Constrained CPD of Complex-Valued Multi-Subject fMRI Data via Alternating Rank-R and Rank-1 Least Squares

Area of Science:

• Neuroimaging
• Signal Processing
• Mathematical Modeling

Background:

• Complex-valued Canonical Polyadic Decomposition (CPD) with spatial phase sparsity (pcsCPD) effectively separates functional Magnetic Resonance Imaging (fMRI) data.
• Band-pass filtering, while reducing noise, can also remove valuable information from fMRI data.

Purpose of the Study:

• To develop a novel constrained CPD algorithm for complex-valued fMRI data that relaxes the model and preserves more information.
• To improve the estimation of brain networks, specifically sensorimotor and auditory networks.

Main Methods:

• Proposed an alternating rank-R and rank-1 least squares optimization to relax the CPD model.
• Developed a constrained CPD algorithm incorporating temporal shift-invariance, spatial sparsity, and orthonormality constraints.
• Implemented a four-step iterative update process including rank-R least-squares fitting and rank-1 least-squares for time courses.

Main Results:

• The proposed algorithm demonstrated improved estimates for task-related sensorimotor and auditory networks in both simulated and real complex-valued fMRI data.
• Outperformed existing methods like pcsCPD and tensorial spatial ICA in network estimation.
• The alternating least squares optimization framework proved flexible for improving CPD-related algorithms.

Conclusions:

• The novel constrained CPD algorithm offers a more robust approach to analyzing complex-valued fMRI data.
• The developed optimization strategy effectively balances model relaxation with essential constraints for accurate brain network analysis.
• This method provides a valuable advancement for neuroimaging research, particularly in identifying task-related functional networks.