Oversampled Graph Laplacian Matrix for Graph Filter Banks

We describe a method of oversampling signals defined on a weighted graph by using an oversampled graph Laplacian matrix. The conventional method of using critically sampled graph filter banks has to decompose the original graph into bipartite subgraphs, and a transform has to be performed on each subgraph because of the spectral folding phenomenon caused by downsampling of graph signals. Therefore, the conventional method cannot always utilize all edges of the original graph in a single stage transformation. Our method is based on oversampling of the underlying graph itself, and it can append nodes and edges to the graph somewhat arbitrarily. We use this approach to make one oversampled bipartite graph that includes all edges of the original non-bipartite graph. We apply the oversampled graph with the critically sampled graph filter bank or the oversampled one for decomposing graph signals and show the performances on some experiments.