訊號和噪訊的權重範數和-估計Tikhonov正則化參數; Estimation of Tikhonov Regularization Parameter by Weighted Sum of Norms of MNE and Noises

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/48260

Title:	訊號和噪訊的權重範數和-估計Tikhonov正則化參數;Estimation of Tikhonov Regularization Parameter by Weighted Sum of Norms of MNE and Noises
Authors:	盧柏宏;Bo-hong Lu
Contributors:	物理研究所
Keywords:	訊號和噪訊的權重範數和;Tikhonov正則化參數;最小範數源迭代法;SIMN;Tikhonov regularization parameter;Weighted Sum of Norms of MNE and Noises
Date:	2011-07-29
Issue Date:	2012-01-05 14:42:48 (UTC+8)
Abstract:	本論文探討用「最小範數源迭代法」(SIMN)做腦磁圖(MEG)的源定位時，其中的Tikhonov正則化參數(Tikhonov regularization parameter)對定位結果的影響，並且提出一個估計Tikhonov正則化參數(Tikhonov regularization parameter)的方法。數值模擬顯示，最佳定位的Tikhonov正則化參數值和訊號-噪訊比(SNR)有關。因此我們提出了一種方法將訊號與噪訊的最小範數估計解(minimum norm estimation, MNE)分別取範數的平方，再取權重和，此權重和對參數的變化會有一個全域極小值。在適當的權重下，權重和極小的參數的定位結果與其他各種方法估算參數的定位結果比較，我們的方法在SNR越小的情況下，定位成功率相對地越好。 In this thesis, the dependence of the MEG source localization accuracies of the inverse algorithm Source Iteration of Minimum Norm(SIMN) on Tikhonov regularization parameter λ is studied and a method is proposed to estimate the Tikhonov regularization parameter λ. Numerical simulations show that the λ values that optimize the localization accuracies of SIMN depond on the Signal-to-Noise Ratio(SNR). To obtain a good estimate of λ a weighted sum of square of norms of minimum norm estimates of source amplitudes and noises is considered. It is shown numerically that, by a proper choice of the weighting factor, the λ value corresponding to the minimum of the weighted sum results in localization accuracy better than that using the λ value estimated from other methods.
Appears in Collections:	[Graduate Institute of Physics] Electronic Thesis & Dissertation

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