Plis Sergey M, George J S, Jun S C, Paré-Blagoev J, Ranken D M, Wood C C, Schmidt D M
Applied Modern Physics Group, Los Alamos National Laboratory, MS-D454, Los Alamos, New Mexico 87545, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Jan;75(1 Pt 1):011928. doi: 10.1103/PhysRevE.75.011928. Epub 2007 Jan 30.
We propose a new model to approximate spatiotemporal noise covariance for use in neural electromagnetic source analysis, which better captures temporal variability in background activity. As with other existing formalisms, our model employs a Kronecker product of matrices representing temporal and spatial covariance. In our model, spatial components are allowed to have differing temporal covariances. Variability is represented as a series of Kronecker products of spatial component covariances and corresponding temporal covariances. Unlike previous attempts to model covariance through a sum of Kronecker products, our model is designed to have a computationally manageable inverse. Despite increased descriptive power, inversion of the model is fast, making it useful in source analysis. We have explored two versions of the model. One is estimated based on the assumption that spatial components of background noise have uncorrelated time courses. Another version, which gives closer approximation, is based on the assumption that time courses are statistically independent. The accuracy of the structural approximation is compared to an existing model, based on a single Kronecker product, using both Frobenius norm of the difference between spatiotemporal sample covariance and a model, and scatter plots. Performance of ours and previous models is compared in source analysis of a large number of single dipole problems with simulated time courses and with background from authentic magnetoencephalography data.
我们提出了一种新模型，用于在神经电磁源分析中近似时空噪声协方差，该模型能更好地捕捉背景活动中的时间变异性。与其他现有形式体系一样，我们的模型采用表示时间和空间协方差的矩阵的克罗内克积。在我们的模型中，空间分量允许具有不同的时间协方差。变异性表示为空间分量协方差与相应时间协方差的一系列克罗内克积。与之前通过克罗内克积之和对协方差进行建模的尝试不同，我们的模型设计为具有计算上易于处理的逆矩阵。尽管描述能力有所增强，但该模型的求逆速度很快，使其在源分析中很有用。我们探索了该模型的两个版本。一个版本是基于背景噪声的空间分量具有不相关时间进程的假设进行估计的。另一个给出更接近近似值的版本是基于时间进程在统计上独立的假设。基于时空样本协方差与模型之间差异的弗罗贝尼乌斯范数以及散点图，将结构近似的准确性与基于单个克罗内克积的现有模型进行比较。在对大量具有模拟时间进程以及真实脑磁图数据背景的单偶极子问题进行源分析时，比较了我们的模型和之前模型的性能。
