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Brain activation detection from magnitude fMRI data using a generalized likelihood ratio test

Functional magnetic resonance (fMRI) studies intend to answer neuroscience questions by statistically analyzing a set of acquired images. Thereby, the aim is to determine those regions in the brain image in which the signal changes upon stimulus presentation. Although MR data are intrinsically complex valued, most tests are commonly applied to magnitude MR images, because these images have the advantage to be immune to incidental phase variations due to various sources. A consequence of transforming the complex valued images into magnitude images is a change of the probability density function (PDF) of the data under concern. Whereas complex data are Gaussian distributed, magnitude data are Rician distributed [1]. Nevertheless, tests applied to magnitude data generally rely on the (false) assumption of Gaussian distributed data. If the signal-to-noise ratio (SNR) of the data is high, this may be a valid assumption since the Rician PDF tends to a Gaussian PDF at increasing levels of the SNR. However, at low SNR, the Rician PDF significantly deviates from a Gaussian PDF. In this paper, we propose a Generalized Likelihood Ratio Test (GLRT) for magnitude fMRI data that fully exploits the knowledge of the Rician PDF.