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A comprehensive representation of the road pavement state of health is of great interest. In recent years, automated data collection and processing technology has been used for pavement inspection. In this paper, a new signal on graph (SoG) model of road pavement distresses is presented with the aim of improving automatic pavement distress detection systems. A novel nonlinear Bayesian estimator in recovering distress metrics is also derived. The performance of the methodology was evaluated on a large dataset of pavement distress values collected in field tests conducted in Kazakhstan. The application of the proposed methodology is effective in recovering acquisition errors, improving road failure detection. Moreover, the output of the Bayesian estimator can be used to identify sections where the measurement acquired by the 3D laser technology is unreliable. Therefore, the presented model could be used to schedule road section maintenance in a better way.

Learning graph structure from observed signals over graph is a crucial task in many graph signal processing (GSP) applications. Existing approaches focus on inferring static graph, typically assuming that all nodes are available. However, these approaches ignore the situation where only a subset of nodes are available from spatiotemporal measurements, and the remaining nodes are never observed due to application-specific constraints, resulting in time-varying graph estimation accuracy declines dramatically. To handle this problem, we propose a framework that consider the presence of hidden nodes to identify time-varying graph. Specifically, we assume that the graph signals are smooth and stationary on the graphs and only a small number of edges are allowed to change between two consecutive graphs. With these assumptions, we present a challenging time-varying graph inference problem, which models the influence of hidden nodes in terms of estimating the graph-shift operator matrices that have a form of graph Laplacian. Moreover, we emphasize similar edge pattern (column-sparsity) between different graphs. Finally, our method is evaluated on both synthetic and real-world data. The experimental results demonstrate the advantage of our method when compared to existing benchmarking methods.

•The relation of brain function with the underlying structural wiring is complex.•We propose new structure-informed graph signal processing (GSP) filtering of functional data.•GSP-derived features allow accurate task decoding and individual fingerprinting.•Functional connectivity from filtered data is more unique to subject and cognition.•The role of structurally aligned and liberal graph frequencies is elucidated. Brain signatures of functional activity have shown promising results in both decoding brain states, meaning distinguishing between different tasks, and fingerprinting, that is identifying individuals within a large group. Importantly, these brain signatures do not account for the underlying brain anatomy on which brain function takes place. Structure-function coupling based on graph signal processing (GSP) has recently revealed a meaningful spatial gradient from unimodal to transmodal regions, on average in healthy subjects during resting-state. Here, we explore the specificity of structure-function coupling to distinct brain states (tasks) and to individual subjects. We used multimodal magnetic resonance imaging of 100 unrelated healthy subjects from the Human Connectome Project both during rest and seven different tasks and adopted a support vector machine classification approach for both decoding and fingerprinting, with various cross-validation settings. We found that structure-function coupling measures allow accurate classifications for both task decoding and fingerprinting. In particular, key information for fingerprinting is found in the more liberal portion of functional signals, with contributions strikingly localized to the fronto-parietal network. Moreover, the liberal portion of functional signals showed a strong correlation with cognitive traits, assessed with partial least square analysis, corroborating its relevance for fingerprinting. By introducing a new perspective on GSP-based signal filtering and FC decomposition, these results show that brain structure-function coupling provides a new class of signatures of cognition and individual brain organization at rest and during tasks. Further, they provide insights on clarifying the role of low and high spatial frequencies of the structural connectome, leading to new understanding of where key structure-function information for characterizing individuals can be found across the structural connectome graph spectrum.

The Normalized Difference Vegetation Index (NDVI) is a crucial remote-sensing metric for assessing land surface vegetation greenness, essential for various studies encompassing phenology, ecology, hydrology, etc. However, effective applications of NDVI data are hindered by data noise due to factors such as cloud contamination, posing challenges for accurate observation. In this study, we proposed a novel approach for employing a Temporal-Difference Graph (TDG) method to reconstruct low-quality pixels in NDVI data. Regarding spatio-temporal NDVI data as a time-varying graph signal, the developed method utilized an optimization algorithm to maximize the spatial smoothness of temporal differences while preserving the spatial NDVI pattern. This approach was further evaluated by reconstructing MODIS/Terra Vegetation Indices 16-Day L3 Global 250 m Grid (MOD13Q1) products over Northwest China. Through quantitative comparison with a previous state-of-the-art method, the Savitzky–Golay (SG) filter method, the obtained results demonstrated the superior performance of the TDG method, and highly accurate results were achieved in both the temporal and spatial domains irrespective of noise types (positively-biased, negatively-biased, or linearly-interpolated noise). In addition, the TDG-based optimization approach shows great robustness to noise intensity within spatio-temporal NDVI data, suggesting promising prospects for its application to similar datasets.

