Graph Wavelet Research Articles

Dynamic PET images denoising using spectral graph wavelet transform.

Positron emission tomography (PET) is a non-invasive molecular imaging method for quantitative observation of physiological and biochemical changes in living organisms. The quality of the reconstructed PET image is limited by many different physical degradation factors. Various denoising methods including Gaussian filtering (GF) and non-local mean (NLM) filtering have been proposed to improve the image quality. However, image denoising usually blurs edges, of which high frequency components are filtered as noises. On the other hand, it is well-known that edges in a PET image are important to detection and recognition of a lesion. Denoising while preserving the edges of PET images remains an important yet challenging problem in PET image processing. In this paper, we propose a novel denoising method with good edge-preserving performance based on spectral graph wavelet transform (SGWT) for dynamic PET images denoising. We firstly generate a composite image from the entire time series, then perform SGWT on the PET images, and finally reconstruct the low graph frequency content to get the denoised dynamic PET images. Experimental results on simulation and in vivo data show that the proposed approach significantly outperforms the GF, NLM and graph filtering methods. Compared with deep learning-based method, the proposed method has the similar denoising performance, but it does not need lots of training data and has low computational complexity.

An Attention and Wavelet Based Spatial-Temporal Graph Neural Network for Traffic Flow and Speed Prediction

Traffic flow prediction is essential to the intelligent transportation system (ITS). However, due to the complex spatial-temporal dependence of traffic flow data, it is insufficient in the extraction of local and global spatial-temporal correlations for the previous process on road network and traffic flow modeling. This paper proposes an attention and wavelet-based spatial-temporal graph neural network for traffic flow and speed prediction (STAGWNN). It integrated attention and graph wavelet neural networks to capture local and global spatial information. Meanwhile, we stacked a gated temporal convolutional network (gated TCN) with a temporal attention mechanism to extract the time series information. The experiment was carried out on real public transportation datasets: PEMS-BAY and PEMSD7(M). The comparison results showed that our proposed model outperformed baseline networks on these datasets, which indicated that STAGWNN could better capture the spatial-temporal correlation information.

(Retracted) Deep graph convolutional network-based high-performance detection method for spectral domain gesture image stream

The use of vision-based high-performance detection technology has become an innovative technical methodology. Gestures can express more actions and even emotions, which is more in line with the design idea of large-scale integrated human–computer interaction software, and then assists the development of emotion recognition and other fields. The emerging deep graph convolutional network can capture the interdependence between instances, and then infer the complete information of the image based on specific features. The two-dimensional discrete wavelet and multi-resolution analysis are used to replace the traditional Fourier transform to realize the convolution operation, which improves the accuracy of the generated graph data. This work studies the spectral clustering method of Graph Wavelet Neural Network and adds the local correlation preserving support vector machine as a classifier. This classifier has a simplified structure compared with the cascade classifier and can achieve faster and stable classification results. On the test set, the average accuracy of the algorithm is 93.40%, the recall rate is 96.27%, and the average detection time per frame is 359 ms.

Modelling traffic as multi-graph signals: Using domain knowledge to enhance the network-level passenger flow prediction in metro systems

Network-level metro passenger flow prediction has always been one of the most important but most challenging scientific problems in intelligent transportation systems (ITS). However, conventional methods ignore the multi-dimensional topological relationships in the subway system or directly learn from the physical topological structure and fail to explore the spatial-temporal evolution of passenger flow fully. Moreover, due to the highly punctual operation feature, the metro system has high-degree controllability and regularity, which is usually not considered in the traditional model. To address this problem, we model a metro system based on various topological structures and propose a novel spatial-temporal multi-graph convolutional wavelet network (ST-MGCWN) with unique metro system state characteristics. The core of this approach is to combine the domain knowledge of transportation and deep learning models. To be precise, there are three main modules in the proposed framework: (i). The graph wavelet convolution captures the dynamic spatial dependence between nodes on the established multiple graphs and synthesizes topological features through the graph fusion module. (ii). The various approaches based on the gated recurrent model are designed to capture the long-term periodicity and short-term trends. (iii). The transformation of the metro state characteristics reflects the change of the train density on the operation diagram, which is approximated by the distribution of the local peaks of passenger flow. Experimental results show that our proposed model achieves up to about 5% improvement over the state-of-the-art approach for the network-level passenger flow prediction task. In addition, we conduct a detailed analysis of the contribution of each component to enhance interpretability and reliability.

