Time-Varying Graph Signal Denoising via Median Filters

Graph Signal Processing (GSP) leverages pair-wise relationship between nodes of a graph to formulate operators on signals defined over the nodes. Most existing graph signal operators in the literature are linear, and can be described by linear transformation matrices. Recently, works are emerging that consider the time correlation of graph signals, leading to time-vertex signal processing. By exploiting the joint correlations across the graph topology and time, better results can be obtained. In this brief, we propose a median operator that will leverage the joint correlation, for denoising time-varying graph signals. The median operator, known for its robustness to outliers in statistics, has been very successful in traditional signal processing, especially for images. The efficient and highly localised graph median filters developed here are applied to denoising real world sensor network data. Real world sensor nodes are usually resource limited in terms of their computational and communication capacity, hence the imperative requirement for efficient localised filters. Comprehensive experimental results will show that in some cases, the performance is significantly better than the equivalent linear operator counterpart.