Graph Signal Processing Tools Research Articles

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.

State Estimation in Partially Observable Power Systems via Graph Signal Processing Tools.

This paper considers the problem of estimating the states in an unobservable power system, where the number of measurements is not sufficiently large for conventional state estimation. Existing methods are either based on pseudo-data that is inaccurate or depends on a large amount of data that is unavailable in current systems. This study proposes novel graph signal processing (GSP) methods to overcome the lack of information. To this end, first, the graph smoothness property of the states (i.e., voltages) is validated through empirical and theoretical analysis. Then, the regularized GSP weighted least squares (GSP-WLS) state estimator is developed by utilizing the state smoothness. In addition, a sensor placement strategy that aims to optimize the estimation performance of the GSP-WLS estimator is proposed. Simulation results on the IEEE 118-bus system show that the GSP methods reduce the estimation error magnitude by up to two orders of magnitude compared to existing methods, using only 70 sampled buses, and increase of up to 30% in the probability of bad data detection for the same probability of false alarms in unobservable systems The results conclude that the proposed methods enable an accurate state estimation, even when the system is unobservable, and significantly reduce the required measurement sensors.

Big Data Analytics Using Graph Signal Processing

The networks are fundamental to our modern world and they appear throughout science and society. Access to a massive amount of data presents a unique opportunity to the researcher’s community. As networks grow in size the complexity increases and our ability to analyze them using the current state of the art is at severe risk of failing to keep pace. Therefore, this paper initiates a discussion on graph signal processing for large-scale data analysis. We first provide a comprehensive overview of core ideas in Graph signal processing (GSP) and their connection to conventional digital signal processing (DSP). We then summarize recent developments in developing basic GSP tools, including methods for graph filtering or graph learning, graph signal, graph Fourier transform (GFT), spectrum, graph frequency, etc. Graph filtering is a basic task that allows for isolating the contribution of individual frequencies and therefore enables the removal of noise. We then consider a graph filter as a model that helps to extend the application of GSP methods to large datasets. To show the suitability and the effeteness, we first created a noisy graph signal and then applied it to the filter. After several rounds of simulation results. We see that the filtered signal appears to be smoother and is closer to the original noise-free distance-based signal. By using this example application, we thoroughly demonstrated that graph filtration is efficient for big data analytics.

Learning spatial filters from EEG signals with Graph Signal Processing methods.

In this paper, we propose to learn a spatial filter directly from Electroencephalography (EEG) signals using graph signal processing tools. We combine a graph learning algorithm with a high-pass graph filter to remove spatially large signals from the raw data. This approach increases topographical localization, and attenuates volume-conducted features. We empirically show that our method gives similar results that the surface Laplacian in the noiseless case while being more robust to noise or defective electrodes.Clinical relevance- The proposed method is an alternative to the surface Laplacian filter that is commonly used for processing EEG signals. It could be used in cases where this standard approach does not provide satisfying results (low signal-to-noise ratios due to a low number of epochs, defective electrodes). This could be particularly interesting in case of an electrode defect, as it can happen in clinical practice.

Population Graph-Based Multi-Model Ensemble Method for Diagnosing Autism Spectrum Disorder.

With the advancement of brain imaging techniques and a variety of machine learning methods, significant progress has been made in brain disorder diagnosis, in particular Autism Spectrum Disorder. The development of machine learning models that can differentiate between healthy subjects and patients is of great importance. Recently, graph neural networks have found increasing application in domains where the population’s structure is modeled as a graph. The application of graphs for analyzing brain imaging datasets helps to discover clusters of individuals with a specific diagnosis. However, the choice of the appropriate population graph becomes a challenge in practice, as no systematic way exists for defining it. To solve this problem, we propose a population graph-based multi-model ensemble, which improves the prediction, regardless of the choice of the underlying graph. First, we construct a set of population graphs using different combinations of imaging and phenotypic features and evaluate them using Graph Signal Processing tools. Subsequently, we utilize a neural network architecture to combine multiple graph-based models. The results demonstrate that the proposed model outperforms the state-of-the-art methods on Autism Brain Imaging Data Exchange (ABIDE) dataset.

