基于时域平滑约束的脑磁时序信号逆问题求解方法

An MEG Inverse Solver by Imposition of Temporal Smoothness Constraint

由脑磁时序信号重建脑内时序神经信号时,除了要保证重建信号位置和强度的准确性,还要避免重建源信号在时域上瞬变.针对这一问题,提出了一种基于时域平滑约束的脑磁时序信号逆问题求解方法.该方法不同于传统最小范数估计算法(Minimum Norm Estimate,MNE),通过引入时域平滑正则算子构造双参数混合正则化,根据广义交叉验证(Generalized Cross-Validation,GCV)原则选取双正则化参数后,根据单正则项的解在源信号中的权重将其进行线性组合估算出源信号.仿真数据实验表明,本文方法比传统MNE方法的总体均方误差小,且各时刻均方误差基本稳定在同一水平;同时本文方法重建的源信号与仿真源信号变化趋势基本一致.真实数据实验发现,本文方法重建结果的曲率变化率为0.0640,而传统MNE方法重建结果的曲率变化率为0.1646.实验结果证明本文方法能重建出空域准确且时域平滑的脑内神经信号.

The magnetoencephalography （MEG） inverse problem refers to the reconstruction of the neural activity of the brain from MEG measurements. A method to solve the MEG inverse problem employing temporal smoothness constraint is proposed under the assumption that time course of the source is smooth in time. Specifically, the temporal smoothness of the source was ensured by imposing a roughness penalty in the minimum norm estimate （MNE） data fitting criterion in the form of dual-parameter regularization. To select two tuning parameters, the generalized cross-validation criterion （GCV） was used. The inverse solutions were obtained as the linear combination of the one-parameter regularized solutions. We evaluated the proposed method by a synthetic example and a real data example. Compared with MNE, the proposed method can get smaller overall mean squared error （MSE） and smaller curvature variability. Moreover, the proposed method can reconstruct the shape of the time course of source better.