Unlimited dynamic range signal recovery for folded graph signals

Abstract

Recovery of a graph signal from samples has many important applications in signal processing over networks and graph-structured data. To capture very high or even unlimited dynamic range signals, modulo sampling has been investigated. Folded signals are signals generated from a modulo operation. In this paper, we investigate the problem of recovering bandlimited graph signals from folded signal samples. We derive sufficient conditions to achieve successful recovery of the graph signal, which can be achieved via integer programming. To resolve the scalability issue of integer programming, we propose a sparse optimization recovery method for graph signals satisfying certain technical conditions. Such an approach requires a novel graph sampling scheme that selects vertices with small signal variation. The proposed algorithm exploits the inherent relationship among the graph vertices in both the vertex and time domains to recover the graph signal from folded samples. Simulations and experiments validate the feasibility of our proposed approach.