A Sparse and Spatially Constrained Generative Regression Model for fMRI Data Analysis

Abstract—In this study, we present an advanced Bayesian frame-work for the analysis of functional magnetic resonance imaging (fMRI) data that simultaneously employs both spatial and sparse properties. The basic building block of our method is the general linear regression model that constitutes a well-known probabilistic approach. By treating regression coefficients as random variables, we can apply an enhanced Gibbs distribution function that cap-tures spatial constrains and at the same time allows sparse repre-sentation of fMRI time series. The proposed scheme is described as a maximum a posteriori approach, where the known expecta-tion maximization algorithm is applied offering closed-form up-date equations for the model parameters. We have demonstrated that our method produces improved performance and functional activation detection capabilities in both simulated data and real applications. Index Terms—Expectation maximization (EM) algorithm, func-tional magnetic resonance imaging (fMRI) analysis, general linea