Solving Incrementally the Fitting and Detection Problems in fMRI Time Series

We tackle the problem of real-time statistical analysis of functional magnetic resonance imaging (fMRI) data. In a recent paper, we proposed an incremental algorithm based on the extended Kalman filter (EKF) to fit fMRI time series in terms of a general linear model with autoregressive errors (GLM-AR model). We here improve the technique using a new Kalman filter variant specifically tailored to the GLM-AR fitting problem, the Refined Kalman Filter (RKF), that avoids both the estimation bias and initialization issues typical from the EKF, at the price of increased memory load. We then demonstrate the ability of the method to perform online analysis on a “functional calibration” eventrelated fMRI protocol.