Graph Signal Processing Opens New Perspectives For Human Brain Imaging

State-of-the-art magnetic resonance imaging (MRI) provides unprecedented opportunities to study brain structure (anatomy) and function (physiology). Based on such data, graph representations can be built where nodes are associated to brain regions and edge weights to strengths of structural or functional connections. In particular, structural graphs capture major physical white matter pathways, while functional graphs map out statistical interdependencies between pairs of regional activity traces. Network analysis of these graphs has revealed emergent system-level properties of brain structure or function, such as efficiency of communication and modular organization. In this tutorial, graph signal processing (GSP) will be presented as a novel framework to integrate brain structure, contained in the structural graph, with brain function, characterized by activity traces that can be considered as time-dependent graph signals. Such a perspective allows to define novel meaningful graph-filtering operations of brain activity that take into account the anatomical backbone. In particular, we will show how activity can be analyzed in terms of being coupled versus decoupled with respect to brain structure. This method has recently showed for the first time how regions organized in terms of their structure-function coupling form a macrostructural gradient with behavioural relevance, spanning from lower level functions (primary sensory, motor) to higher-level cognitive domains (memory, emotion). In addition, we will also describe how the derived structure-function relationships can be considered more in depth, in terms of their temporal dynamic properties, and at the finer-grained scale of individual sub-networks. From the methodological perspective, the well-known Fourier phase randomization method to generate surrogate data can also be adapted to this new setting. We will show how to generate surrogate data of graph signals in this way, which allows a non-parametric evaluation of the statistical significance of the observed measures.