Irregularity-Aware Graph Fourier Transforms Article Swipe
Related Concepts
Graph
Computer science
Fourier transform
Mathematics
Theoretical computer science
Mathematical analysis
Benjamin Girault
,
Antonio Ortega
,
Shrikanth Narayanan
·
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1802.10220
· OA: W4298370222
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1802.10220
· OA: W4298370222
In this paper, we present a novel generalization of the graph Fourier transform (GFT). Our approach is based on separately considering the definitions of signal energy and signal variation, leading to several possible orthonormal GFTs. Our approach includes traditional definitions of the GFT as special cases, while also leading to new GFT designs that are better at taking into account the irregular nature of the graph. As an illustration, in the context of sensor networks we use the Voronoi cell area of vertices in our GFT definition, showing that it leads to a more sensible definition of graph signal energy even when sampling is highly irregular.
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