Papers › Localized Fourier Analysis for Graph Signal Processing
Localized Fourier Analysis for Graph Signal Processing
Basile de Loynes, Fabien Navarro, Baptiste Olivier
We propose a new point of view in the study of Fourier analysis on graphs, taking advantage of localization in the Fourier domain. For a signal f on vertices of a weighted graph 𝒢 with Laplacian matrix ℒ, standard Fourier analysis of f relies on the study of functions g(ℒ)f for some filters g on I_ℒ, the smallest interval containing the Laplacian spectrum sp(ℒ) ⊂I_ℒ. We show that for carefully chosen partitions I_ℒ = ⊔_(1≤k≤K) Iₖ (Iₖ ⊂I_ℒ), there are many advantages in understanding the collection (g(ℒ_(Iₖ))f)_(1≤k≤K) instead of g(ℒ)f directly, where ℒ_I is the projected matrix P_I(ℒ)ℒ. First, the partition provides a convenient modelling for the study of theoretical properties of Fourier analysis and allows for new results in graph signal analysis (\emph{e.g.} noise level estimation, Fourier support approximation). We extend the study of spectral graph wavelets to wavelets localized in the Fourier domain, called LocLets, and we show that well-known frames can be written in terms of LocLets. From a practical perspective, we highlight the interest of the proposed localized Fourier analysis through many experiments that show significant improvements in two different tasks on large graphs, noise level estimation and signal denoising. Moreover, efficient strategies permit to compute sequence (g(ℒ_(Iₖ))f)_(1≤k≤K) with the same time complexity as for the computation of g(ℒ)f.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Tasks
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections