On Folded Graph Signals | IEEE Conference Publication | IEEE Xplore

On Folded Graph Signals

Publisher: IEEE

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 anal...View more

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.
Date of Conference: 11-14 November 2019
Date Added to IEEE Xplore: 28 January 2020
ISBN Information:
Publisher: IEEE
Conference Location: Ottawa, ON, Canada

I. Introduction

Graph signal processing is an emerging field that studies multidimensional signals embedded in a graph which represents the inherent relationship among the different entities [1]. Graph signal processing has attracted an increased attention as it allows us to capture complex correlations in many practical problems. Thus, it has been readily applied for various problems consisting of signal recovery, prediction, and anomaly detection [2]. Recently, much work has been devoted to graph sampling, which studies recovery of entire graph signal using observations at only some of the nodes [3]–[8].

References

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