Spline-Like Wavelet Filterbanks With Perfect Reconstruction on Arbitrary Graphs
Junxia You, Lihua Yang · IEEE Transactions on Signal and Information Processing over Networks · 2023
In this work, we propose a class of spline-like wavelet filterbanks for graph signals. These filterbanks possess the properties of critical sampling and perfect reconstruction. The analysis filters are localized in the graph domain because they are polynomials in the normalized adjacency matrix of the graph. We generalize the spline-like filters in the literature so that the lowpass filter and the highpass filter can respectively remove the$s$highest frequency components and the$r$lowest frequency components of the signal, where$r$and$s$are hyperparameters specified by the users. Optimization models are formulated for the analysis filters to approximate the desired responses. Experimental results demonstrate the good locality and denoising ability of the proposed filterbanks.