Graph signal processing (GSP) is an important methodology for studying data residing on irregular structures. Because acquired data are increasingly taking the form of multiway tensors, new signal processing tools are needed to maximally utilize the multiway structure within the data. In this article, we review modern signal processing frameworks that generalize GSP to multiway data, starting from graph signals coupled to familiar regular axes, such as time in sensor networks, and then extending to general graphs across all tensor modes. This widely applicable paradigm motivates reformulating and improving classical problems and approaches to creatively address the challenges in tensor-based data. We synthesize common themes arising from current efforts to combine GSP with tensor analysis and highlight future directions in extending GSP to the multiway paradigm.

中文翻译：

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张量上的多路图信号处理：不规则几何的综合分析

图信号处理 (GSP) 是研究驻留在不规则结构上的数据的重要方法。由于获取的数据越来越多地采用多路张量的形式，因此需要新的信号处理工具来最大限度地利用数据中的多路结构。在本文中，我们回顾了将 GSP 推广到多路数据的现代信号处理框架，从耦合到熟悉的规则轴（例如传感器网络中的时间）的图形信号开始，然后扩展到所有张量模式的通用图形。这种广泛适用的范式促使重新制定和改进经典问题和方法，以创造性地解决基于张量的数据中的挑战。