Simultaneously capturing excessive variations and smooth dynamics of the underlying neural activity using spatiotemporal basis expansion and multisubject fMRI data.

In the last decade, dictionary learning (DL) has gained popularity over independent component analysis (ICA) within the blind source separation (BSS) framework for functional magnetic resonance imaging (fMRI) signals. Despite its rising popularity, a primary challenge in DL remains model fitting. It is susceptible to overfitting because the conventional loss function strives to correspond too closely to the training data. However, in the case of multi-subject (MS) analysis, it becomes imperative to overfit in order to acquire the source diversities across different brains. In this paper, an attempt has been made to resolve this predicament by concurrently preserving and mitigating the effect of high variance. A novel algorithm named joint analysis and synthesis DL (JASDL) has been proposed that simultaneously learns the overfitted trends to retain the data-centric cross-subject diversities and wellfitted trends by adequately regularizing the model complexity. This fusion was achieved by benefiting from modeling each subject's data in terms of both spatiotemporal (ST) prior information (PI) and MS-ST components. The PI consisted of biological priors derived from neuroscience knowledge, such as brain network templates, and mathematical priors derived from basis functions, such as three-dimensional (3D) cubic basis splines (B-splines). In contrast, MS-ST components were estimated using the computationally most parsimonious sparse ST blind source separation (ssBSS) method. Using the proposed analysis/synthesis cost function that exploits tri and quad-factorization for matrix approximation, the JASDL algorithm can model temporal smoothness and spatial reduction of false positives while retaining MS variations. Its efficacy was evaluated by comparing it with existing DL techniques using both experimental and synthetic fMRI datasets. Overall, the mean of correlation and F-score was found to be [Formula: see text] higher for the JASDL synthesis dictionary than the state-of-the-art subject-wise sequential DL (swsDL).