Graph filter design by ring-decomposition for 2-connected graphs

Abstract

The graph filter is an essential part of graph signal processing. And the design of filters is booming in various applications. However, most previous works on graph filter design consider the entire graph as their object and concentrate on global processing. That causes less efficiency and little attention to some detailed information hidden in graph signals. This paper proposes a framework to design graph filters, named Ring-Decomposition-based Filter (RDF), on 2-connected graphs constructed from a ring by adding paths. The approach designs ring filters to capture small-scale features after decomposing the given graph into a set of rings. Experimental results show that the proposed graph filters outperform the baselines on synthetic and real-world graph signals for denoising and outlier detection tasks. In addition, a computational cost analysis is given to illustrate the efficiency of the proposed graph filters.