Online Graph Models: Tackling the Challenges of Non-Gaussian Noise in Adaptive Filtering

Adaptive filtering faces significant challenges in handling complex non-Gaussian noise, while graph signal processing (GSP) excels at processing data with intricate structures. This brief introduces a novel method for solving non-Gaussian noise from the perspective of the graph domain for the first time. Specifically, we develop an online time-varying graph model based on the filter error signal and propose a corresponding graph topology transformation strategy. Utilizing a graph smoothness measure, we introduce a new adaptive filtering cost function, in which the graph Laplacian matrix plays a direct role in the filter update process. Subsequently, we derive the graph smoothness recursive adaptive filtering (GS-RAF) algorithm, rigorously analyze its theoretical performance, and validate its efficacy through simulations and echo cancellation experiments. The corresponding MATLAB (MathWorks, USA) codes of the simulations are publicly available at: https://github.com/smartXiaoz/GS-RAF.git.