Chapter 31 - Graph Signal Processing on Neuronal Networks

Abstract

Advanced neuroimaging technology has enabled the study of both the structure and function of the brain in more detail than before. The high volume of multisubject, multimodal neuroimaging data poses challenges to the signal processing community as the data is high-dimensional, sensitive to noise, and suffers from high variability across subjects. While many discoveries in neuroscience have been made using massively univariate statistics or time-series analysis, there has been a paradigm shift toward the use of multivariate analysis, graph theoretic methods, and machine learning to decode brain function. Tools from network science and graph theory have been employed to analyze the functional connectivity of the brain by associating nodes with distinct brain regions and edges with pairwise interactions between them. However, these methods focus solely on the network topology and organization without directly correlating the activity in these brain regions with the underlying network. Graph signal processing (GSP) offers a promising tool to address this important gap in the study of neuronal networks. This new framework merges neuroimaging data such as functional magnetic resonance imaging (fMRI) and electroencephalography (EEG) with the underlying graphical structure to extract rich brain activity missed by analyzing the networks or the signals alone. Given a connectivity network and neuroimaging signals defined on this network, we first illustrate how GSP can be used for robust dimensionality reduction, signal detection and classification, and filtering to extract brain activity corresponding to different levels of spatial variation. We then present GSP-based methods for learning functional connectivity networks given the observed neuroimaging data and the use of graph-based spectral analysis for data and network denoising. Finally, we present how GSP methods can be extended to study the temporal dynamics of functional connectivity networks of the brain.