Graph Frequency Analysis of Brain Signals

Abstract

This paper presents methods to analyze functional brain networks and signals from graph spectral perspectives. The notion of frequency and filters traditionally defined for signals supported on regular domains such as discrete time and image grids has been recently generalized to irregular graph domains, and defines brain graph frequencies associated with different levels of spatial smoothness across the brain regions. Brain network frequency also enables the decomposition of brain signals into pieces corresponding to smooth or rapid variations. We relate graph frequency with principal component analysis when the networks of interest denote functional connectivity. The methods are utilized to analyze brain networks and signals as subjects master a simple motor skill. We observe that brain signals corresponding to different graph frequencies exhibit different levels of adaptability throughout learning. Further, we notice a strong association between graph spectral properties of brain networks and the level of exposure to tasks performed, and recognize the most contributing and important frequency signatures at different levels of task familiarity.

Functional Annotation of Human Cognitive States using Deep Graph Convolution

“…This method has gained more and more attention in neuroscience studies, for instance parcellating brain areas (Johansen-Berg et al , 2004;Fan et al , 2016) , identifying functional areas and networks (Craddock et al , 2012;Atasoy, Donnelly and Pearson, 2016) , and generating connectivity gradients (Margulies et al , 2016) . Recently, studies have found that, by decomposing the task-evoked fMRI signals using GSP, the resultant graph representations strongly associated with cognitive performance and learning (Huang et al , 2016;Medaglia et al , 2018) . These findings brought new opportunities for the application of GSP on neuroimaging analysis.…”

Graph Signal Processing in a Nutshell

“…A work by Nguyen et al represented the human body as a threedimensional dynamic mesh and applied graph wavelet filter banks to compress information of position and color, outperforming usual methods for coding of the human body [47]. The processing of brain signals may be, however, the most intriguing and prolific of such applications, arising through the assignment of signals such as fMRI readings to graphs defined by functional brain networks [48], [49], which have for example demonstrated a close relation between the signals' lowest and highest frequency components and the learning of a motor task [50]. 231 As mentioned in the Subsection V-B, the regularization of a discrete-valued graph signal was used for data classification in [23].…”

Collaborative filtering via graph signal processing

“…Differently, the high pass component focuses on the differences between users with similar taste for the particular item. With this interpretation one can see (8) as a filter that eliminates the irrelevant features (middle frequencies), smoothes out the similar components (low frequencies) and preserves the discriminative features (high frequencies). This band-stop behavior where both high and low graph frequencies are preserved is not uncommon in image processing (image de-noising and image sharpening, respectively) [13], and was also observed in brain signal analytics [8], [14].…”