Critical Sampling For Wavelet Filterbanks On Arbitrary Graphs

Current formulations of critically-sampled graph wavelet filterbanks work only for bipartite graphs where downsampling signals on either partition leads to a spectrum folding phenomenon. The lack of such a natural downsampling scheme for arbitrary graphs poses difficulties in designing filterbanks. In this paper, we propose a critical sampling scheme on an arbitrary graph that chooses a sampling set for each channel, given a set of analysis/synthesis filters, by seeking to minimize a bound on the overall reconstruction error associated with the filterbank. Our algorithm is efficient since it requires a few simple graph filtering operations in each iteration. Our initial experiments show that its output is consistent with the sampling scheme for bipartite graphs and results in superior performance over other methods.