Case study for graph signal denoising by graph structure similarity

We study the denoising performance of several graph wavelet filter banks and image modeling with graph to enhance understanding of the relationship between graph signals and underlying structure. We design a new metric for measuring graph structure similarity (GSSIM) to evaluate those methods. GSSIM is positively related to PSNR as an index of corrupted signal with an additive Gaussian noise in the references and it is aware of graph structure. Subgraph-Based filter banks are superior to others in graph signal denoising. We introduce the idea of group-based approaches by removing edges between different groups, a set of communities with similar average. It can improve the signal to noise ratio substantially and reduce the high frequency loss. We demonstrate GSSIM is promise through intuitive examples. Group-based analysis improves the denoising effect of all the methods studied.