Quantum mechanics

Algorithm

Theoretical computer science

Computer science

Orthonormal basis

Physics

Graph

Mathematics

Mathematical analysis

Geometry

Voronoi diagram

Fourier transform

IEEE Transactions on Signal Processing

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.

Irregularity-Aware Graph Fourier Transforms