相关论文: Graph Fourier Transform based on Directed Laplacia…

Infrastructure monitoring is critical for safe operations and sustainability. Water distribution networks (WDNs) are large-scale networked critical systems with complex cascade dynamics which are difficult to predict. Ubiquitous monitoring…

Graph signal processing (GSP) is a framework to analyze and process graph-structured data. Many research works focus on developing tools such as Graph Fourier transforms (GFT), filters, and neural network models to handle graph signals.…

We study the Laplacian of the undirected De Bruijn graph over an alphabet $A$ of order $k$. While the eigenvalues of this Laplacian were found in 1998 by Delorme and Tillich [1], an explicit description of its eigenvectors has remained…

We review the properties of eigenvectors for the graph Laplacian matrix, aiming at predicting a specific eigenvalue/vector from the geometry of the graph. After considering classical graphs for which the spectrum is known, we focus on…

Vertex-frequency analysis, particularly the windowed graph Fourier transform (WGFT), is a significant challenge in graph signal processing. Tight frame theories is known for its low computational complexity in signal reconstruction, while…

Fourier representation (FR) is an indispensable mathematical formulation for modeling and analysis of physical phenomenon, engineering systems and signals in numerous applications. In this study, we present the generalized Fourier…

We consider the Dyson hierarchical graph $\mathcal{G}$, that is a weighted fully-connected graph, where the pattern of weights is ruled by the parameter $\sigma \in (1/2, 1]$. Exploiting the deterministic recursivity through which…

Graph filtering is the cornerstone operation in graph signal processing (GSP). Thus, understanding it is key in developing potent GSP methods. Graph filters are local and distributed linear operations, whose output depends only on the local…

In the graph signal processing (GSP) literature, graph Laplacian regularizer (GLR) was used for signal restoration to promote piecewise smooth / constant reconstruction with respect to an underlying graph. However, for signals slowly…

We consider a generalization of the diffusion equation on graphs. This generalized diffusion equation gives rise to both normal and superdiffusive processes on infinite one-dimensional graphs. The generalization is based on the $k$-path…

Modern compression systems use linear transformations in their encoding and decoding processes, with transforms providing compact signal representations. While multiple data-dependent transforms for image/video coding can adapt to diverse…

Directional transforms have recently raised a lot of interest thanks to their numerous applications in signal compression and analysis. In this letter, we introduce a generalization of the discrete Fourier transform, called steerable DFT…

Complex spatial dependencies in transportation networks make traffic prediction extremely challenging. Much existing work is devoted to learning dynamic graph structures among sensors, and the strategy of mining spatial dependencies from…

Graph Convolutional Networks (GCNs) have fueled a surge of research interest due to their encouraging performance on graph learning tasks, but they are also shown vulnerability to adversarial attacks. In this paper, an effective graph…

Basic operations in graph signal processing consist in processing signals indexed on graphs either by filtering them, to extract specific part out of them, or by changing their domain of representation, using some transformation or…

Most codec designs rely on the mean squared error (MSE) as a fidelity metric in rate-distortion optimization, which allows to choose the optimal parameters in the transform domain but may fail to reflect perceptual quality. Alternative…

We propose an inexact method for the graph Fourier transform of a graph signal, as defined by the signal decomposition over the Jordan subspaces of the graph adjacency matrix. This method projects the signal over the generalized eigenspaces…

In this paper, we define a new transform called the Gabor quaternionic Fourier transform (GQFT), which generalizes the classical windowed Fourier transform to quaternion valued-signals, we give several important properties such as the…

Transformers have achieved remarkable success in time series modeling, yet their internal mechanisms remain opaque. This work demystifies the Transformer encoder by establishing its fundamental equivalence to a Graph Convolutional Network…

Implementing linear transformations is a key task in the decentralized signal processing framework, which performs learning tasks on data sets distributed over multi-node networks. That kind of network can be represented by a graph.…