A sparse Bayesian method for determination of flexible design matrix for fMRI data analysis

The construction of a design matrix is critical to the accurate detection of activation regions of the brain in functional magnetic resonance imaging (fMRI). The design matrix should be flexible to capture the unknown slowly varying drifts as well as robust enough to avoid overfitting. In this paper, a sparse Bayesian learning method is proposed to determine a suitable design matrix for fMRI data analysis. Based on a generalized linear model, this learning method lets the data itself determine the form of the regressors in the design matrix. It automatically finds those regressors that are relevant to the generation of the fMRI data and discards the others that are irrelevant. The proposed approach integrates the advantages of currently employed methods of fMRI data analysis (the model-driven and the data-driven methods). Results from the simulation studies clearly reveal the superiority of the proposed scheme to the conventional t-test method of fMRI data analysis.