誌 謝 iii
目錄 iv
表目錄 vi
圖目錄 vii
一 緒論 1
1.1研究背景 1
1.2大腦的構造 4
1.3大腦的功能性 5
1.4 論文結構 5
1.5 研究範圍 7
二 正向模型 9
2.1 頭模型 9
2.1.1 國際10-20制系統定位 9
2.1.2 球體模型 11
2.2 單層殼體模型 11
2.3 多層殼體模型 15
2.4 sun方法 17
2.5 獲得矩陣 20
三 逆向問題 22
3.1 資料模式 26
3.2 過濾方法 28
3.3 最大對比雷達掃描 31
3.4最小平方估計法 36
四 實驗 39
4.1實驗設計 39
4.2硬體系統 40
4.3軟體系統 43
4.4實驗結果 46
五 問題與討論 49
附錄一 50
附錄二 52
附錄三 54
參考文獻 104

[1] Mingui Sun, “An efficient algorithm for computing multishell spherical volume conductor models in eeg dipole source localization,” IEEE Transactions on Biomedical, vol. 44, no. 12, pp. 1243-1252, Dec. 1997.
[2] 鄭志瑜， “Neuromagnetic source estimation and coherence mapping of brain activities,” 碩士論文，新竹，國立交通大學，2005。
[3] Christoph M. Michel, Micah M. Murray, Goran Lantz, Sara Gonzalez, Laurent Spinelli, Rolando Grave de Peralt, “EEG source imaging,” Clinical Neurophysiology, vol. 115, pp. 2195–2222, 2004.
[4] 楊仲凱， “ Eeg source estimation using overlapping-sphere forward model and hierarchical-search beamforming,” 碩士論文，新竹，國立交通大學 ，2005。
[5] 劉明機，《應用腦波控制於電腦游標》，碩士論文，台南，國立台南大學，2006。
[6] P. Berg and M. Scherg, “A fast method for forward computation of multiple-shell spherical head models,” Electroencephalography and Clinical Neurophysiology, vol. 90, pp. 58-64, 1994.
[7] B. Neil Cuffin, “A method for localizing eeg sources in realistic head models,” IEEE Transactions on Biomedical Engineering, vol. 42, no. 1, pp. 68-71, Jan. 1995.
[8] 林清山(1992)，心理與教育統計學。台北市:東華。
[9] Lay, David C., Linear algebra and its applications. 3rd edition, Addison-Wesley, 2002.
[10] Jerrold E. Marsden, Elementary classical analysis. 2nd edition, W.H. Freeman, 1993.
[11] Yong-Sheng Chen, “Maximum contrast beamformer for electromagnetic mapping of brain activity,” IEEE Transactions on Biomedical, vol. 53, pp. 1765-1774, Sep. 2006.
[12] Stephen H. Friedberg, Linear algebra. 2nd edition, Prentice-Hall, 1992.
[13] William H. Press, Numerical recipes in c. 2nd edition, New York: Cambridge University Press, 1992.
[14] 關尚勇，林吉和(2002)，破解腦電波。台北市:藝軒。
[15] Yehuda Salu, Leonardo G. Cohen, Douglas Rose, Susumu Sato, Conrad Kufta, Mark Hallett, “An improved method for localizing electric brain dipoles,” IEEE Transactions on Biomedical Engineering, vol. 37, no. 7, pp. 699-705, Jul. 1990.
[16] S. L. Salas, Calculus. 6th edition, New York: John Wiley & Sons , 1990.