Automatic HyperParameter Estimation in fMRI

摘要

Maximum a posteriori (MAP) in the scope of the Bayesian framework is a common criterion used in a large number of estimation and decision problems. In image reconstruction problems, typically, the image to be estimated is modeled as a Markov Random Fields (MRF) described by a Gibbs distribution. In this case, the Gibbs energy depends on a multiplicative coefficient, called hyperparameter, that is usually manually tuned [14] in a trial and error basis. In this paper we propose an automatic hyperparameter estimation method designed in the scope of functional Magnetic Resonance Imaging (fMRI) to identify activated brain areas based on Blood Oxygen Level Dependent (BOLD) signal. This problem is formulated as classical binary detection problem in a Bayesian framework where the estimation and inference steps are joined together. The prior terms, incorporating the a priori physiological knowledge about the Hemodynamic Response Function (HRF), drift and spatial correlation across the brain (using edge preserving priors), are automatically tuned with the new proposed method. Results on real and synthetic data are presented and compared against the conventional General Linear Model (GLM) approach.