A spatially constrained low-rank matrix factorization for the functional parcellation of the brain

We propose a new matrix recovery framework to partition brain activity using time series of resting-state functional Magnetic Resonance Imaging (fMRI). Spatial clusters are obtained with a new low-rank factorization algorithm that offers the ability to add different types of constraints. As an example we add a total variation type cost function in order to exploit neighborhood constraints. We first validate the performance of our algorithm on simulated data, which allows us to show that the neighborhood constraint improves the recovery in noisy or undersampled set-ups. Then we conduct experiments on real-world data, where we simulated an accelerated acquisition by randomly undersampling the time series. The obtained parcellation are reproducible when analysing data from different sets of individuals, and the estimation is robust to undersampling.