基于正则化方法的加权最小模估计在脑磁源成像中的应用

Application of Weighted Minimum-norm Estimation with Tikhonov Regularization for Neuromagnetic Source Imaging

脑磁图 ( m agnetoencephalography,MEG)逆问题的研究 ,根据点源和分布源两种源模型 ,可分为偶极子定位和磁源成像两大类求逆方法。采用非参数的分布源模型 ,MEG逆问题转化为一个病态的欠定方程组的求解。本文系统地阐述了结合 Tikhonov正则技术的加权最小模磁源重建方法 ,着重介绍了深度归一化算法、低分辨率脑电磁断层成像技术、局部欠定系统解法、选择性最小模方法 ,此外还从广义的加权最小模估计角度对最大熵重建方法 ,融合其它脑功能成像技术的方法以及最大后验概率估计方法加以解释和分析。不同的磁源成像方法目的都是通过引入合适的约束条件 ,从算法公式本身及神经细胞活动的特性中加以修正 ,减少逆问题的不适定程度 ,因此均可认为是使用正则方法来约束解空间 ,从而获得与测量磁场数据相拟合的并具有神经生理学和解剖学意义下的最合理的解。基于正则化技术的加权最小模估计是 MEG逆问题研究中最早开展、并已被广泛应用的磁源分布图像重建方法 。

In magnetoencepholography(MEG) inverse research, according to the point source model and distributed source model, the neuromagnetic source reconstruction methods are classified as parametric current dipole localization and nonparametric source imaging (or current density reconstruction). MEG source imaging technique can be formulated as an inherent ill-posed and highly underdetermined linear inverse problem. In order to yield a robust and plausible neural current distribution image, various approaches have been proposed. Among those, the weighted minimum-norm estimation with Tikhonov regularization is a popular technique. The authors present a relatively overall theoretical framework Followed by a discussion of the development, several regularized minimum-norm algorithms have been described in detail, including the depth normalization, low resolution electromagnetic tomography(LORETA), focal underdetermined system solver(FOCUSS), selective minimum-norm(SMN). In addition, some other imaging methods, e.g., maximum entropy method(MEM), the method incorporating other brain functional information such as fMRI data and maximum a posteriori(MAP) method using Markov random field model, are explained as well. From the generalized point of view based on minimum-norm estimation with Tikhonov regularization, all these algorithms are aiming to resolve the tradeoff between fidelity to the measured data and the constraints assumptions about the neural source configuration such as anatomical and physiological information. In conclusion, almost all the source imaging approaches can be consistent with the regularized minimum-norm estimation to some extent.