Two-Channel Critically-Sampled Graph Wavelets With Spectral Domain Sampling
Akie Sakiyama, Kana Watanabe, Yuichi Tanaka, Antonio Ortega · 2018
We propose two-channel critically-sampled wavelet transforms for signals on undirected graphs that utilize spectral domain sampling. Unlike conventional approaches based on vertex domain sampling, our proposed transforms have the following desirable properties: 1) perfect reconstruction regardless of the characteristics of the underlying graphs and graph variation operators, and 2) symmetric structure, i.e., both analysis and synthesis filter banks are built using similar building blocks. The relationships between the proposed wavelets and those using the vertex domain sampling are also described. The effectiveness of our approach is evaluated by comparing their performance in terms of nonlinear approximation and denoising with that of conventional graph wavelets and filter banks.