论文标题
时间vertex图中的最佳分数傅立叶过滤信号处理
Optimal Fractional Fourier Filtering in Time-vertex Graphs signal processing
论文作者
论文摘要
图形信号处理（GSP）是处理位于不规则域中的数据的有效工具。在GSP中，最佳图形滤波器是基本技术之一，因为它可以从变形和嘈杂的版本中恢复原始信号的能力。但是，当前大多数研究都集中在静态图形信号以及普通的空间/时间或频域。随时间变化的图形信号具有捕获现实世界数据功能的强大能力，而分数域可以提供更合适的空间来分离信号和噪声。在本文中，使用产品图形框架开发了最佳的时间Vertex图形滤镜及其Wiener-HOPF方程。此外，还使用图形分数拉普拉斯运算符和图分数傅立叶变换开发了分数域中最佳的时间vertex图形滤波器。现实世界数据集上的数值模拟将证明比普通域中的最佳时间范围域中最佳的时间vertex图形滤波器的优越性，以及在分数域中的最佳静态图形滤波器。
Graph signal processing (GSP) is an effective tool in dealing with data residing in irregular domains. In GSP, the optimal graph filter is one of the essential techniques, owing to its ability to recover the original signal from the distorted and noisy version. However, most current research focuses on static graph signals and ordinary space/time or frequency domains. The time-varying graph signals have a strong ability to capture the features of real-world data, and fractional domains can provide a more suitable space to separate the signal and noise. In this paper, the optimal time-vertex graph filter and its Wiener-Hopf equation are developed, using the product graph framework. Furthermore, the optimal time-vertex graph filter in fractional domains is also developed, using the graph fractional Laplacian operator and graph fractional Fourier transform. Numerical simulations on real-world datasets will demonstrate the superiority of the optimal time-vertex graph filter in fractional domains over the optimal time-vertex graph filter in ordinary domains and the optimal static graph filter in fractional domains.
