Spline-Like Wavelet Filterbanks for Multiresolution Analysis of Graph-Structured Data

Multiresolution analysis is important for understanding graph signals, which represent graph-structured data. Wavelet filterbanks permit multiscale analysis and processing of graph signals-particularly, useful for harvesting large-scale data. Inspired by first-order spline wavelets in classical signal processing, we introduce two-channel (low-pass and high-pass) wavelet filterbanks for graph signals. This class of filterbanks boasts several useful properties, such as critical sampling, perfect reconstruction, and graph invariance. We consider an application in graph semi-supervised learning and propose a wavelet-regularized semi-supervised learning algorithm that is competitive for certain synthetic and real-world data.