fMRI BOLD signal decomposition using a multivariate low-rank model

Standard methodologies for functional Magnetic Resonance Imaging (fMRI) data analysis decompose the observed Blood Oxygenation Level Dependent (BOLD) signals using voxel-wise linear model and perform maximum likelihood estimation to get the parameters associated with the regressors. In task fMRI, the latter are usually defined from the experimental paradigm and some confounds whereas in resting-state acquisitions, a seed-voxel time-course may be used as predictor. Nowadays, most fMRI datasets offer resting-state acquisitions, requiring multivariate approaches (e.g., PCA, ICA, etc) to extract meaningful information in a data-driven manner. Here, we propose a novel low-rank model of fMRI BOLD data but instead of considering a dimension reduction in space as in ICA, our model relies on convolutional sparse coding between the hemodynamic system and a few temporal atoms which code for the neural activity inducing signals. A rank -1 constraint is also associated with each temporal atom to spatially map its influence in the brain. Within a variational framework, the joint estimation of the neural signals and the associated spatial maps is formulated as a nonconvex optimization problem. A local minimizer is computed using an efficient alternate minimization algorithm. The proposed approach is first validated on simulations and then applied to task fMRI data for illustration purpose. Its comparison to a state-of-the-art approach suggests that our method is competitive regarding the uncovered neural fingerprints while offering a richer decomposition in time and space.