Localized Spectral Graph Filter Frames: A Unifying Framework, Survey of Design Considerations, and Numerical Comparison

A major line of work in graph signal processing [2] during the past 10 years has been to design new transform methods that account for the underlying graph structure to identify and exploit structure in data residing on a connected, weighted, undirected graph. The most common approach is to construc...

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Bibliographic Details
Published inIEEE signal processing magazine Vol. 37; no. 6; pp. 43 - 63
Main Author Shuman, David I.
Format Magazine Article
LanguageEnglish
Published New York IEEE 01.11.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Data analysis
Data compression
Density functional theory
Dictionaries
Eigenvalues and eigenfunctions
Filter banks
Graphical models
Inverse problems
Laplace equations
Low-pass filters
Machine learning
Noise reduction
Signal processing
Statistical analysis
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Summary:A major line of work in graph signal processing [2] during the past 10 years has been to design new transform methods that account for the underlying graph structure to identify and exploit structure in data residing on a connected, weighted, undirected graph. The most common approach is to construct a dictionary of atoms (building block signals) and represent the graph signal of interest as a linear combination of these atoms. Such representations enable visual analysis of data, statistical analysis of data, and data compression, and they can also be leveraged as regularizers in machine learning and ill-posed inverse problems, such as inpainting, denoising, and classification.
ISSN:1053-5888
1558-0792
DOI:10.1109/MSP.2020.3015024