Graph Fourier Transform Based on Norm Variation Minimization
arXiv:1908.06672 · doi:10.1016/j.acha.2020.04.001
Abstract
The definition of the graph Fourier transform is a fundamental issue in graph signal processing. Conventional graph Fourier transform is defined through the eigenvectors of the graph Laplacian matrix, which minimize the norm signal variation. However, the computation of Laplacian eigenvectors is expensive when the graph is large. In this paper, we propose an alternative definition of graph Fourier transform based on the norm variation minimization. We obtain a necessary condition satisfied by the Fourier basis, and provide a fast greedy algorithm to approximate the Fourier basis. Numerical experiments show the effectiveness of the greedy algorithm. Moreover, the Fourier transform under the greedy basis demonstrates a similar rate of decay to that of Laplacian basis for simulated or real signals.
References in corpus (8)
- The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
- Discrete Signal Processing on Graphs
- Discrete Signal Processing on Graphs: Sampling Theory
- A Spectral Graph Uncertainty Principle
- On the Graph Fourier Transform for Directed Graphs
- Sparse Representation on Graphs by Tight Wavelet Frames and Applications
- Subgraph-based filterbanks for graph signals
- Approximate fast graph Fourier transforms via multi-layer sparse approximations