簡易檢索 / 詳目顯示
| 研究生： |
黃時霖 Shi-Lin Huang |
|---|---|
| 論文名稱： |
利用SVD方法估計Tikhonov正則化參數 Estimation of Tikhonov Regularization Parameter by SVD |
| 指導教授： |
王敏生
M. S. Wang |
| 口試委員: | |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 生物物理研究所 Graduate Institute of Biophysics |
| 畢業學年度： | 98 |
| 語文別： | 英文 |
| 論文頁數： | 34 |
| 中文關鍵詞： | 深度權重 、SIMN 、奇異值分解 、腦磁圖儀 |
| 外文關鍵詞： | Depth weighting, SIMN, SVD, MEG |
| 相關次數： | 點閱：19 下載：0 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
在此篇論文中，我們提出了一種對Tikhonov正則化(regularization)參數估計的方法，此方法是先對lead-field做奇異值分解(singular value decomposition, SVD)，得到一組訊號空間的基向量，再將訊號投影到和小奇異值對應的基向量，得到的投影分量主要來自雜訊的貢獻。藉此我們可以估計雜訊功率(power)，並估計Tikhonov正則化參數值。數值模擬顯示，在以最小範數的源分佈迭代法 (source iteration of minimum norm, SIMN)定位二維和三維頭模型的腦磁波源時，利用這個方法估計腦磁波的Tikhonov正則化參數，得到的源定位結果和lead-field的深度權重(depth weighting)無關。
In this thesis, a method is proposed to estimate the Tikhonov regularization parameter. The signal is projected to the basis vectors of signal space obtained from singular value decomposition of lead-field matrix. The components along the basis vectors corresponding to small singular values are primarily from noises. They provide an estimate of noise power which is used to estimate Tikhonov regularization parameter. Numerical simulations show that, applying this method to the noise regularization of MEG data from both 2D and 3D head model, source localization results obtained by source iteration of minimum norm (SIMN) are little dependent on depth weighting of the lead-field matrix.
Aine, C.J., 1995. A conceptual overview and critique of functional neuroimaging techniques in humans—I: MRI/fMRI and PET. Crit. Rev. Neurobiol. 9, 229–309.
Fuchs, M., Wagner, M., Kohler, T. and Wischmann, H.A., 1999. Linear and nonlinear current density reconstructions. J. Clin. Neurophysiol. 16, 267–295.
Geselowitz, D.B., 1967. On bioelectric potentials in an inhomogeneous volume conductor. Biophys. J. 7, 1–11.
Golub, G. H. and Reinsch, C., 1970. Singular value decomposition and least squares solutions. Numer. Math., 14, 403-420
Grave de Peralta-Menendez, R., Hauk, O., Gonzalez-Andino, S., Vogt, H., and Michel, C., 1997. Linear inverse solutions with optimal resolution kernels applied to electromagnetic tomography. NeuroImage 5, 454-467.
Grave de Peralta-Menendez, R., Gonzalez-Andino, S., 1998. A critical analysis of linear inverse solutions to the neuroelectromagnetic inverse problem. IEEE Trans. Biomed. Eng. 45, 440–448.
Hämäläinen, M.S. and Sarvas, J.,1989. Realistic conductor geometry model of the human head for interpretation of neuromagnetic data. IEEE Trans. Biomed. Eng. 36, 165-171.
Hansen, P.C. and O’Leary, D.P., 1993. The use of the L-curve in the regularization of discrete ill-posed problems. SIAM J. SCI. Comput. 14, 1487-1503.
Liang, W.-K., Wang, M.S., 2009. Source reconstruction of brain electromagnetic fields—Source iteration of minimum norm (SIMN). NeuroImage, 47, 1301-1311
Liang, W.-K., Wang, M.S., 2010. Effect of depth-weighting on MEG/EEG Noise Regularization. to be published.
Lin, F.-H., Belliveau, J.W., Dale, A.M. and Hämäläinen, M.S., 2006. Distributed current estimates using cortical orientation constraints. Hum. Brain. Mapp. 27, 1-31
Mosher, J.C., Leahy, R.M. and Lewis P.S., 1999. EEG and MEG: Forward solutions for inverse methods. IEEE Trans. Biomed. Eng. 46, 245–259.
Mosher, J.C., Baillet, S., and Leahy, R.M., 2003. Equivalence of linear approaches in bioelectromagnetic inverse solutions. IEEE Workshop on Statistical Signal Processing, St. Loius, Missouri, Sep 28 – Oct 01, 294-297
Phillips, C., Rugg, M.D., Friston, K.J., 2002. Systematic Regularization of Linear Inverse Solutions of the EEG Source Localization Problem, NeuroImage, 17, 287-301.
