A Graph Signal Processing Perspective on Functional Brain Imaging

Abstract

Modern neuroimaging techniques provide us with unique views on brain structure and function; i.e., how the brain is wired, and where and when activity takes place. Data acquired using these techniques can be analyzed in terms of its network structure to reveal organizing principles at the systems level. Graph representations are versatile models where nodes are associated to brain regions and edges to structural or functional connections. Structural graphs model neural pathways in white matter that are the anatomical backbone between regions. Functional graphs are built based on functional connectivity, which is a pairwise measure of statistical interdependency between activity traces of regions. Therefore, most research to date has focused on analyzing these graphs reflecting structure or function.Graph signal processing (GSP) is an emerging area of research where signals recorded at the nodes of the graph are studied atop the underlying graph structure. An increasing number of fundamental operations have been generalized to the graph setting, allowing to analyze the signals from a new viewpoint. Here, we review GSP for brain imaging data and discuss their potential to integrate brain structure, contained in the graph itself, with brain function, residing in the graph signals. We review how brain activity can be meaningfully filtered based on concepts of spectral modes derived from brain structure. We also derive other operations such as surrogate data generation or decompositions informed by cognitive systems. In sum, GSP offers a novel framework for the analysis of brain imaging data.

Structural mediation of human brain activity revealed by white-matter interpolation of fMRI

“…S4), thus enabling to reconstruct structure-function networks at an unparalleled spatial resolution. As an increasing number of operations are generalized from classical signal processing to the graph setting [22,27], promising avenues arise to explore the many facets of brain structure and function.…”

“…Lately, to further transcend our current understanding of structure-function relationships, attention has been set on studying SC and FC through the lens of more technical frameworks borrowed from other research fields, such as propagator-based methods [18][19][20], and control network theoretical tools [21]. Graph signal processing (GSP) for neuroimaging is another emerging field [22], where initially, a graph is defined by identifying regions in GM as nodes, and mapping strength of their SC through WM to edge weights. Functional data are then interpreted as time-dependent graph signals, on which connectomeinformed signal processing operations can be performed.…”

Spectral Graph Wavelet Transform as Feature Extractor for Machine Learning in Neuroimaging

“…While there is a growing literature applying GSP to neuroscientific questions, (for a review, see [8]), most studies use GSP to derive descriptors (such as alignement of functional signals to the underlying graph [9]) that are further analyzed using inference based statistics (e.g. [10]).…”

Energy Efficient WSN: a Cross-layer Graph Signal Processing Solution to Information Redundancy

“…where the columns of U = [u 1 u 2 ...u N ] are the eigenvectors of L and Λ = diag(λ 1 , λ 2 , ..., λ N , ) is a diagonal matrix containing the N eigenvalues λ i associated with the eigenvectors u i in U. U T is the Graph Fourier Transform (GFT), which contains information on the variability of signals over the graph in a similar way as the Fourier transform does for time-domain signals [17]. If one defines a graph signal x as the signal sampled over all the vertices of the graph, then the GFT of x can be defined as…”