Robust adaptive graph signal estimation using Pseudo–Huber loss

Graph Signal Processing (GSP) has become a crucial tool for analyzing data distributed over irregular and complex domains. Most widely used representations in GSP are the Graph Fourier Transform (GFT) and the Graph Shift Operator (GSO). GFT is the frequency-domain representation, which is suitable only for prior known band-limited signals. In contrast, the GSO is based on vertex domain formulation, making it suitable for adaptive filtering operations. In real-world scenarios, graph signals are often corrupted by non-Gaussian and impulsive noise, whereas most existing algorithms assume Gaussian noise conditions and are based on GFT representation. To address these challenges, this paper proposes a Graph Pseudo–Huber Loss Adaptive Filter (G-PHLAF) based on GSO. Theoretical convergence analysis in the mean square sense proves that the proposed approach provides better performance and enhanced robustness against non-Gaussian noise when compared to other competing algorithms. Further, extensive experiments on Brazilian temperature and real-time air quality datasets confirm the suitability of the proposed approach for robust graph signal estimation under uncertain and noisy conditions.