Related papers: Graph Signal Processing -- Part II: Processing and…
In the field of graph signal processing (GSP), directed graphs present a particular challenge for the "standard approaches" of GSP to due to their asymmetric nature. The presence of negative- or complex-weight directed edges, a graphical…
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…
Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains…
Contemporary data is often supported by an irregular structure, which can be conveniently captured by a graph. Accounting for this graph support is crucial to analyze the data, leading to an area known as graph signal processing (GSP). The…
Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal…
We present a framework for representing and modeling data on graphs. Based on this framework, we study three typical classes of graph signals: smooth graph signals, piecewise-constant graph signals, and piecewise-smooth graph signals. For…
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…
Graph signal processing is a framework to handle graph structured data. The fundamental concept is graph shift operator, giving rise to the graph Fourier transform. While the graph Fourier transform is a centralized procedure, distributed…
As irregularly structured data representations, graphs have received a large amount of attention in recent years and have been widely applied to various real-world scenarios such as social, traffic, and energy settings. Compared to…
Graph signal processing analyzes signals supported on the nodes of a graph by defining the shift operator in terms of a matrix, such as the graph adjacency matrix or Laplacian matrix, related to the structure of the graph. With respect to…
Vertex based and spectral based GSP sampling has been studied recently. The literature recognizes that methods in one domain do not have a counterpart in the other domain. This paper shows that in fact one can develop a unified graph signal…
Graph Fourier transform (GFT) is a fundamental concept in graph signal processing. In this paper, based on singular value decomposition of Laplacian, we introduce a novel definition of GFT on directed graphs, and use singular values of…
In classic graph signal processing, given a real-valued graph signal, its graph Fourier transform is typically defined as the series of inner products between the signal and each eigenvector of the graph Laplacian. Unfortunately, this…
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…
On the Euclidean domains of classical signal processing, linking of signal samples to the underlying coordinate structure is straightforward. While graph adjacency matrices totally define the quantitative associations among the underlying…
One of the most crucial challenges in graph signal processing is the sampling of bandlimited graph signals, i.e., signals that are sparse in a well-defined graph Fourier domain. So far, the prior art is mostly focused on (sub)sampling…
Signal analysis on graphs relies heavily on the graph Fourier transform, which is defined as the projection of a signal onto an eigenbasis of the associated shift operator. Large graphs of similar structure may be represented by a graphon.…
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…
Graph signal processing represents an important advancement in the field of data analysis, extending conventional signal processing methodologies to complex networks and thereby facilitating the exploration of informative patterns and…
Sampling methods for graph signals in the graph spectral domain are presented. Though conventional sampling of graph signals can be regarded as sampling in the graph vertex domain, it does not have the desired characteristics in regard to…