General linear models under Rician noise for fMRI data

When analyzing fMRI data to study the brain process, one faces two challenges: (i) the correct noise distribution and (ii) the brain dynamics. In general, the brain dynamics are modeled under the simplifying, but wrong assumption that the noise follows a Gaussian distribution. In this paper, we model the brain dynamics under the correct Rice distribution. We implement the hemodynamic response function into a Rice framework and apply the standard General Linear Model (GLM) which is linear-in-the-parameters and can easily be solved. Next, the statistical properties of the least squares estimator are investigated via a simulation experiment.