相关论文: Unitary Shift Operators on a Graph
In graph signal processing, many studies assume that the underlying network is undirected. Although the digraph model is rarely adopted, it is more appropriate for many applications, especially for real world networks. In this paper, we…
Graph fractional Fourier transform (GFRFT) is an extension of graph Fourier transform (GFT) that provides an additional fractional analysis tool for graph signal processing (GSP) by generalizing temporal-vertex domain Fourier analysis to…
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…
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…
This paper introduces Generalized Fourier transform (GFT) that is an extension or the generalization of the Fourier transform (FT). The Unilateral Laplace transform (LT) is observed to be the special case of GFT. GFT, as proposed in this…
Graph spectral representations are fundamental in graph signal processing, offering a rigorous framework for analyzing and processing graph-structured data. The graph fractional Fourier transform (GFRFT) extends the classical graph Fourier…
We propose Hilbert transform (HT) and analytic signal (AS) construction for signals over graphs. This is motivated by the popularity of HT, AS, and modulation analysis in conventional signal processing, and the observation that…
The graph fractional Fourier transform (GFRFT) applies a single global fractional order to all graph frequencies, which restricts its adaptability to diverse signal characteristics across the spectral domain. To address this limitation, in…
Graph signal processing, like the graph Fourier transform, requires the full graph signal at every vertex of the graph. However, in practice, only signals at a subset of vertices may be available. We propose a subgraph signal processing…
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…
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,…
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…
Traditional directed graph signal processing generally depends on fixed representation matrices, whose rigid structures limit the model's ability to adapt to complex graph topologies. To address this issue, this study employed the unified…
In many domains data is currently represented as graphs and therefore, the graph representation of this data becomes increasingly important in machine learning. Network data is, implicitly or explicitly, always represented using a graph…
With the wide application of spectral and algebraic theory in discrete signal processing techniques in the field of graph signal processing, an increasing number of signal processing methods have been proposed, such as the graph Fourier…
Many real-world networks are characterized by directionality; however, the absence of an appropriate Fourier basis hinders the effective implementation of graph signal processing techniques. Inspired by discrete signal processing, where…
Graph signal processing (GSP) has become an important tool in many areas such as image processing, networking learning and analysis of social network data. In this paper, we propose a broader framework that not only encompasses traditional…
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,…
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…
Graph signal processing extends spectral analysis to data supported on irregular domains. Existing fractional transforms for two-dimensional graph signals, including the two-dimensional graph fractional Fourier transform (GFRFT), typically…