GSP Analysis of Brain Imaging Data from Athletes with History of Multiple Concussions Study of neurological disorders affecting the structurefunction relationships in the brain has been an ongoing challenge in neuroscience. Joint analysis of structure and function of the brain may disentangle a number of mechanisms and operations that can help interpret the interdependence between white matter degeneration and degradation of cognitive abilities. In this scenario, graph signal processing analysis of different signals generated within the physical structure of the brain may provide new insights and corroborate existing clinical findings. This paper illustrates the utility of graph signal processing tools in the joint analysis of diffusion and functional magnetic resonance imaging (i.e. dMRI and fMRI) data collected from a population of former athletes with a history of multiple concussions, and healthy subjects. Specifically, the distributions of the energy of lowgraphfrequency components of the functional networks (derived from fMRI) are observed to be significantly different for frontotemporal regions of the brain in athletes and healthy subjects. Furthermore, for the two groups of subjects, we observe significantly different associations between the ages of subjects and the energies of high graph frequency components in lingual region. While the effect on frontotemporal regions for former athletes is in line with the existing clinical studies on concussion, significantly different associations between age and features extracted using GSP for the two groups of subjects could inform future clinical applications and medical diagnosis.

Scaleresolved analysis of brain functional connectivity networks with spectral entropy Abstract   Functional connectivity is derived from interregional correlations in spontaneous fluctuations of brain activity, and can be represented in terms of complete graphs with continuous (realvalued) edges. The structure of functional connectivity networks is strongly affected by signal processing procedures to remove the effects of motion, physiological noise and other sources of experimental error. However, in the absence of an established ground truth, it is difficult to determine the optimal procedure, and no consensus has been reached on the most effective approach to remove nuisance signals without unduly affecting the network intrinsic structural features. Here, we use a novel informationtheoretic approach, based on von Neumann entropy, which provides a measure of information encoded in the networks at different scales. We also define a measure of distance between networks, based on information divergence, and optimal null models appropriate for the description of functional connectivity networks, to test for the presence of nontrivial structural patterns that are not the result of simple local constraints. This formalism enables a scaleresolved analysis of the distance between a functional connectivity network and its maximally random counterpart, thus providing a means to assess the effects of noise and image processing on network structure. We apply this novel approach to address a few open questions in the analysis of brain functional connectivity networks. Specifically, we demonstrate a strongly beneficial effect of network sparsification by removal of the weakest links, and the existence of an optimal threshold that maximizes the ability to extract information on largescale network structures. Additionally, we investigate the effects of different degrees of motion at different scales, and compare the most popular processing pipelines designed to mitigate its deleterious effect on functional connectivity networks. We show that network sparsification, in combination with motion correction algorithms, dramatically improves detection of large scale network structure.