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Critically-sampled perfect-reconstruction spline-wavelet filterbanks for graph signals

Inspired by first-order spline wavelets in classical signal processing, we introduce two-channel (low-pass and high-pass), critically-sampled, perfect-reconstruction filterbanks for signals defined on circulant graphs, which accommodate linear shift-invariant filtering. We then generalize to filters that process signals defined on noncirculant graphs. We apply these filters, which can be tuned to approximate desired frequency responses, to signals defined on synthetic graphs and examine their performance.