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.

Hyperspectral imaging has broad applications and impacts in areas including environmental science, weather, and geo/space exploration. The intrinsic spectral–spatial structures and potential multi-level features in different frequency bands make multilayer graph an intuitive model for hyperspectral images (HSI). To study the underlying characteristics of HSI and to take the advantage of graph signal processing (GSP) tools, this work proposes a multilayer graph spectral analysis for hyperspectral images based on multilayer graph signal processing (M-GSP). More specifically, we present multilayer graph (MLG) models and tensor representations for HSI. By exploring multilayer graph spectral space, we develop MLG-based methods for HSI applications, including unsupervised segmentation and supervised classification. Our experimental results demonstrate the strength of M-GSP in HSI processing and spectral–spatial information extraction.

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.

Target position estimation is one of the important research directions in array signal processing. In recent years, the research of target azimuth estimation based on graph signal processing (GSP) has sprung up, which provides new ideas for the Direction of Arrival (DoA) application. In this article, by extending GSP-based DOA to joint azimuth and distance estimation and constructing a fully connected graph signal model, a multi-target joint azimuth and distance estimation method based on GSP is proposed. Firstly, the fully connection graph model is established related to the phase information of a linear array. For the fully connection graph, the Fourier transform method is used to solve the estimated response function, and the one-dimensional estimation of azimuth and distance is completed, respectively. Finally, the azimuth and distance estimation information are combined, and the false points in the merging process are removed by using CLEAN algorithm to complete the two-dimensional estimation of targets. The simulation results show that the proposed method has a smaller mean square error than the Multiple Signal Classification (MUSIC) algorithm in azimuth estimation under the condition of a low signal-to-noise ratio and more accurate response values than the MUSIC algorithm in distance estimation under any signal-to-noise ratio in multi-target estimation.

Graph filter is one of the cornerstones of graph signal processing that can extract desired features from graph signal and filter out noise signal. In the majority of existing research, graph signal operators are designed to be linear and are applicable solely to time-invariant graph signals. Recently, some studies have extended graph signal processing to time-vertex graph signals. Combining the correlation between graph topology and time can obtain better results. This paper proposes an adaptive weighted median filter for pulsed noise in time-varying graph signals. It uses joint correlation to denoise time-varying graph signals and can adjust filtering window and node weights according to whether node information is destroyed by noise. The proposed filter has the advantages of high efficiency and high localization. Information only needs to be exchanged with one-hop neighbors, and it can be implemented in a distributed manner. Three real sensor network data sets are used for denoising experiments here, and the comprehensive experimental results show that the proposed filters perform better in most cases.

Topological signal processing is emerging alongside Graph Signal Processing (GSP) in various applications, incorporating higher-order connectivity structures—such as faces—in addition to nodes and edges, for enriched connectivity modeling. Rich point clouds acquired by multi-camera systems in Visual Simultaneous Localization and Mapping (V-SLAM) are typically processed using graph-based methods. In this work, we introduce a topological signal processing (TSP) framework that integrates texture information extracted from V-SLAM; we refer to this framework as TSP-SLAM. We show how TSP-SLAM enables the extension of graph-based point cloud processing to more advanced topological signal processing techniques. We demonstrate, on real stereo data, that TSP-SLAM enables a richer point cloud representation by associating signals not only with vertices but also with edges and faces of the mesh computed from the point cloud. Numerical results show that TSP-SLAM supports the design of topological filtering algorithms by exploiting the mapping between the 3D mesh faces, edges and vertices and their 2D image projections. These findings confirm the potential of TSP-SLAM for topological signal processing of point cloud data acquired in challenging V-SLAM environments.