Rician Distributed FMRI: Asymptotic Power Analysis and Cramér–Rao Lower Bounds

Traditional functional MRI detection statistics for activation and hemodynamic response modeling assume Gaussian data, which is true only for high signal-to-noise ratio (SNR). The correct distribution is Rician. In this correspondence, we provide two new developments in the Rician case. First, a derivation of the theoretical asymptotic power function (as the number of samples goes to infinity). Second, the derivation of a Cramér-Rao lower bound. This allows a correct assessment of the impact of various signal and noise levels on detection power for activation and/or hemodynamic response parameter estimation accuracy. Based on our analysis, we are able to extend existing definitions of SNR by considering variation not only in baseline but also in drifts.