The modeling of time-varying graph signals as stationary time-vertex stochastic processes permits the inference of missing signal values by efficiently employing the correlation patterns of the process across different graph nodes and time instants. In this study, we first propose an algorithm for computing graph autoregressive moving average (graph ARMA) processes based on learning the joint time-vertex power spectral density of the process from its incomplete realizations. Our solution relies on first roughly estimating the joint spectrum of the process from partially observed realizations and then refining this estimate by projecting it onto the spectrum manifold of the ARMA process. We then present a theoretical analysis of the sample complexity of learning graph ARMA processes. Experimental results show that the proposed approach achieves improvement in the time-vertex signal estimation performance in comparison with reference approaches in the literature.

翻译：将时变图信号建模为平稳时间-顶点随机过程，可以通过有效利用该过程在不同图节点和时间瞬间上的相关模式来推断缺失信号值。本研究首先提出一种算法，基于从不完整实现中学习联合时间-顶点功率谱密度，来计算图自回归移动平均（图ARMA）过程。该解决方案首先从部分观测的实现中粗略估计过程的联合谱，然后通过将该估计投影到ARMA过程的谱流形上进行精化。随后，本文对学习图ARMA过程的样本复杂度进行了理论分析。实验结果表明，与文献中的参考方法相比，所提出的方法在时间-顶点信号估计性能上实现了改进。