Oversampled Graph Laplacian Matrix for Graph Filter Banks


Using an oversampled graph Laplacian matrix, we describe a method for oversampling signals that are defined on a weighted graph. Because of the spectral folding phenomenon, which is brought on by the downsampling of graph signals, the traditional method of employing critically sampled graph filter banks requires the original graph to be decomposed into bipartite subgraphs. Additionally, a transform must be carried out on each of the subgraphs. As a result, the traditional method is unable to consistently utilize all of the edges of the initial graph in a single stage transformation. Our method is based on oversampling the underlying graph itself, and it has the ability to append nodes and edges to the graph in a relatively arbitrary fashion. Using this strategy, we will create one oversampled bipartite graph that contains all of the edges that were present in the initial non-bipartite graph. For the purpose of decomposing graph signals, we apply the oversampled graph in conjunction with either the critically sampled graph filter bank or the oversampled one. We then show the performances of this method on a few experiments.

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