Sparse Group Bases for Multisubject fMRI Data

Considering that functional magnetic resonance imaging (fMRI) signals from multiple subjects (MS) can be represented together as a sum of common and a sum of distinct rank-1 matrices, a new MS dictionary learning (DL) algorithm named sparse group (common + distinct) bases (sgBACES) is proposed. Unlike existing MS-DL algorithms that ignore fMRI data’s prior information, it is formulated as a penalized plus constrained rank-1 matrix approximation, where $l_{1}$ norm-based adaptive sparse penalty, $l_{0}$ norm-based dictionary regularization, and lag-1 based autocorrelation maximization have been introduced in the minimization problem. Besides, spatial dependence among neighbouring voxels has been exploited for fine-tuning the sparsity parameters. To my best knowledge, the sgBACES algorithm is the first to effectively take temporal and spatial prior information into account for an MS-fMRI-DL framework. It also has the advantage of not requiring a separate sparse coding stage. Studies based on synthetic and experimental fMRI datasets are used to compare the performance of sgBACES with the state-of-the-art algorithms in terms of correlation strength and computation time. It emerged that the proposed sgBACES algorithm enhanced the signal-to-noise ratio (SNR) of the recovered time courses (TCs) and the precision of the recovered spatial maps (SMs). A 10.2% increase in the mean correlation value over the ShSSDL algorithm is observed for motor-task based fMRI data.