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Reconstruction of Graph Signals: Percolation from a Single Seeding Node

Abstract: 

Schemes to reconstruct signals defined in the nodes of a graph are proposed. Our focus is on reconstructing bandlimited graph signals, which are signals that admit a sparse representation in a frequency domain related to the structure of the graph. The schemes, which are designed within the framework of linear shift-invariant graph filters, consider that the signal is injected at a single seeding node. After several sequential applications of the graph-shift operator -- which computes linear combinations of the information available at neighboring nodes -- the seeding signal percolates across the graph. We show that if the node is allowed to change the seeding signal with each application of the shift operator, the original bandlimited signal can be recovered. Conditions under which such a recovery is feasible are identified for two different reconstruction schemes. We illustrate both reconstruction schemes in synthetic graph signals and we analyze their performance in noisy real-world scenarios.

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Paper Details

Authors:
Antonio G. Marques, Geert Leus, Alejandro Ribeiro
Submitted On:
23 February 2016 - 1:44pm
Short Link:
Type:
Presentation Slides
Event:
Presenter's Name:
Alejandro Ribeiro
Document Year:
2015
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GlobalSIP_Interpolation_2015_upload.pdf

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[1] Antonio G. Marques, Geert Leus, Alejandro Ribeiro, "Reconstruction of Graph Signals: Percolation from a Single Seeding Node", IEEE SigPort, 2015. [Online]. Available: http://sigport.org/473. Accessed: Sep. 21, 2020.
@article{473-15,
url = {http://sigport.org/473},
author = {Antonio G. Marques; Geert Leus; Alejandro Ribeiro },
publisher = {IEEE SigPort},
title = {Reconstruction of Graph Signals: Percolation from a Single Seeding Node},
year = {2015} }
TY - EJOUR
T1 - Reconstruction of Graph Signals: Percolation from a Single Seeding Node
AU - Antonio G. Marques; Geert Leus; Alejandro Ribeiro
PY - 2015
PB - IEEE SigPort
UR - http://sigport.org/473
ER -
Antonio G. Marques, Geert Leus, Alejandro Ribeiro. (2015). Reconstruction of Graph Signals: Percolation from a Single Seeding Node. IEEE SigPort. http://sigport.org/473
Antonio G. Marques, Geert Leus, Alejandro Ribeiro, 2015. Reconstruction of Graph Signals: Percolation from a Single Seeding Node. Available at: http://sigport.org/473.
Antonio G. Marques, Geert Leus, Alejandro Ribeiro. (2015). "Reconstruction of Graph Signals: Percolation from a Single Seeding Node." Web.
1. Antonio G. Marques, Geert Leus, Alejandro Ribeiro. Reconstruction of Graph Signals: Percolation from a Single Seeding Node [Internet]. IEEE SigPort; 2015. Available from : http://sigport.org/473