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.

我们提出了一个图信号模型，并将信号恢复任务转化为对应的优化问题，通过交替方向乘子方法提供一般解决方案，然后展示了信号修复、矩阵完成、鲁棒主元分析和异常检测等都与图信号恢复有关，提供了相应的特定解决方案和理论分析，最后在在线博客分类、桥梁状况识别、温度估计、推荐系统和在线博客分类专家意见结合等实际恢复问题上验证了所提出的方法。