On Folded Graph Signals

Feng Ji, Pratibha, Wee Peng Tay

Abstract: Graph sampling allows a multidimensional signal generated on a graph to be represented by the signal at a smaller set of sampled nodes. On the other hand, self-reset analog-to-digital converters (ADCs) are used to sample high dynamic range signals resulting in modulo-operation based folded signals at the sampled nodes. In this paper, we study the problem of continuous-time graph signal recovery from the folded signals at discrete samples. We present a theoretical graph sampling rate that is sufficient for successful reconstruction of the graph signals from the folded signals. We deduce an optimal sample rate to recover a bandlimited continuous-time graph signal, such that integer programming can be applied for small graphs. To resolve the scalability issue of integer programming, we propose a sparse optimization based recovery method for graph signals satisfying certain conditions. Such an approach requires a novel graph sampling scheme that selects nodes with small signal variation. The proposed algorithm emphasizes that in our spatio-temporal sampling scenario, the inherent relationship among the graph nodes should be exploited in addition to the temporal correlation in the graph signal at different nodes to recover the signal.