Graph wavelets for fault localization in optical mesh networks

• Real-time fault detection and localization mechanism in Elastic Optical Networks (EONs). • Alarm correlation strategies fail in the face of static threshold settings. • Detects and localizes silent network failures. • Multi-resolution analysis based on graph wavelets to address fault detection and localization problems. • Exceeds alarm based engines for fault detection and localization accuracy. EONs (Elastic Optical Networks) form the backbone of web-scale cloud infrastructure. These networks should deal with network faults and restoration in real-time with high accuracy and scalability. Thus, fault management functions to detect and localize such failures, play a critical role in modern day EONs. Network impairments are complex in nature in optical networks such as fiber losses, NLI (Non Linear Impairments) and ASE (Amplified Stimulated Emission). Currently, pre-engineered thresholds are used to detect failures in optical networks. Traditional alarm correlation strategies fail in the face of these static threshold settings. In this work, we introduce a real-time fault detection and localization mechanism, which is agnostic to such pre-engineered threshold settings. We apply multi-resolution analysis based on graph wavelets to address fault detection and localization problems. Thus, we propose to use spectrograms and wavelet coefficients to identify the irregularities in an otherwise smooth graph signal. We present a real-time fault localization analysis based on a novel Wavelet Coefficients Trail (WCT) algorithm to root-cause a client signal failure due to OSNR (Optical Signal to Noise Ratio) degradation. We apply the proposed techniques and algorithms to simulated and actual network data. Our results indicate that the proposed methods can root-cause OSNR degradation to major/minor deviations in received power on optical spans. In conclusion, we present a fault localization framework based on graph wavelets in optical mesh networks.

Early Forecast of Traffic Accident Impact Based on a Single-Snapshot Observation (Student Abstract)

Predicting and quantifying the impact of traffic accidents is necessary and critical to Intelligent Transport Systems (ITS). As a state-of-the-art technique in graph learning, current graph neural networks heavily rely on graph Fourier transform, assuming homophily among the neighborhood. However, the homophily assumption makes it challenging to characterize abrupt signals such as traffic accidents. Our paper proposes an abrupt graph wavelet network (AGWN) to model traffic accidents and predict their time durations using only one single snapshot.

Data-Wise Spatial Regional Consistency Re-Enhancement for Hyperspectral Image Classification

Effectively using rich spatial and spectral information is the core issue of hyperspectral image (HSI) classification. The recently proposed Diverse Region-based Convolutional Neural Network (DRCNN) achieves good results by weighted averaging the features extracted from several predefined regions, thus exploring the use of spatial consistency to some extent. However, such feature-wise spatial regional consistency enhancement does not effectively address the issue of wrong classifications at the edge of regions, especially when the edge is winding and rough. To improve the feature-wise approach, Data-wise spAtial regioNal Consistency re-Enhancement (“DANCE”) is proposed. Firstly, the HSIs are decomposed once using the Spectral Graph Wavelet (SGW) to enhance the intra-class correlation. Then, the image components in different frequency domains obtained from the weight map are filtered using a Gaussian filter to “debur” the non-smooth region edge. Next, the reconstructed image is obtained based on all filtered frequency domain components using inverse SGW transform. Finally, a DRCNN is used for further feature extraction and classification. Experimental results show that the proposed method achieves the goal of pixel level re-enhancement with image spatial consistency, and can effectively improve not only the performance of the DRCNN, but also that of other feature-wise approaches.

Progress prediction of Parkinson's disease based on graph wavelet transform and attention weighted random forest

