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

Li-Dan Kuang,Fengyu Cong,Xiao-Feng Gong,Qiu-Hua Lin,Vince D Calhoun,Yu-Ping Wang

doi:10.1109/tmi.2019.2936046

Abstract

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 complex-valued 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 l0 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 shift-invariant CPD and ICA, the proposed method detects 178.7% more contiguous task-related activations.

Highlights

T ENSOR decomposition applied to multi-subject functional magnetic resonance imaging data is of growing interest, as such approaches enable us to make use of the multiway structure of fMRI data in terms of space, time and subject/trial [1]–[3]
To evaluate the efficacy of the proposed pcsCPD method, we carry out extensive experiments using both simulated and experimental complex-valued fMRI data, with comparison to the following three algorithms: (1) csCPD; (2) Canonical polyadic decomposition (CPD) using the COMFAC algorithm, which is a fast implementation of trilinear alternative least squares (ALS) [33]; and (3) T-sICA using the complex-valued entropy bound minimization (EBM) algorithm [34] to perform independent component analysis (ICA)
CPD can obtain better performance for the case of s, t = 0 where the simulated fMRI data conforms to the CPD model, but it sharply degrades with the increase in s and t

Summary

Introduction

T ENSOR decomposition applied to multi-subject functional magnetic resonance imaging (fMRI) data is of growing interest, as such approaches enable us to make use of the multiway structure of fMRI data in terms of space, time and subject/trial [1]–[3]. CPD has been widely applied to multi-trial/subject fMRI data since 2004 to extract shared spatial maps (SMs), shared time courses (TCs), and trial/subject-specific intensities [1], [2], [8]–[11]. CPD is a complementary method to independent vector analysis (IVA), which emphasizes the capture of inter-subject variability and the decomposition of multi-subject fMRI data into individual SMs and TCs [12]. Multi-subject fMRI data tend to violate the CPD model since the data involve larger inter-subject spatial and temporal variability than multi-trial fMRI data. For this reason, some constraints on spatial and temporal modalities were imposed to make the CPD model more rigid.

Methods

Results

Conclusion