This article provides an overview of the current landscape of signal processing (SP) on directed graphs (digraphs). Directionality is inherent to many real-world (information, transportation, biological) networks, and it should play an integral role in processing and learning from network data. We thus lay out a comprehensive review of recent advances in SP on digraphs, offering insights through comparisons with results available for undirected graphs, discussing emerging directions, establishing links with related areas in machine learning and causal inference in statistics as well as illustrating their practical relevance to timely applications. To this end, we begin by surveying (orthonormal) signal representations and their graph-frequency interpretations based on novel measurements of signal variation for digraphs. We then move on to filtering, a central component in deriving a comprehensive theory of SP on digraphs. Indeed, through the lens of filter-based generative signal models, we explore a unified framework to study inverse problems (e.g., sampling and deconvolution on networks), the statistical analysis of random signals, and the topology inference of digraphs from nodal observations.

中文翻译：

---

有向图上的信号处理：边方向性在处理和学习网络数据时的作用


本文概述了有向图（有向图）上的信号处理 (SP) 的当前前景。方向性是许多现实世界（信息、交通、生物）网络所固有的，它应该在处理和学习网络数据中发挥不可或缺的作用。因此，我们对有向图 SP 的最新进展进行了全面回顾，通过与无向图可用结果的比较提供见解，讨论新兴方向，与机器学习和统计学中的因果推理相关领域建立联系，并说明它们的实际相关性以便及时申请。为此，我们首先基于有向图信号变化的新颖测量来调查（正交）信号表示及其图频率解释。然后我们继续讨论过滤，这是推导有向图 SP 综合理论的核心组成部分。事实上，通过基于滤波器的生成信号模型，我们探索了一个统一的框架来研究逆问题（例如，网络上的采样和反卷积）、随机信号的统计分析以及节点观测有向图的拓扑推断。