Theory and Design of Joint Time-Vertex Nonsubsampled Filter Banks

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.