Topics in Graph Signal Processing: Convolution and Modulation

Shi, John; Moura, J.M.F.

doi:10.1109/ieeeconf44664.2019.9049012

Cited by 15 publications

(18 citation statements)

References 45 publications

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“…Similar concepts were also presented in [21] as well as [3,4,10,16]. Specifically, [21] considered the same framework as [9]. However, although the dual graph presented in [21] specializes to classical temporal signal processing, it misses certain desirable properties that we discuss in the current paper.…”

Section: Introductionmentioning

confidence: 95%

“…We first proposed this idea in [9], and the current work can be considered an extension of that paper. Similar concepts were also presented in [21] as well as [3,4,10,16]. Specifically, [21] considered the same framework as [9].…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, [21] considered the same framework as [9]. However, although the dual graph presented in [21] specializes to classical temporal signal processing, it misses certain desirable properties that we discuss in the current paper. For instance reordering the nodes of the primal graph or re-ordering the graph frequency modes and related graph frequencies, both lead to a different dual graph whereas the primal graph basically did not change.…”

Section: Introductionmentioning

confidence: 99%

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The Dual Graph Shift Operator: Identifying the Support of the Frequency Domain

Leus

Segarra

Ribeiro

et al. 2021

J Fourier Anal Appl

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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 two most important tools in GSP are the graph shift operator (GSO), which is a sparse matrix accounting for the topology of the graph, and the graph Fourier transform (GFT), which maps graph signals into a frequency domain spanned by a number of graph-related Fourier-like basis vectors. This alternative representation of a graph signal is denominated the graph frequency signal. Several attempts have been undertaken in order to interpret the support of this graph frequency signal, but they all resulted in a one-dimensional interpretation. However, if the support of the original signal is captured by a graph, why would the graph frequency signal have a simple one-dimensional support? Departing from existing work, we propose an irregular support for the graph frequency signal, which we coin dual graph. A dual GSO leads to a better interpretation of the graph frequency signal and its domain, helps to understand how the different graph frequencies are related and clustered, enables the development of better graph filters and filter banks, and facilitates the generalization of classical SP results to the graph domain.

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Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Dual Graph Shift Operator: Identifying the Support of the Frequency Domain

Leus

Segarra

Ribeiro

et al. 2021

J Fourier Anal Appl

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show abstract

“…Graph signal processing extends classical digital signal processing (DSP) technologies to signals that reside on irregular structures [1,2]. Some important concepts in DSP have been extended to GSP, such as the graph shift, graph Fourier transform (GFT) [3], graph filter [4,5,6], graph convolution and modulation [7], etc. Among these concepts, Graph filter and GFT are important tools to process the graph signal.…”

Section: Introductionmentioning

confidence: 99%

“…Among these concepts, Graph filter and GFT are important tools to process the graph signal. They have shown their advantage in graph neural networks [7,8], graph signal denoising [9,10,11], graph signal recovery [12], speech enhancement [13,14] and others.…”

Section: Introductionmentioning

confidence: 99%

Optimal Fractional Fourier Filtering in Time-vertex Graphs signal processing

Ge¹,

Guo²,

Wang³

et al. 2022

Preprint

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Graph signal processing (GSP) is an effective tool in dealing with data residing on irregular domains. In GSP, the optimal graph filter is one of the essential techniques, owing to its ability to recover the original signal from the distorted and noisy version. However, most current research focuses on static graph signals and ordinary space/time or frequency domains. The time-varying graph signals have a strong ability to capture the features of real-world data, and fractional domains can provide a more suitable space to separate the signal and noise. In this paper, the optimal time-vertex graph filter and its Wiener-Hopf equation are developed, using the product graph framework. Furthermore, the optimal time-vertex graph filter in fractional domains is also developed, using the graph fractional Laplacian operator and graph fractional Fourier transform.Numerical simulations on real-world datasets will demonstrate the superiority of the optimal time-vertex graph filter in fractional domains over the optimal time-vertex graph filter in ordinary domains and the optimal static graph filter in fractional domains.

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The Optimal Joint Time-Vertex Graph Filter Design: From Ordinary Graph Fourier Domains to Fractional Graph Fourier Domains

Guo

Wang

et al. 2023

Circuits Syst Signal Process

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Topics in Graph Signal Processing: Convolution and Modulation

Cited by 15 publications

References 45 publications

The Dual Graph Shift Operator: Identifying the Support of the Frequency Domain

The Dual Graph Shift Operator: Identifying the Support of the Frequency Domain

Optimal Fractional Fourier Filtering in Time-vertex Graphs signal processing

The Optimal Joint Time-Vertex Graph Filter Design: From Ordinary Graph Fourier Domains to Fractional Graph Fourier Domains

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