Nonsubsampled Graph Filter Banks: Theory and Distributed Algorithms

In this paper, we consider nonsubsampled graph filter banks (NSGFBs) to process data on a sparse graph. The analysis filter banks of NSGFBs have small bandwidth, pass/block the normalized constant signal, and have stability on ℓ 2 . Given an analysis filter bank with small bandwidth, we introduce al...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 67; no. 15; pp. 3938 - 3953
Main Authors: Jiang, Junzheng, Cheng, Cheng, Sun, Qiyu
Format: Journal Article
Language:English
Published: New York IEEE 01.08.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Bandwidth
Data processing
distributed algorithm
Filter banks
graph filter bank
Graph signal processing
Iterative algorithms
Iterative methods
Laplace equations
Noise
Noise (mathematics)
Noise reduction
nonsubsampled
Optimization
Shot noise
Signal reconstruction
spatially distributed network
Stability analysis
Symmetric matrices
Wavelet transforms
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary:In this paper, we consider nonsubsampled graph filter banks (NSGFBs) to process data on a sparse graph. The analysis filter banks of NSGFBs have small bandwidth, pass/block the normalized constant signal, and have stability on ℓ 2 . Given an analysis filter bank with small bandwidth, we introduce algebraic and optimization methods to construct well-localized synthesis filter banks such that the corresponding NSGFBs provide a perfect signal reconstruction in the noiseless setting. We also prove that the proposed NSGFBs can control the resonance effect in the presence of bounded noise and they can limit the influence of shot noise primarily to a small neighborhood near its location on the graph. We later introduce an iterative algorithm to implement the proposed NSGFBs in a distributed manner, and develop an NSGFB-based denoising technique which is demonstrated to have satisfactory performance on noise suppression.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2019.2922160