Distributed Spatial Filtering Over Networked Systems

This letter concerns distributed spatial filtering over networked systems, i.e., transforming signal values given for nodes to those with a desired spatial frequency characteristic via a distributed computation. An existing filtering algorithm can achieve only low-pass filter characteristics, which limits its range of applications. To address this limitation, we extend the aforementioned filtering algorithm using an additional design parameter. We then present a characterization of all the realizable filter characteristics as a necessary and sufficient condition for achieving distributed spatial filtering. As a result, it is shown that the extended algorithm increases the range of the realizable filter characteristics. The proposed method is verified not only by simulation but also by denoising experiments for a real sensor network. The results show that the proposed method effectively reduces spatial noise and achieves higher performance than an average consensus algorithm and an average filter.