Wiener filters on graphs and distributed implementations

Abstract

In this paper, we introduce Wiener filters to recover deterministic and (wide-band) stationary graph signals from their observations corrupted by random noises, and we propose distributed algorithms to implement the Wiener filters. Furthermore, the proposed algorithms can be implemented on distributed networks in which agents are equipped with a data processing subsystem for limited data storage and computation power, and with a one-hop communication subsystem for direct data exchange only with their adjacent agents. Our simulations indicate that the proposed Wiener filtering procedure works well on estimating synthetic (wide-band) stationary signals and real temperature datasets from their noisy observations.