Sensor network data denoising via recursive graph median filters

Weighted Mean and Median graph Filters with Attenuation Factor for Sensor Network

“…In this section, we discuss how to improve the k-hop graph and the node selecting graph. In [21], the node selecting graph selects the same nodes for a central node x t,i , at instance t − 1, t and t − 1. Intuitively, as the distance from instance t increases, the relationship of nodes in different instances for the node in instance t weakens.…”

“…We believe that the neighbor nodes of x t,i in instance t are different from the nodes in instances t − 1 and t + 1. Besides, the node selecting graph in [21] only consider the neighbor nodes in instances t − 1 and t − 1, and more instances should be included.…”

“…The median filter with weight the node selecting graph performs in the same way as in [21] except that the selected vertices are different.…”

“…However, this filter is mainly applied to the static graph model, and the current graph signal is constructed under the time-varying graph model [19]. In [20,21], the author proposed the application of k-hop graphs and recursive median filters to time-varying graph signals. However, the k-hop graph considers the neighbors of different node hops have the same importance.…”

“…1) We propose a weighted node selecting graph and use it to improve the recursive median graph filter. The weighted node selecting graph considers the nodes at multiple moments before and after the central node, instead of the non-weight attenuation graph in [21], which only considers the two times before and after the central node.…”