Signal Recovery on Graphs: Variation Minimization

We consider the problem of signal recovery on graphs. Graphs model data with complex structure as signals on a graph. Graph signal recovery recovers one or multiple smooth graph signals from noisy, corrupted, or incomplete measurements. We formulate graph signal recovery as an optimization problem, for which we provide a general solution through the alternating direction methods of multipliers. We show how signal inpainting, matrix completion, robust principal component analysis, and anomaly detection all relate to graph signal recovery and provide corresponding specific solutions and theoretical analysis. We validate the proposed methods on real-world recovery problems, including online blog classification, bridge condition identification, temperature estimation, recommender system for jokes, and expert opinion combination of online blog classification.

I. Introduction

With the explosive growth of information and communication, signals are being generated at an unprecedented rate from various sources, including social networks, citation, biological, and physical infrastructures [1], [2]. Unlike time-series or images, these signals have complex, irregular structure, which requires novel processing techniques leading to the emerging field of signal processing on graphs.