  We consider the problem of signal recovery on graphs as graphs model data
with complex structure as signals on a graph. Graph signal recovery implies
recovery of one or multiple smooth graph signals from noisy, corrupted, or
incomplete measurements. We propose a graph signal model and formulate signal
recovery as a corresponding optimization problem. We provide a general solution
by using the alternating direction methods of multipliers. We next 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. Finally, we validate
the proposed methods on real-world recovery problems, including online blog
classification, bridge condition identification, temperature estimation,
recommender system, and expert opinion combination of online blog
classification.
