平稳时点信号处理
Towards stationary time-vertex signal processing
摘要：
基于图的信号处理方法已显示出分析具有不规则结构的数据的希望，例如社交、交通和传感器网络中的数据。然而，尽管这些系统通常是动态的，但用于图形信号处理的最先进的方法忽略了时间维度，独立地处理连续的图形信号或取全局平均值。为了解决这个问题，本文考虑时变图形信号的统计分析。我们引入了一个新的定义的联合（时间顶点）平稳性，推广了经典的时间平稳性的定义和最近的定义适合于图。联合平稳性产生了一个可扩展的维纳优化框架，用于联合去噪，半监督学习，或更一般地逆线性算子，这是可证明的最佳。对真实天气数据的实验结果表明，考虑到图形和时间维度联合重建工作可以产生显着的精度提高。
英文摘要：
Graph-based methods for signal processing have shown promise for the analysis of data exhibiting irregular structure, such as those found in social, transportation, and sensor networks. Yet, though these systems are often dynamic, state-of-the-art methods for signal processing on graphs ignore the dimension of time, treating successive graph signals independently or taking a global average. To address this shortcoming, this paper considers the statistical analysis of time-varying graph signals. We introduce a novel definition of joint (time-vertex) stationarity, which generalizes the classical definition of time stationarity and the more recent definition appropriate for graphs. Joint stationarity gives rise to a scalable Wiener optimization framework for joint denoising, semi-supervised learning, or more generally inversing a linear operator, that is provably optimal. Experimental results on real weather data demonstrate that taking into account graph and time dimensions jointly can yield significant accuracy improvements in the reconstruction effort.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
