Graph slepians to strike a balance between local and global network interactions: Application to functional brain imaging

Brain function exhibits coordinated activity patterns that are also reflected in anatomy, a finding that can be harnessed to constrain the dynamics of functional time series to the underlying structure while performing various signal processing operations. Graph signal processing (GSP) is such a framework, which we here equip with a new tool to uncover localised functional brain interactions. The functional magnetic resonance imaging (fMRI) signal is projected onto a collection of Slepian vectors defined on a graph extracted from structural and diffusion MRI data. This decomposition allows a multi-bandwidth description of signals that are maximally concentrated within a subset of nodes, as is often the case for neural activity. On simulated data, we compare this technique to classical Laplacian and localised Laplacian filtering. We then present, on real fMRI data, an illustration of the Slepians potential to retrieve localised interaction patterns in the context of a visual stimulation task