A sparse based approach for detecting activations in fMRI

In this paper, we propose a simple approach for detecting activated voxels in fMRI data by exploiting the inherent sparsity property of the BOLD signal. The proposed approach addresses the solution of the inverse problem induced by the General Linear Model through an l₀-regularized Least Absolute Deviation (l₀-LAD) regression method. Under this framework, the activated voxels are detected by a two-stages process: estimation and basis selection. First, an estimate of the coefficients that minimizes the absolute deviation error is found by means of the weighted median operator. Then, a thresholding operator is applied on the estimated value in order to decide whether or not a stimulus is present in the observed BOLD signal. The threshold parameter turns out to be the regularization parameter that controls the model sparseness. The method was proven on real fMRI data leading to similar activated regions than those activated by the Statistical Parametric Mapping (SPM) software.