Structured dissociative PCA methods for high dimensional neuroimaging signal decomposition.

Sparse principal component analysis (SPCA) and independent component analysis (ICA) pipelines are widely used for fMRI blind source separation. However,  applying sparsity and independence constraints in isolation can distort spatial coherence and degrade source recovery when networks overlap or exhibit strong spatial dependencies. To address these shortcomings, we propose a novel unified structured dissociative PCA framework that performs source separation by jointly learning dissociation matrices (unmixers) for singular value decomposition (SVD) and representation matrices (reconstructors) for structured basis representation within a single decomposition. Our approach integrates spatiotemporal priors (temporal DCTs, spatial splines, and hemodynamic response models) into the SVD decomposition and solves it using two algorithms: block coordinate descent (SDPCAG) and coordinate descent (SDPCAC). Both algorithms employ adaptive row-wise sparsity to disentangle overlapping sources and denoise each source through correlation-guided least-squares reconstruction with domain specific constraints. This dual-decomposition strategy, which learned iteratively, allows precise recovery of spatially coherent brain networks while maintaining temporal fidelity. The effectiveness of the proposed algorithms is illustrated on three types of fMRI datasets including synthetic, block-design, and event-related paradigms. Across all scenarios, the proposed methods consistently achieved superior performance compared to existing state-of-the-art techniques, including PMD, ACSDBE, and SICA. Overall, SDPCAG achieved a 22% improvement over ACSDBE in source recovery accuracy. Computationally, SDPCAG achieved 1.6 times faster execution compared to SDPCAC across the experimental datasets while producing comparable results. The source codes are available at https://github.com/usmankhalid06/SDPCA .