Shift-Invariant Canonical Polyadic Decomposition of Complex-Valued Multi-Subject fMRI Data With a Phase Sparsity Constraint

• Published in: IEEE transactions on medical imaging Vol. 39; no. 4; pp. 844 - 853
• Main Authors: Kuang, Li-Dan, Lin, Qiu-Hua, Gong, Xiao-Feng, Cong, Fengyu, Wang, Yu-Ping, Calhoun, Vince D.
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.04.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Brain - diagnostic imaging; Canonical polyadic decomposition (CPD); complex-valued fMRI data; Computer simulation; Data models; Decomposition; Delay effects; Frequency-domain analysis; Functional magnetic resonance imaging; Humans; Image Processing, Computer-Assisted - methods; Invariants; Load modeling; Magnetic Resonance Imaging - methods; Noise levels; Noise reduction; shift-invariant; Signal Processing, Computer-Assisted; source phase sparsity; Sparsity; spatiotemporal constraints; Spatiotemporal phenomena; Tensors; Timing
• ISSN: 0278-0062; 1558-254X
• DOI: 10.1109/TMI.2019.2936046

Canonical polyadic decomposition (CPD) of multi-subject complex-valued fMRI data can be used to provide spatially and temporally shared components among groups with both magnitude and phase information. However, the CPD model is not well formulated due to the large subject variability in the spatial and temporal modalities, as well as the high noise level in complexvalued fMRI data. Considering that the shift-invariant CPD can model temporal variability across subjects, we propose to further impose a phase sparsity constraint on the shared spatial maps to denoise the complex-valued components and to model the inter-subject spatial variability as well. More precisely, subject-specific time delays are first estimated for the complex-valued shared time courses in the framework of real-valued shift-invariant CPD. Source phase sparsity is then imposed on the complex-valued shared spatial maps. A smoothed ℓ 0 norm is specifically used to reduce voxels with large phase values after phase de-ambiguity based on the small phase characteristic of BOLD-related voxels. The results from both the simulated and experimental fMRI data demonstrate improvements of the proposed method over three complex-valued algorithms, namely, tensor-based spatial ICA, shift-invariant CPD and CPD without spatiotemporal constraints. When comparing with a real-valued algorithm combining shiftinvariant CPD and ICA, the proposed method detects 178.7% more contiguous task-related activations.