Rician distributed functional MRI: Asymptotic power analysis of likelihood ratio tests for activation detection

Since voxel time courses in functional magnetic resonance imaging (fMRI) are mostly produced from complex-valued data by taking the magnitudes, they obey Rician distributions, which can be approximated as Gaussian distributions only when signal-to-noise ratios (SNRs) are high. In this paper, we derive the asymptotic power of our recently developed activation detection statistic for Rician fMRI. The analysis shows that the asymptotic power is dependent only on the ratios of signal parameters to noise parameter of Rician distributed voxel time series, and allows us to better understand the nature of low SNRs in fMRI data analysis. Based on the power analysis, a more general and descriptive definition of SNR is provided than classical one.