腦電磁場的源定位

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梁偉光(Wei-Kuang Liang) 查詢紙本館藏

畢業系所

物理學系

論文名稱

腦電磁場的源定位
(Source Localization of Brain Electromagnetic Fields)

相關論文

★ 腦磁波之腦部訊號源定位	★ 利用SVD方法估計Tikhonov正則化參數
★ 訊號和噪訊的權重範數和-估計Tikhonov正則化參數	★ 基於最小範數法的腦電磁訊號源定位

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摘要(中)

我們提出了一種能對腦磁圖(MEG)或腦電圖(EEG)的訊號源作良好定位的方法—源分布迭代最小範數法(source iteration of minimum norm, SIMN)。SIMN是利用最小範數反運算(minimum norm psudoinverse, MNP) 來估算在每一格點上所有電流偶極的總源強度，並以其來作為下一迭代步中每一格點上源的數目(源分布)。每一電流偶極的源強度是由MNP在由解析矩陣(resolution matrix)中對應於該電流偶極的三行所形成的三維子空間中的投影向量長來估算。對於無雜訊單一點源的MEG或EEG訊號，SIMN永遠可以正確的定位；對於無雜訊的多點源的MEG或EEG訊號，在源與源之間沒有強的內部互消的條件下，SIMN同樣可以正確的定位每一個點源，並得到正確的強度和方向。對於有雜訊的情況，我們引進雜訊源(noise sources)的構想，並利用提可諾夫規整化(Tikhonov regularization) 來起始雜訊源的數目。數值模擬顯示，在有雜訊的情況下，SIMN的定位能力優於目前常用的多種源定位法。SIMN 對雜訊的耐受力可藉由適當的深度權重(depth weighting)來達到最佳化。本文最後也展示了將SIMN應用在真實MEG及EEG數據上的結果。

摘要(英)

A recursive scheme aiming at obtaining sparse and focal brain electromagnetic source distribution is proposed based on the interpretation that the weighted minimum norm is the minimum norm estimates of amplitudes on grid points for the source distribution specified by the diagonal elements of the weight matrix. The source distribution is updated so that, at each grid point, the number of current dipoles equals the total source strength estimate of the pre-specified current dipoles. The source strength of a pre-specified free orientation current dipole is estimated by projecting the vector of minimum norm estimate to the space spanned by the corresponding three column vectors of the resolution matrix. The norm of the projected vector yields the source strength estimate of the current dipole. Exact inverse solutions are obtained by this source iteration of minimum norm (SIMN) algorithm for noiseless MEG signals from multi-point sources provided the sources are sufficiently sparse and there are no substantial cancellations among the signals of the sources. For noisy data, a set of “noise sources” is introduced. The diagonal matrix formed by the “noise source numbers” plays the role of regularization matrix and Tikhonov regularization is applied to initialize the “noise-source numbers”. The noise tolerance of SIMN can be optimized by applying depth weighting to the lead fields with a suitable depth weighting parameter. Applications to the source localization of real EEG and MEG data are also presented.

關鍵字(中)

★ 反問題
★ 源定位
★ 源重建
★ 逆運算
★ 腦磁圖
★ 腦電圖
★ 源迭代最小範數

關鍵字(英)

★ MEG
★ source localization
★ source reconstruction
★ source iteration
★ SIMN
★ inverse problem
★ EEG

論文目次

Introduction 1
Chapter 1 Origin of brain electromagnetic fields 7
1.1 Physics of EEG and MEG 7
1.2 Quasistatic electromagnetic surface integrals 9
1.3 Current dipole 10
Chapter 2 Source localization of brain electromagnetic fields 12
2.1 Minimum norm pseudoinverse for arbitrary source distribution 12
2.2 Source iteration of minimum norm (SIMN) 14
2.3 Estimate of source strength and recursion relation of SIMN 15
2.4 Noise sources and noise lead fields 18
2.5 Depth weighting 21
2.6 Algorithm of SIMN 24
Chapter 3 Numerical simulations 26
3.1 Forward model – MNI template, BEM 26
3.2 Noise free MEG data cases 27
3.3 Noisy MEG data cases 34
3.4 Effect of depth weighting on noise regularization 39
3.5 The optimal p value for location-wise depth weighting 44
3.5.1 Optimization in MNI template 44
3.5.2 Optimization in a real brain 52
Chapter 4 Application of SIMN to real EEG and MEG data 54
4.1 EEG data of go/no-go visual categorization task 54
4.2 MEG data of face perception experiment 57
Summary 66
References 67

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指導教授

王敏生(M. S. Wang)

審核日期

2009-7-22

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