Coupled Shift-Invariant Tensorial Spatial ICA Applied to Multi-Group Complex-Valued Task-Related and Resting-State fMRI Data

Multi-subject complex-valued fMRI data, inheriting high noise and spatiotemporal variability, do not well conform canonical polyadic decomposition (CPD) model. Therefore, spatial independence, phase sparsity and temporal shift-invariance have been added in CPD model, e.g., shift-invariant tensorial spatial independent component analysis (sT-sICA). However, different subjects may belong to different groups and scans, paradigms and responses may vary among groups. Considering that coupled CPD (CCPD) can preserve common and different information among different groups, we propose a novel coupled sT-sICA in the framework of shift-invariant CCPD model. We estimate shared spatial maps (SMs) by performing three-stage principal component analysis and ICA, and calculate group-specific time courses (TCs), subject-specific time delays and intensities by conducting complex-valued shift-invariant rank-one matrix approximation. Actual task-related and resting-state fMRI data experiments verify that the proposed method extracts better shared SMs and group-specific TCs and captures larger temporal differences between healthy controls and schizophrenic patients than sT-sICA and CCPD.