图信号处理中平移算子的推广
Translation Operator in Graph Signal Processing: A Generalized Approach
摘要：
平移（移位）的概念在经典信号处理中是直接的，然而，它在不规则图结构上是具有挑战性的。在这项工作中，我们提出了一种方法来表征在各种信号域的翻译算子。通过对经典域的自然推广，可以描述图翻译运算符的抽象表示。然后，我们提出了一个等距平移算子的联合时间-顶点域一致的抽象形式的其他区域的翻译操作。我们还展示了这一概念和薛定谔方程之间的联系，一个动态系统，有趣地描述了背后的想法图上的翻译。
英文摘要：
The notion of translation (shift) is straightforward in classical signal processing, however, it is challenging on an irregular graph structure. In this work, we present an approach to characterize the translation operator in various signal domains. By a natural generalization from classical domains, one can characterize an abstract representation for the graph translation operator. Then we propose an isometric translation operator in joint time-vertex domain consistent with the abstract form of translation operators in other domains. We also demonstrate the connection between this notion and the Schrödinger equation on a dynamic system which intriguingly describes the idea behind translation on graph.
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