Wavelets on Graphs via Spectral Graph Theory
a day ago
- #graph signal processing
- #spectral graph theory
- #wavelet transforms
- Proposes a method for constructing wavelet transforms on functions defined on vertices of finite weighted graphs.
- Uses spectral graph theory, defining scaling via the graph Fourier domain based on the graph Laplacian's spectral decomposition.
- Defines scaled wavelet operator using a wavelet generating kernel and scale parameter, applied to an indicator function for localization.
- Ensures invertibility through an admissibility condition on the kernel and analyzes wavelet localization at fine scales.
- Introduces a fast Chebyshev polynomial approximation algorithm to compute transforms without diagonalizing the Laplacian.
- Demonstrates potential applications with examples of wavelets on graphs from various problem domains.