Oversampled graph laplacian matrix for graph signals

In this paper, we propose oversampling of graph signals by using oversampled graph Laplacian matrix. The conventional critically sampled graph filter banks have to decompose an original graph into bipartite subgraphs, and the transform has to be performed on each subgraph due to the spectral folding phenomenon caused by downsampling of graph signals. Therefore, they cannot always utilize all edges of the original graph for the one-stage transformation. Our proposed 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 filter bank for decomposing graph signals, and show the performance of graph signal denoising.