The progress prediction of Parkinson's disease (PD) is one of the most important issues in early diagnosis of PD. Many researches have been conducted in this field, however, most existing methods focus on the selection of baseline features and regressors to reduce prediction errors. Different from the previous studies, the main goal of this paper is to obtain more effective features by feature transformation of baseline features to improve the prediction performance. Therefore, this paper proposes a prediction model based on graph wavelet transform (GWT) and attention weighted random forest (RF). Firstly, a clustering algorithm is adopted to reduce the prediction error of the model. Next, a multi-scale analysis of the feature vectors by GWT is conducted to yield a frequency feature representation that is more relevant to the target value. Finally, the frequency features are input into the attention weighted RF to predict the severity of PD, allowing the results of decision trees with better predictive performance in the RF to be highlighted while reducing the risk of overfitting. The effectiveness of the method is evaluated on the Parkinson's telemonitoring dataset collected by the University of Oxford. The experimental results show that the mean absolute error and root mean squared error of the proposed method for predicting PD severity (motor- and total-UPDRS) are 1.53, 2.13 and 1.91, 2.70, respectively. Compared with the quoted optimal method, the errors are reduced by 7.27%, 4.05% and 5.45%, 1.10%, respectively. This indicates that the proposed method has better prediction performance.

Dual graph wavelet neural network for graph-based semi-supervised classification

Vertex classification is an important graph mining technique and has important applications in fields such as social recommendation and e-Commerce recommendation. Existing classification methods fail to make full use of the graph topology to improve the classification performance. To alleviate it, we propose a Dual Graph Wavelet neural Network composed of two identical graph wavelet neural networks sharing network parameters. These two networks are integrated with a semi-supervised loss function and carry out supervised learning and unsupervised learning on two matrixes representing the graph topology extracted from the same graph dataset, respectively. One matrix embeds the local consistency information and the other the global consistency information. To reduce the computational complexity of the convolution operation of the graph wavelet neural network, we design an approximate scheme based on the first type Chebyshev polynomial. Experimental results show that the proposed network significantly outperforms the state-of-the-art approaches for vertex classification on all three benchmark datasets and the proposed approximation scheme is validated for datasets with low vertex average degree when the approximation order is small.

A sparse graph wavelet convolution neural network for video-based person re-identification

Video-based person re-identification (Re-ID) aims to match identical person sequences captured across non-overlapping surveillance areas. It is an essential yet challenging task to effectively embed spatial and temporal information into the video feature representation. For one thing, we observe that different frames in the video can provide complementary information for each other. Also, local features which is lost due to target occlusion or visual ambiguity in one frame can be supplemented by the same pedestrian part in other frames. For another thing, graph neural network enables the contextual interactions between relevant regional features. Therefore, we propose a novel sparse graph wavelet convolution neural network (SGWCNN) for video-based person Re-ID. Distinct from previous graph-based Re-ID methods, we exploit the weighted sparse graph to model the semantic relation among the local patches of pedestrians in the video. Each local patch in one frame can extract supplementary information from highly related patches in other frames. Moreover, to effectively solve the problems of short time occlusion and pedestrian misalignment, the graph wavelet convolution neural network is adopted for feature propagation to refine regional features iteratively. Experiments and evaluation on three challenging benchmarks, that is, MARS, DukeMTMC-VideoReID, and iLIDS-VID, show that the proposed SGWCNN effectively improves the performance of video-based person re-identification.

Localized Fourier analysis for graph signal processing

We propose a new point of view in the study of Fourier analysis on graphs, taking advantage of localization in the Fourier domain. For a signal $f$ on vertices of a weighted graph $\mathcal{G}$ with Laplacian matrix $\mathcal{L}$, standard Fourier analysis of $f$ relies on the study of functions $g(\mathcal{L})f$ for some filters $g$ on $I_\mathcal{L}$, the smallest interval containing the Laplacian spectrum ${\mathrm sp}(\mathcal{L}) \subset I_\mathcal{L}$. We show that for carefully chosen partitions $I_\mathcal{L} = \sqcup_{1\leq k\leq K} I_k$ ($I_k \subset I_\mathcal{L}$), there are many advantages in understanding the collection $(g(\mathcal{L}_{I_k})f)_{1\leq k\leq K}$ instead of $g(\mathcal{L})f$ directly, where $\mathcal{L}_I$ is the projected matrix $P_I(\mathcal{L})\mathcal{L}$. First, the partition provides a convenient modelling for the study of theoretical properties of Fourier analysis and allows for new results in graph signal analysis (\emph{e.g.} noise level estimation, Fourier support approximation). We extend the study of spectral graph wavelets to wavelets localized in the Fourier domain, called LocLets, and we show that well-known frames can be written in terms of LocLets. From a practical perspective, we highlight the interest of the proposed localized Fourier analysis through many experiments that show significant improvements in two different tasks on large graphs, noise level estimation and signal denoising. Moreover, efficient strategies permit to compute sequence $(g(\mathcal{L}_{I_k})f)_{1\leq k\leq K}$ with the same time complexity as for the computation of $g(\mathcal{L})f$.

