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

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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.