Space-Time analysis of 4-dimensional data of the blood flow measurement in brains

虽然功能磁共振成像数据是时间依赖性的数据，它已被空间统计学家分析没有适当注意的动态部分。这是因为数据同时也是空间数据，在发展的早期，统计分析已经由空间统计学专家完成。在本研究中，我们采取了一种反转的方法，我们把数据作为一个14万维的时间序列，并试图找到一些因果结构的数据使用时间序列分析的创新方法。我们也将同样的思想应用到了空间卡尔曼滤波的脑电数据反问题的求解中。这就为不适定问题的逆解的动态延拓提供了一个有用的工具。

Although fMRI data is time-dependent data, it has been analyzed by spatial statisticians without proper attention to the dynamic part. This is because the data is also spatial data at the same time and the statistical analysis has been done by specialists of spatial statistics in the early stage of the development. In the present study, we take a reversal approach, where we treat the data as a 140,000 dimensional time series and tried to find some causal structure in the data using the innovation approach in time series analysis. We also applied the same idea to the solution of inverse problem for EEG data using spatial Kalman filtering scheme. This provides us with a useful tool for dynamic extension of Inverse Solution of ill-posed problems.