Multimodal Dynamic Brain Connectivity Analysis Based on Graph Signal Processing for Former Athletes With History of Multiple Concussions

The study of structure-function relationships in the brain has been an active area of research in neuroscience. The availability of brain imaging data that captures the structural connectivity and functional co-activation of the brain regions has led to the study of multimodal technical frameworks that can help disentangle the mechanisms linking cognitive abilities and brain structural alterations. This paper analyzes the diffusion and resting state functional magnetic resonance imaging (dMRI and rs-fMRI) data collected from a population consisting of former athletes with a history of multiple concussions and healthy controls with no reported history of concussion. For each subject, the structural connectome is represented by a graph with its nodes associated with cortical brain regions and the adjacency matrix derived from dMRI. Each cortical brain region is associated with a blood oxygen level dependent (BOLD) signal derived from fMRI. This paper uses the tools from graph signal processing (GSP) to select the brain regions of interest (ROIs) that have significant statistical differences in the extracted high and low graph frequency components of the region specific BOLD signal across former athletes and healthy controls, where the graph frequencies represent the extent of spatial variations of the BOLD signal across the brain. The selected ROIs have also been previously identified to be affected in the existing clinical studies on traumatic brain injuries (TBI). Furthermore, the dynamic functional connectivity profiles of the selected ROIs are determined by leveraging the high and low graph frequency components of the BOLD signal and a sliding window based approach. Interestingly, the graph frequency functional connectivity profiles reveal unique characteristics that are not apparent in the unimodal dynamic functional connectivity profiles based on fMRI. Our analysis reveals statistically significant differences in the dwell times in multiple dynamic graph frequency functional connectivity states for the two groups of subjects. Therefore, the results presented in this paper underline the significance of graph signal processing tools for multimodal analysis of brain imaging data and also provide promising direction for applications in clinical research and medical diagnosis.

Graph Signal Processing in the Presence of Topology Uncertainties

The goal of this paper is to expand graph signal processing tools to deal with cases where the graph topology is not perfectly known. Assuming that the uncertainty affects only a limited number of edges, we make use of small perturbation analysis to derive closed form expressions instrumental to formulate signal processing algorithms that are resilient to imperfect knowledge of the graph topology . Then, we formulate a Bayesian approach to estimate the presence/absence of uncertain edges based only on the observed data and on the statistics of the data. Finally, we exploit our perturbation analysis to analyze clustering and semi-supervised learning algorithms. Numerical tests confirm the benefits of our perturbation-aware methods.

Ship Detection in SAR Images Based on Maxtree Representation and Graph Signal Processing

This paper discusses an image processing architecture and tools to address the problem of ship detection in synthetic-aperture radar images. The detection strategy relies on a tree-based representation of images, here a Maxtree, and graph signal processing tools. Radiometric as well as geometric attributes are evaluated and associated with the Maxtree nodes. They form graph attribute signals which are processed with graph filters. The goal of this filtering step is to exploit the correlation existing between attribute values on neighboring tree nodes. Considering that trees are specific graphs where the connectivity toward ancestors and descendants may have a different meaning, we analyze several linear, nonlinear, and morphological filtering strategies. Beside graph filters , two new filtering notions emerge from this analysis: tree and branch filters . Finally, we discuss a ship detection architecture that involves graph signal filters and machine learning tools. This architecture demonstrates the interest of applying graph signal processing tools on the tree-based representation of images and of going beyond classical graph filters. The resulting approach significantly outperforms state-of-the-art algorithms. Finally, a MATLAB toolbox allowing users to experiment with the tools discussed in this paper on Maxtree or Mintree has been created and made public.

Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2-D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this paper, we overview recent graph spectral techniques in GSP specifically for image/video processing. The topics covered include image compression, image restoration, image filtering, and image segmentation.

Graph Signal Processing: Overview, Challenges, and Applications

Research in graph signal processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper, we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing, along with a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas. We then summarize recent advances in developing basic GSP tools, including methods for sampling, filtering, or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning.

Characterization and Inference of Graph Diffusion Processes From Observations of Stationary Signals

Many tools from the field of graph signal processing exploit knowledge of the underlying graph's structure (e.g., as encoded in the Laplacian matrix) to process signals on the graph. Therefore, in the case when no graph is available, graph signal processing tools cannot be used anymore. Researchers have proposed approaches to infer a graph topology from observations of signals on its vertices. Since the problem is ill-posed, these approaches make assumptions, such as smoothness of the signals on the graph, or sparsity priors. In this paper, we propose a characterization of the space of valid graphs, in the sense that they can explain stationary signals. To simplify the exposition in this paper, we focus here on the case where signals were i.i.d. at some point back in time and were observed after diffusion on a graph. We show that the set of graphs verifying this assumption has a strong connection with the eigenvectors of the covariance matrix, and forms a convex set. Along with a theoretical study in which these eigenvectors are assumed to be known, we consider the practical case when the observations are noisy, and experimentally observe how fast the set of valid graphs converges to the set obtained when the exact eigenvectors are known, as the number of observations grows. To illustrate how this characterization can be used for graph recovery, we present two methods for selecting a particular point in this set under chosen criteria, namely graph simplicity and sparsity. Additionally, we introduce a measure to evaluate how much a graph is adapted to signals under a stationarity assumption. Finally, we evaluate how state-of-the-art methods relate to this framework through experiments on a dataset of temperatures.