Critically-Sampled Graph Filter Banks with Spectral Domain Sampling

This paper presents a framework for perfect reconstruction two-channel critically-sampled graph filter banks with spectral domain sampling. Graph signals have a unique characteristic: sampling in the vertex and graph spectral domains are generally different, in contrast to classical signal processing. Conventional graph filter banks are designed using vertex domain sampling, whereas the proposed approach utilizes a novel spectral domain sampling. Our proposed technique leads to perfect reconstruction transforms for any type of undirected graphs and can be applied both to combinatorial and symmetric normalized graph Laplacians. Some filter bank designs and an experiment on nonlinear approximation are shown to validate their effectiveness.