Constrained coupled CPD of complex-valued multi-slice multi-subject fMRI data

Li-Dan Kuang, Hao Zhu, Lei Long, Ting Tang, Yan Gui, Jin Zhang

Abstract: Considering that the four-way complex-valued multi-subject fMRI tensor inevitably contains the large unwanted brain-out voxels, this paper innovatively combines multi-subject brain-in fMRI data with same slices as three-way multi-slice multi-subject fMRI tensors and thus brain-out voxels are discarded. Additionally, adjacent-slice fMRI tensors can be further merged, and multi-slice multi-subject fMRI tensors of N groups are formed, and are jointly decomposed by a novel spatiotemporally constrained coupled canonical polyadic decomposition (CCPD) by sharing temporal and subject modes but allowing slice-group differences. The spatial phase sparsity and orthonormality constraints are added on rank-R least-squares fit of N-slice-group shared spatial maps (SMs) to reduce noise effect, cross-talk among components and inter-subject spatial variability which naturally occur in complex-valued fMRI data. To alleviate CCPD model and allow inter-subject temporal variability, the alternating shift-invariant rank-1 least-squares optimization is performed to update shared time courses (TCs), subject-specific time delays and intensities. Results of simulated and experimental fMRI analyses demonstrate that the proposed methods with different N groups outperformed the competing methods by 6.21 %∼23.61 % in terms of shared task-related SMs and TCs. The proposed methods with N=45 and N=3 respectively obtain the best performance in the presence of strong noise levels and slightly strong noise levels cases.