相关论文: Multi-dimensional Graph Fourier Transform
A mathematical relation between elements of one- and multi-dimensional discrete Fourier transforms (DFT) is found. A method of analysing the multi-dimensional data by their single one-dimensional (1-D) DFT is offered. An experiment of…
The paper presents the graph Fourier transform (GFT) of a signal in terms of its spectral decomposition over the Jordan subspaces of the graph adjacency matrix $A$. This representation is unique and coordinate free, and it leads to…
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
Incorporating graphs in the analysis of multivariate signals is becoming a standard way to understand the interdependency of activity recorded at different sites. The new research frontier in this direction includes the important problem of…
The focus of Part I of this monograph has been on both the fundamental properties, graph topologies, and spectral representations of graphs. Part II embarks on these concepts to address the algorithmic and practical issues centered round…
Recent progress in graph signal processing (GSP) has addressed a number of problems, including sampling and filtering. Proposed methods have focused on generic graphs and defined signals with certain characteristics, e.g., bandlimited…
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…
Time-varying graph signals are alternative representation of multivariate (or multichannel) signals in which a single time-series is associated with each of the nodes or vertex of a graph. Aided by the graph-theoretic tools, time-varying…
In this paper, we redefine the Graph Fourier Transform (GFT) under the DSP$_\mathrm{G}$ framework. We consider the Jordan eigenvectors of the directed Laplacian as graph harmonics and the corresponding eigenvalues as the graph frequencies.…
We propose novel two-channel filter banks for signals on graphs. Our designs can be applied to arbitrary graphs, given a positive semi definite variation operator, while using arbitrary vertex partitions for downsampling. The proposed…
The graph Fourier transform (GFT) is an important tool for graph signal processing, with applications ranging from graph-based image processing to spectral clustering. However, unlike the discrete Fourier transform, the GFT typically does…
In this paper, we present a novel generalization of the graph Fourier transform (GFT). Our approach is based on separately considering the definitions of signal energy and signal variation, leading to several possible orthonormal GFTs. Our…
Graph signal processing (GSP) leverages the inherent signal structure within graphs to extract high-dimensional data without relying on translation invariance. It has emerged as a crucial tool across multiple fields, including learning and…
Graph signal processing (GSP) facilitates the analysis of high-dimensional data on non-Euclidean domains by utilizing graph signals defined on graph vertices. In addition to static data, each vertex can provide continuous time-series…
We study the problem of constructing a graph Fourier transform (GFT) for directed graphs (digraphs), which decomposes graph signals into different modes of variation with respect to the underlying network. Accordingly, to capture low,…
Graphons are infinite-dimensional objects that represent the limit of convergent sequences of graphs as their number of nodes goes to infinity. This paper derives a theory of graphon signal processing centered on the notions of graphon…
Multivariate signals, which are measured simultaneously over time and acquired by sensor networks, are becoming increasingly common. The emerging field of graph signal processing (GSP) promises to analyse spectral characteristics of these…
The graph Hilbert transform (GHT) is a key tool in constructing analytic signals and extracting envelope and phase information in graph signal processing. However, its utility is limited by confinement to the graph Fourier domain, a fixed…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
We study the problem of constructing a graph Fourier transform (GFT) for directed graphs (digraphs), which decomposes graph signals into different modes of variation with respect to the underlying network. Accordingly, to capture low,…