Graph Signal Denoising Method via Hybrid Neumann-Series and Edge-Variant Graph Filters

In this study, a Tikhonov-based graph signal denoising method is presented. First, the signal denoising problem is formulated as a minimization problem and its optimal solution is required to compute the matrix inverse which only allows the centralized processing. To avoid solving matrix inverse and obtain the distributed implementation, two methods are studied. One is the Neumann-series (NS) method; the other is the edge-variant (EV) filter. As a result, EV filter has faster convergence speed than NS method. However, at steady state, NS method has smaller approximation error than EV filter. Thus, a hybrid denoising method of NS and EV filters is proposed in this paper to get fast convergence speed and smaller approximation error simultaneously. The data from sensor network and social network are used to examine the correctness of the proposed graph signal denoising approach.