A Robust and Scalable Method with an Analytic Solution for Multi-Subject FMRI Data Analysis

Joint blind source separation (JBSS) is a powerful framework for extracting latent sources from multiple datasets while keeping their coherence across multiple linked datasets. Algorithms for JBSS, while offering the capability of improved estimation performance, often incur high computational complexity and hence are not scalable to studies with hundreds or thousands of datasets. In this paper, we propose a simple yet efficient method for source separation that exploits both the correlation among sources within each dataset and across the datasets. The proposed method, named reference-guided component analysis (RGCA), uses source templates as references to (i) guide the separation of sources on each dataset and (ii) establish source dependence and automatically align them across the datasets. In addition, we promote independence among latent sources within each dataset by adding orthogonal constraints on the demixing vectors. The resulting optimization admits an analytic solution that enables extremely fast implementation of RGCA. Our numerical results demonstrate that RGCA obtains competitive performance while having a runtime far superior to other JBSS methods. The proposed method provides a robust and scalable solution to multi-subject functional magnetic resonance imaging (fMRI) studies, enabling joint analysis of thousands of subjects within a few minutes.