Recovery of Time Series of Graph Signals Over Dynamic Topology

Conventional studies on time-varying graph signal recovery involve leveraging priors of both temporal and vertex domains for effective estimations. However, these methods all assume a static graph, in spite of the time-varying signals. We believe that such assumption, a static graph signal model, is insufficient to represent some cases where the underlying graph is explicitly dynamic. In this paper, we propose a novel recovering framework for dynamic graph signal models that leverage both temporal and vertex-domain priors. To achieve this, we introduce regularization terms in a convex optimization problem that capture behaviors of graph signals in the two domains, respectively, and integrate the dynamics of the dynamic graph topology into the formulation. We compare the proposed framework to the conventional framework through experiments on synthetic datasets to show the advantageous results of our method in numerous settings.

I. Introduction

The concept of graph signal, defined by signal values observed on the vertex set of a graph , has been intensely researched as an approach to represent data of irregular structures. Conventional signal processing is based on spatially or temporally regular structures, e.g. images and sounds, and thus, the relations between signal values are also regular, which provides no further information for us to leverage. On the other hand, graph signal representations and graph signal processing [1]–[3] explicitly represent relations between signal values with vertices and weighed edges, which we can exploit as priors in the vertex domain. Data of irregular structures such as traffic and sensor network data, mesh data, and biomedical data all benefit from such representation.