Name
Title | ||
|---|---|---|
A Framework of Adaptive Multiscale Wavelet Decomposition for Signals on Undirected Graphs |
Abstract | ||
|---|---|---|
The state-of-the-art graph wavelet decomposition was constructed by maximum spanning tree (MST)-based downsampling and two-channel graph wavelet filter banks. In this work, we first show that: 1) the existing MST-based downsampling could become unbalanced, i.e., the sampling rate is far from 1/2, which eventually leads to low representation efficiency of the wavelet decomposition; and 2) not only low-pass components, but also some high-pass ones can be decomposed to potentially achieve better decomposition performance. Based on these observations, we propose a new framework of adaptive multiscale graph wavelet decomposition for signals defined on undirected graphs. Specifically, our framework consists of two phases. Phase 1, called pre-processing, addresses the downsampling unbalance issues. We design maximal decomposition level estimation, unbalance detection, and unbalance reduction algorithms such that the downsampling rates of all levels are close to 1/2. Phase 2 concerns about adaptively finding low- or high-pass components that are worthy to be decomposed to improve the compactness of the decomposition. We suggest a graph signal Shannon-entropy-based adaptive decomposition algorithm. With applications on synthetic and real-world graph signals, we demonstrate that our framework provides better performance in terms of downsampling balance and signal compression, compared with other graph wavelet decomposition methods. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1109/TSP.2019.2896246 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
Wavelet packets,Signal processing,Eigenvalues and eigenfunctions,Laplace equations,Information science,Discrete wavelet transforms | Graph,Signal processing,Mathematical optimization,Sampling (signal processing),Algorithm,Compact space,Spanning tree,Upsampling,Wavelet packet decomposition,Mathematics,Signal compression | Journal |
Volume | Issue | ISSN |
67 | 7 | 1053-587X |
Citations | PageRank | References |
2 | 0.36 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xianwei Zheng | 1 | 14 | 4.75 |
| Yuan Yan Tang | 2 | 10 | 2.23 |
| Jiantao Zhou | 3 | 580 | 78.87 |