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

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/43756

Title:	利用SVD方法估計Tikhonov正則化參數;Estimation of Tikhonov Regularization Parameter by SVD
Authors:	黃時霖;Shi-Lin Huang
Contributors:	生物物理研究所
Keywords:	深度權重;SIMN;奇異值分解;腦磁圖儀;Depth weighting;SIMN;SVD;MEG
Date:	2010-07-21
Issue Date:	2010-12-08 14:18:22 (UTC+8)
Publisher:	國立中央大學
Abstract:	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.
Appears in Collections:	[Graduate Institute of Biophysics] Electronic Thesis & Dissertation

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