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姓名 盧柏宏(Bo-hong Lu) 查詢紙本館藏 畢業系所 物理學系 論文名稱 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)相關論文
★ 腦磁波之腦部訊號源定位 ★ 腦電磁場的源定位 ★ 利用SVD方法估計Tikhonov正則化參數 ★ 基於最小範數法的腦電磁訊號源定位 檔案 [Endnote RIS 格式]
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摘要(中) 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。
摘要(英) 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.
關鍵字(中) ★ 訊號和噪訊的權重範數和
★ Tikhonov正則化參數
★ 最小範數源迭代法關鍵字(英) ★ SIMN
★ Tikhonov regularization parameter
★ Weighted Sum of Norms of MNE and Noises論文目次 中文摘要………………………………………………………………i
Abstract………………………………………………………………ii
目錄………………………………………………………………iii
圖目錄………………………………………………………………iv
符號說明………………………………………………………………v
第一章、緒論…………………………………………………………1
1-1腦腦神經活…………………………………………………1
1-2量測腦神經衝動儀器-腦磁圖與腦電圖…………………2
1-3腦腦磁圖與腦電圖遭遇的問題………………………………3
第二章、腦磁圖與腦電圖的理論……………………………………5
2-1準靜近似下的馬克斯威爾方程組…………………………5
2-2磁場與電位的積分公式……………………………………7
2-3電流偶極……………………………………………………9
2-4源與訊號關係式……………………………………………10
第三章、最小範數源迭代法…………………………………………11
3-1無雜訊下的最小範數源迭代法……………………………11
3-2有雜訊下的最小範數源迭代法……………………………12
3-3最小範數源迭代法的演算步驟……………………………13
第四章、訊號和噪訊的權重範數和…………………………………15
4-1三維空間的頭模型…………………………………………15
4-2估計Tikhonov正則化參數的方法………………………17
4-2-1定位成功率最佳的?值……………………………………18
4-2-2訊號和噪訊的權重範數和的理論…………………………25
4-2-3數值模擬的結果……………………………………………26
4-3總結…………………………………………………………33
參考文獻………………………………………………………………34
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指導教授 王敏生(M.S.Wang) 審核日期 2011-7-29 推文 plurk
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