Robust Adaptive Estimation of Graph Signals Based on Welsch Loss

This paper considers the problem of adaptive estimation of graph signals under the impulsive noise environment. The existing least mean squares (LMS) approach suffers from severe performance degradation under an impulsive environment that widely occurs in various practical applications. We present a novel adaptive estimation over graphs based on Welsch loss (WL-G) to handle the problems related to impulsive interference. The proposed WL-G algorithm can efficiently reconstruct graph signals from the observations with impulsive noises by formulating the reconstruction problem as an optimization based on Welsch loss. An analysis on the performance of the WL-G is presented to develop effective sampling strategies for graph signals. A novel graph sampling approach is also proposed and used in conjunction with the WL-G to tackle the time-varying case. The performance advantages of the proposed WL-G over the existing LMS regarding graph signal reconstruction under impulsive noise environment are demonstrated.