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。 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.
