基于四阶累积量矩阵子空间分解的脑电逆问题算法

Electroencephalography Inverse Problem by Subspace Decomposition of the Fourth-order Cumulant Matrix

根据头表观测电位反演脑电源的空间位置是脑电研究中的一个重要问题。基于四阶累积量矩阵的子空间分解，提出了一种新的脑电逆问题算法。与现有的基于二阶统计量矩阵的子空间分解算法相比，二阶方法存在对空间相关噪音敏感的问题，而四阶方法可以抑制在时间方向上呈高斯分布，在空间方向相关的噪音，从而显示了四阶方法的较好性能。

It is an important topic in electroencephalography (EEG) research to localize the EEG activity sources from the scalp recordings. In this paper, based on the fourth-order cumulant matrix, a new sub-space decomposition algorithm is proposed for the EEG inverse problem. As the second-order moments (cumulants) has the drawback of being sensitive to the noise covariance. Using the fourth-order cumulants we need not know the noise covariances, as long as the noise is Gaussian. Computer simulation study on a three-layer concentric sphere head model shows its better performance than the two-order cumulate method in depressing the spatial coherent Gaussian noise.