In wireless sensor networks (WSN) for environmental monitoring, the sensor nodes typically have limited computational and communication resources. Furthermore, the sensors often operate in a harsh environment, and the measurements can be subjected to significant levels of noise. In this work, with these considerations in mind, we propose an efficient method to denoise the sensor data. Using concepts from graph signal processing, the WSN is first modelled using an extended graph. The time-vertex graph jointly models the correlations between neighbouring sensor nodes and across the time dimension. A recursive graph median filter is developed that can be highly localized, and can be implemented with distributed processing. The filter is applied to the denoising of data that is subjected, simultaneously, to Gaussian noise and impulsive noise. Extensive experimental results, using three real-world measurement datasets, will demonstrate that the recursive filter significantly outperforms the equivalent linear filter and nonrecursive median filter, at high noise levels.

在用于环境监测的无线传感器网络 (WSN) 中，传感器节点通常具有有限的计算和通信资源。此外，传感器通常在恶劣的环境中运行，并且测量可能会受到很大的噪音影响。在这项工作中，考虑到这些因素，我们提出了一种有效的方法来对传感器数据进行去噪。使用图信号处理的概念，首先使用扩展图对 WSN 进行建模。时间顶点图联合建模相邻传感器节点之间和跨时间维度的相关性。开发了一种递归图中值滤波器，它可以高度局部化，并且可以通过分布式处理来实现。该滤波器用于对同时受到高斯噪声和脉冲噪声影响的数据进行去噪。