GA-GWNN: Detecting anomalies of online learners by granular computing and graph wavelet convolutional neural network

GA-GWNN: Detecting anomalies of online learners by granular computing and graph wavelet convolutional neural network

3D Spectral Graph Wavelet Point Signatures in Pre-Processing Stage for Mobile Laser Scanning Point Cloud Registration in Unstructured Orchard Environments

3D Spectral Graph Wavelet Point Signatures in Pre-Processing Stage for Mobile Laser Scanning Point Cloud Registration in Unstructured Orchard Environments

Spectral Mappings for Graph Wavelets

Graph wavelet filters can be used to construct dictionaries of atoms, and signals defined over graphs can be represented as linear combinations of these atoms. These representations can facilitate the development of various signal processing tasks, e.g. denoising or feature extraction. We present here a method to construct these filters, using mappings on simple prototype filters, that readily allows for spectral domain shaping. Two types of spectral maps will be developed in this work. The first type of maps sharpens (increase the frequency selectivity) of the prototype filter. The second type of maps is equivalent to upsampling in the spectral domain, and can be used to construct a’trous like transforms. The a’trous like transform allows for a tree-structured implementation, and is reminiscent of the classical a’trous (with-holes) wavelet transform. The resulting filters, constructed using these maps, are polynomial functions, and can therefore be implemented without the need for any approximation or eigendecomposition. Both non-redundant and redundant frames can be constructed with these filters. A variety of design examples will be presented to demonstrate the versatility of the proposed method. Applications of the filters to non-linear approximation and denoising will also be considered.

Analysis of the Spatio-Temporal Dynamics of COVID-19 in Massachusetts via Spectral Graph Wavelet Theory

The rapid spread of COVID-19 disease has had a significant impact on the world. In this paper, we study COVID-19 data interpretation and visualization using open-data sources for 351 cities and towns in Massachusetts from December 6, 2020 to September 25, 2021. Because cities are embedded in rather complex transportation networks, we construct the spatio-temporal dynamic graph model, in which the graph attention neural network is utilized as a deep learning method to learn the pandemic transition probability among major cities in Massachusetts. Using the spectral graph wavelet transform (SGWT), we process the COVID-19 data on the dynamic graph, which enables us to design effective tools to analyze and detect spatio-temporal patterns in the pandemic spreading. We design a new node classification method, which effectively identifies the anomaly cities based on spectral graph wavelet coefficients. It can assist administrations or public health organizations in monitoring the spread of the pandemic and developing preventive measures. Unlike most work focusing on the evolution of confirmed cases over time, we focus on the spatio-temporal patterns of pandemic evolution among cities. Through the data analysis and visualization, a better understanding of the epidemiological development at the city level is obtained and can be helpful with city-specific surveillance.

Graph Neural Networks With Lifting-Based Adaptive Graph Wavelets

Spectral-based graph neural networks (SGNNs) have been attracting increasing attention in graph representation learning. However, existing SGNNs are limited in implementing graph filters with rigid transforms and cannot adapt to signals residing on graphs and tasks at hand. In this paper, we propose a novel class of graph neural networks that realizes graph filters with adaptive graph wavelets. Specifically, the adaptive graph wavelets are learned with neural network-parameterized lifting structures, where structure-aware attention-based lifting operations are developed to jointly consider graph structures and node features. We propose to lift based on diffusion wavelets to alleviate the structural information loss induced by partitioning non-bipartite graphs. By design, the locality and sparsity of the resulting wavelet transform as well as the scalability of the lifting structure are guaranteed. We further derive a soft-thresholding filtering operation by learning sparse graph representations in terms of the learned wavelets, yielding a localized, efficient, and scalable wavelet-based graph filters. To ensure that the learned graph representations are invariant to node permutations, a layer is employed at the input of the networks to reorder the nodes according to their local topology information. We evaluate the proposed networks in both node-level and graph-level representation learning tasks on benchmark citation and bioinformatics graph datasets. Extensive experiments demonstrate the superiority of the proposed networks over existing SGNNs in terms of accuracy, efficiency, and scalability.

