Graph signal processing (GSP) is a field that deals with data residing on irregular domains, i.e. graph signals. In this field, the graph filter bank is one of the most important developments, owing to its ability to provide multiresolution analysis of graph signals. However, most of the current research on graph filter bank focuses on static graph signals. The research does not exploit the temporal correlations of time-varying signals in real-world applications, such as in wireless sensor networks. In this paper, the theory and design of joint time-vertex nonsubsampled filter bank are developed, using a generalized product graph framework. Several methods are proposed to design the filter bank with perfect reconstruction, while still achieving filters with good spectral characteristics. A notable feature of the designed filter bank is that it can be completely realized in a distributed manner. The subband filters are either of polynomial type or defined implicitly via iterative equations. In either case, implementing the subband filters requires only the exchange of information between neighboring nodes. The filter banks are therefore of low implementation complexity and suitable for processing large time-varying datasets. Numerical examples will demonstrate the effectiveness of the proposed designed methods. Application in time-varying graph signal denoising will show the superiority of joint time-vertex filter bank over other methods.

中文翻译：

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联合时间顶点非下采样滤波器组的理论与设计

图形信号处理（GSP）是处理驻留在不规则域（即图形信号）上的数据的领域。在该领域，图形滤波器组是最重要的发展之一，因为它具有提供图形信号多分辨率分析的能力。然而，当前关于图滤波器组的大多数研究都集中在静态图信号上。该研究未利用诸如无线传感器网络之类的实际应用中时变信号的时间相关性。本文采用广义乘积图框架，开发了联合时间-顶点非下采样滤波器组的理论和设计。提出了几种方法来设计具有完美重构的滤波器组，同时仍能实现具有良好光谱特性的滤波器。设计的滤波器组的显着特点是可以完全分布式地实现。子带滤波器可以是多项式类型，也可以通过迭代方程式隐式定义。在任一情况下，实现子带滤波器仅需要相邻节点之间的信息交换。因此，滤波器组的实现复杂度较低，并且适合于处理较大的时变数据集。数值示例将证明所提出的设计方法的有效性。在时变图信号去噪中的应用将显示联合时顶点滤波器组比其他方法的优越性。实现子带滤波器仅需要相邻节点之间的信息交换。因此，滤波器组的实现复杂度较低，并且适合于处理较大的时变数据集。数值示例将证明所提出的设计方法的有效性。在时变图信号去噪中的应用将显示联合时顶点滤波器组比其他方法的优越性。实现子带滤波器仅需要相邻节点之间的信息交换。因此，滤波器组的实现复杂度较低，并且适合于处理较大的时变数据集。数值示例将证明所提出的设计方法的有效性。在时变图信号去噪中的应用将显示联合时顶点滤波器组比其他方法的优越性。