利用SVD方法估計Tikhonov正則化參數

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黃時霖(Shi-Lin Huang) 查詢紙本館藏

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生物物理研究所

論文名稱

利用SVD方法估計Tikhonov正則化參數
(Estimation of Tikhonov Regularization Parameter by SVD)

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摘要(中)

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。

摘要(英)

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.

關鍵字(中)

★ 深度權重
★ SIMN
★ 奇異值分解
★ 腦磁圖儀

關鍵字(英)

★ Depth weighting
★ SIMN
★ SVD
★ MEG

論文目次

摘要 I
Abstract II
Introduction 1
Chapter 1 Physics of EEG and MEG 4
1.1 Quasistatic approximation of Maxwell’s equation 4
1.2 Integral formulas for electromagnetic field 5
1.3 Current dipole 7
Chapter 2 Source Iteration of Minimum Norm 9
2.1 Source iteration of minimum norm (SIMN) — Noise free cases 9
2.2 Source iteration of minimum norm (SIMN) — Noisy cases 11
2.3 The algorithm of SIMN 13
Chapter 3 Estimation of Tikhonov Regularization Parameter by SVD 14
3.1 Depth weighting 14
3.2 Singular value decomposition (SVD) 15
3.3 Estimation of noise power by SVD 15
3.4 Estimation of Tikhonov regularization parameter 17
Chapter 4 Numerical simulations 21
4.1 3D head model — Montreal Phantom model 21
4.2 2D cortex model 24
4.3 Results and discussions 27
Summary 27
References 28

參考文獻

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.

指導教授

王敏生(M. S. Wang)

審核日期

2010-7-21

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