Connectome spectrum electromagnetic tomography: A method to reconstruct electrical brain source networks at high-spatial resolution

Connectome spectrum electromagnetic tomography (CSET) combines diffusion MRI-derived structural connectivity data with well-established graph signal processing tools to solve the M/EEG inverse problem. Using simulated EEG signals from fMRI responses, and two EEG datasets on visual-evoked potentials, we provide evidence supporting that (i) CSET captures realistic neurophysiological patterns with better accuracy than state-of-the-art methods, (ii) CSET can reconstruct brain responses more accurately and with more robustness to intrinsic noise in the EEG signal. These results demonstrate that CSET offers high spatio-temporal accuracy, enabling neuroscientists to extend their research beyond the current limitations of low sampling frequency in functional MRI and the poor spatial resolution of M/EEG.

Functional network estimation using multigraph learning with application to brain maturation study

Although most dramatic structural changes occur in the perinatal period, a growing body of evidences demonstrates that adolescence and early adulthood are also important for substantial neurodevelopment. We were thus motivated to explore brain development during puberty by evaluating functional connectivity network (FCN) differences between childhood and young adulthood using multi-paradigm task-based functional magnetic resonance imaging (fMRI) measurements. Different from conventional multigraph based FCN construction methods where the graph network was built independently for each modality/paradigm, we proposed a multigraph learning model in this work. It promises a better fitting to FCN construction by jointly estimating brain network from multi-paradigm fMRI time series, which may share common graph structures. To investigate the hub regions of the brain, we further conducted graph Fourier transform (GFT) to divide the fMRI BOLD time series of a node within the brain network into a range of frequencies. Then we identified the hub regions characterizing brain maturity through eigen-analysis of the low frequency components, which were believed to represent the organized structures shared by a large population. The proposed method was evaluated using both synthetic and real data, which demonstrated its effectiveness in extracting informative brain connectivity patterns. We detected 14 hub regions from the child group and 12 hub regions from the young adult group. We show the significance of these findings with a discussion of their functions and activation patterns as a function of age. In summary, our proposed method can extract brain connectivity network more accurately by considering the latent common structures between different fMRI paradigms, which are significant for both understanding brain development and recognizing population groups of different ages.

Random-Walk Laplacian for Frequency Analysis in Periodic Graphs

This paper presents the benefits of using the random-walk normalized Laplacian matrix as a graph-shift operator and defines the frequencies of a graph by the eigenvalues of this matrix. A criterion to order these frequencies is proposed based on the Euclidean distance between a graph signal and its shifted version with the transition matrix as shift operator. Further, the frequencies of a periodic graph built through the repeated concatenation of a basic graph are studied. We show that when a graph is replicated, the graph frequency domain is interpolated by an upsampling factor equal to the number of replicas of the basic graph, similarly to the effect of zero-padding in digital signal processing.

A New Surrogating Algorithm by the Complex Graph Fourier Transform (CGFT)

The essential step of surrogating algorithms is phase randomizing the Fourier transform while preserving the original spectrum amplitude before computing the inverse Fourier transform. In this paper, we propose a new method which considers the graph Fourier transform. In this manner, much more flexibility is gained to define properties of the original graph signal which are to be preserved in the surrogates. The complex case is considered to allow unconstrained phase randomization in the transformed domain, hence we define a Hermitian Laplacian matrix that models the graph topology, whose eigenvectors form the basis of a complex graph Fourier transform. We have shown that the Hermitian Laplacian matrix may have negative eigenvalues. We also show in the paper that preserving the graph spectrum amplitude implies several invariances that can be controlled by the selected Hermitian Laplacian matrix. The interest of surrogating graph signals has been illustrated in the context of scarcity of instances in classifier training.