Two-Channel Critically-Sampled Graph Filter Banks With Spectral Domain Sampling

We propose two-channel critically-sampled filter banks for signals on undirected graphs that utilize spectral domain sampling. Unlike conventional approaches based on vertex domain sampling, our transforms have the following desirable properties: 1) perfect reconstruction regardless of the character...

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Bibliographic Details
Published in:arXiv.org 2019-01
Main Authors: Sakiyama, Akie, Watanabe, Kana, Tanaka, Yuichi, Ortega, Antonio
Format: Article
Language:English
Subjects:
Filter banks
Graphs
Noise reduction
Reconstruction
Sampling
Spectra
Wavelet transforms
Online Access:Get full text
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Description
Summary:We propose two-channel critically-sampled filter banks for signals on undirected graphs that utilize spectral domain sampling. Unlike conventional approaches based on vertex domain sampling, our transforms have the following desirable properties: 1) perfect reconstruction regardless of the characteristics of the underlying graphs and graph variation operators and 2) a symmetric structure; i.e., both analysis and synthesis filter banks are built using similar building blocks. Along with the structure of the filter banks, this paper also proves the general criterion for perfect reconstruction and theoretically shows that the vertex and spectral domain sampling coincide for a special case. The effectiveness of our approach is evaluated by comparing its performance in nonlinear approximation and denoising with various conventional graph transforms.
ISSN:2331-8422
DOI:10.48550/arxiv.1804.08811