A Distributed Tracking Algorithm for Reconstruction of Graph Signals

TL;DR

This paper introduces a distributed least squares reconstruction algorithm for efficiently recovering time-varying signals on large-scale graphs, ensuring convergence and effective tracking in distributed sensor networks.

Contribution

It proposes a novel distributed algorithm with decay scheme for reconstructing and tracking graph signals, including convergence proofs and error bounds.

Findings

DLSR effectively tracks slowly time-varying graph signals.

The algorithm guarantees convergence and perfect reconstruction for time-invariant signals.

Numerical experiments validate the algorithm's performance on synthetic and real data.

Abstract

The rapid development of signal processing on graphs provides a new perspective for processing large-scale data associated with irregular domains. In many practical applications, it is necessary to handle massive data sets through complex networks, in which most nodes have limited computing power. Designing efficient distributed algorithms is critical for this task. This paper focuses on the distributed reconstruction of a time-varying bandlimited graph signal based on observations sampled at a subset of selected nodes. A distributed least square reconstruction (DLSR) algorithm is proposed to recover the unknown signal iteratively, by allowing neighboring nodes to communicate with one another and make fast updates. DLSR uses a decay scheme to annihilate the out-of-band energy occurring in the reconstruction process, which is inevitably caused by the transmission delay in distributed systems. Proof of convergence and error bounds for DLSR are provided in this paper, suggesting that the algorithm is able to track time-varying graph signals and perfectly reconstruct time-invariant signals. The DLSR algorithm is numerically experimented with synthetic data and real-world sensor network data, which verifies its ability in tracking slowly time-varying graph signals.