Implications of the Rician distribution for fMRI generalized likelihood ratio tests

In functional magnetic resonance imaging (fMRI), the general linear model test (GLMT) is widely used for brain activation detection. However, the GLMT relies on the assumption that the noise corrupting the data is Gaussian distributed. Because the majority of fMRI studies employ magnitude image reconstructions, which are Rician distributed, this assumption is invalid and has significant consequences in case the signal-to-noise ratio (SNR) is low. In this study, we show that the GLMT should not be used at low SNR. Furthermore, we propose a generalized likelihood ratio test for magnitude MR data that has the same performance compared to the GLMT for high SNR, but performs significantly better than the GLMT for low SNR.