Imperial College London
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ProfessorPier LuigiDragotti

Faculty of Engineering, Department of Electrical and Electronic Engineering

Professor of Signal Processing
 
 
 
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Contact

 

+44 (0)20 7594 6192p.dragotti

 
 
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Location

 

814Electrical EngineeringSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Kotzagiannidis:2019:10.1016/j.acha.2017.10.002,
author = {Kotzagiannidis, MS and Dragotti, PL},
doi = {10.1016/j.acha.2017.10.002},
journal = {Applied and Computational Harmonic Analysis},
pages = {481--515},
title = {Splines and Wavelets on Circulant Graphs},
url = {http://dx.doi.org/10.1016/j.acha.2017.10.002},
volume = {47},
year = {2019}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We present novel families of wavelets and associated filterbanks for the analysis and representation of functions defined on circulant graphs. In this work, we leverage the inherent vanishing moment property of the circulant graph Laplacian operator, and by extension, the e-graph Laplacian, which is established as a parameterization of the former with respect to the degree per node, for the design of vertex-localized and critically-sampled higher-order graph (e-)spline wavelet filterbanks, which can reproduce and annihilate classes of (exponential) polynomial signals on circulant graphs. In addition, we discuss similarities and analogies of the detected properties and resulting constructions with splines and spline wavelets in the Euclidean domain. Ultimately, we consider generalizations to arbitrary graphs in the form of graph approximations, with focus on graph product decompositions. In particular, we proceed to show how the use of graph products facilitates a multi-dimensional extension of the proposed constructions and properties.
AU  - Kotzagiannidis,MS
AU  - Dragotti,PL
DO  - 10.1016/j.acha.2017.10.002
EP  - 515
PY  - 2019///
SN  - 1096-603X
SP  - 481
TI  - Splines and Wavelets on Circulant Graphs
T2  - Applied and Computational Harmonic Analysis
UR  - http://dx.doi.org/10.1016/j.acha.2017.10.002
UR  - http://hdl.handle.net/10044/1/53058
VL  - 47
ER  -
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