Adaptive weighted median filtering for time-varying graph signals

Graph filter is one of the cornerstones of graph signal processing that can extract desired features from graph signal and filter out noise signal. In the majority of existing research, graph signal operators are designed to be linear and are applicable solely to time-invariant graph signals. Recently, some studies have extended graph signal processing to time-vertex graph signals. Combining the correlation between graph topology and time can obtain better results. This paper proposes an adaptive weighted median filter for pulsed noise in time-varying graph signals. It uses joint correlation to denoise time-varying graph signals and can adjust filtering window and node weights according to whether node information is destroyed by noise. The proposed filter has the advantages of high efficiency and high localization. Information only needs to be exchanged with one-hop neighbors, and it can be implemented in a distributed manner. Three real sensor network data sets are used for denoising experiments here, and the comprehensive experimental results show that the proposed filters perform better in most cases.