Edge-aware image graph expansion methods for oversampled graph Laplacian matrix

Graph signals can represent high-dimensional data effectively and images can also be viewed as signals on weighted graphs by connecting the pixels with their neighboring ones. Recently, we proposed the graph oversampling methods for signal processing on graphs that appends nodes and links to the original graph to obtain an oversampled graph Laplacian matrix. In this paper, we consider new over-sampling methods of image graphs. By using the graph oversampling, we can make a bipartite graph that considers rectangular and diagonal connections simultaneously, while it cannot be realized by conventional critically sampled bipartite graphs. Furthermore, expanding the graphs according to the edge information enables us to decompose the image with the edge-preserving property. We perform the critically sampled graph filter bank on the oversampled graph and show that the proposed method outperforms other transforms, including the critically sampled graph filter banks and the graph Laplacian pyramid, in non-linear approximation and denoising experiments.