fMRI Detection via Variational EM Approach

In this paper, we study Gaussian Random Fields (GRFs) as spatial smoothing priors in Functional Magnetic Resonance Imaging (fMRI) detection, and we solve GRFs using the variational Expectation-Maximization (EM) algorithm. Relatively high noise in fMRI images presents a serious challenge for the detection algorithms, creating a need for spatial regularization of the signals. Spatial regularization is usually employed before or after detection, forming a two-process detector. In a two-process detector, defects produced in the first process usually interfere with the performance of the second process. Among all two-process detectors, the Gaussian-smoothing-based detector, which performs detection on spatially smoothed signals, is the most popular. Gaussian filters, traditionally employed to boost the signal-to-noise ratio, often remove small activation regions. This is mainly caused by applying a fixed, but arbitrary, Gaussian filter uniformly over the entire image. In this work, we propose the EM-GRF-based detector that iterates between these two processes, so that parameters of the Gaussian filter are readjusted according to the feedback from detection, and the parameters for detection are readjusted according to the feedback from the filtered results. In addition, we compare the performance of this detector with the Gaussian-smoothing-based detector through ROC analysis on simulated data, and demonstrate their applications in a real fMRI study.