A General Convolution Theorem for Graph Data

This paper focuses on the field of graph signal processing (GSP) and studies the node-varying graph filter (NV-GF) which has been proposed as a way to broaden the applicability of the classical graph filter (C-GF). In particular, we state and prove a new convolution theorem for a NV-GF which extends both the one for a C-GF and the one for a time-varying filter. The theorem relies on the definition of a so-called dual graph which characterizes the support of the frequency domain. The dual graph concept has been studied only very recently and many versions exist, yet the proposed convolution theorem is independent of the particular version. More interestingly, using non-stationary graph data on the primal graph, we can use the proposed convolution theorem to learn the dual graph and thereby introduce an innovative data-driven dual graph estimation technique.