Multi-scale and multi-level shape descriptor learning via a hybrid fusion network

Discriminative and informative 3D shape descriptors are of fundamental significance to computer graphics applications, especially in the fields of geometry modeling and shape analysis. 3D shape descriptors, which reveal extrinsic/intrinsic properties of 3D shapes, have been well studied for decades and proved to be useful and effective in various analysis and synthesis tasks. Nonetheless, existing descriptors are mainly founded upon certain local differential attributes or global shape spectra, and certain combinations of both types. Conventional descriptors are typically customized for specific tasks with priori domain knowledge, which severely prevents their applications from widespread use. Recently, neural networks, benefiting from their powerful data-driven capability for general feature extraction from raw data without any domain knowledge, have achieved great success in many areas including shape analysis. In this paper, we present a novel hybrid fusion network (HFN) that learns multi-scale and multi-level shape representations via uniformly integrating a traditional region-based descriptor with modern neural networks. On one hand, we exploit the spectral graph wavelets (SGWs) to extract the shapes’ local-to-global features. On the other hand, the shapes are fed into a convolutional neural network to generate multi-level features simultaneously. Then a hierarchical fusion network learns a general and unified representation from these two different types of features which capture multi-scale and multi-level properties of the underlying shapes. Extensive experiments and comprehensive comparisons demonstrate our HFN can achieve better performance in common shape analysis tasks, such as shape retrieval and recognition, and the learned hybrid descriptor is robust, informative, and discriminative with more potential for widespread applications.

DATA-DRIVEN LEARNING OF GEOMETRIC SCATTERING MODULES FOR GNNS.

We propose a new graph neural network (GNN) module, based on relaxations of recently proposed geometric scattering transforms, which consist of a cascade of graph wavelet filters. Our learnable geometric scattering (LEGS) module enables adaptive tuning of the wavelets to encourage band-pass features to emerge in learned representations. The incorporation of our LEGS-module in GNNs enables the learning of longer-range graph relations compared to many popular GNNs, which often rely on encoding graph structure via smoothness or similarity between neighbors. Further, its wavelet priors result in simplified architectures with significantly fewer learned parameters compared to competing GNNs. We demonstrate the predictive performance of LEGS-based networks on graph classification benchmarks, as well as the descriptive quality of their learned features in biochemical graph data exploration tasks.

Graph signal processing based underwater image enhancement techniques

This paper presents two new methods based on graph signal processing (GSP) techniques to enhance underwater images. The proposed schemes utilize the graph Fourier transform (GFT) and graph wavelet filterbanks in place of the conventional Fourier and wavelet transforms. Initially, the raw images are represented on a chosen graph structure, and then the root-filtering is applied in the GFT and graph wavelet transform (GWT) domains in the present work. It is observed that the root-filtering parameter plays a crucial role in the image enhancement process. The root filtering method highlights the high frequency terms, which pertain to edges and textural elements with smaller amplitudes, while de-emphasizing the higher magnitude frequency components. As a result, the high frequency components are accentuated in contrast to the lower frequencies, resulting in a sharper and more visually appealing image. The simulation results of the proposed techniques are compared with the existing enhancement methods. It is shown that the proposed approaches offer more improvement in the enhanced image quality than the current methods considered in this paper. It is also seen that the root-filtering parameter in the range of 0.75 to 0.95 and Mexican hat wavelet in the proposed graph wavelet filterbank based approach with N = 5 improve the quality of enhancement of underwater images.

Spectral Graph Wavelet Based Image Steganography Using SVD and Arnold Transform

Steganography is the process of concealing sensitive information within cover medium. This study offers an efficient and safe innovative image steganography approach based on graph signal processing (GSP). To scramble the secret image, Arnold cat map transform is used, then Spectral graph wavelet is used to change the cover and scrambled secret image, followed by singular vector decomposition (SVD) of the modified cover image. To create the stego image, an alpha blending process is used. To produce the stego image, GSP-based synthesis is used. By maintaining the inter-pixel correlation, GSP improves the visual quality of the produced stego image. The effects of image processing attacks on the suggested approach are examined. The investigational results and assessment indicate that the proposed steganography scheme is more efficient and robust in terms of quality measures. The quality of stego image is evaluated in respect of PSNR, NCC, SC and AD performance metrics.