Joint Signal Recovery and Graph Learning from Incomplete Time-Series

TL;DR

This paper introduces a novel algorithm for jointly recovering signals and learning underlying graphs from incomplete time-series data, addressing challenges where data is missing and the graph model is unknown.

Contribution

It presents a semi-blind, iterative method based on BSUM for simultaneous graph learning and signal recovery from incomplete observations.

Findings

Effective in synthetic and real data scenarios

Outperforms existing methods in incomplete data settings

Demonstrates accurate graph and signal reconstruction

Abstract

Learning a graph from data is the key to taking advantage of graph signal processing tools. Most of the conventional algorithms for graph learning require complete data statistics, which might not be available in some scenarios. In this work, we aim to learn a graph from incomplete time-series observations. From another viewpoint, we consider the problem of semi-blind recovery of time-varying graph signals where the underlying graph model is unknown. We propose an algorithm based on the method of block successive upperbound minimization (BSUM), for simultaneous inference of the signal and the graph from incomplete data. Simulation results on synthetic and real time-series demonstrate the performance of the proposed method for graph learning and signal recovery.