Normalized Least Mean M-Estimator for Adaptive Graph Signal Recovery

This paper addresses the problem of recovering the graph signal over sensor networks with abnormal observations. The conventional adaptive graph recovery approach, namely, the graph least mean square (LMS) algorithm, cannot reconstruct the graph signal corrupted by non-Gaussian noise. A normalized least mean M-estimator algorithm is devised to balance efficiency and robustness. Our method combines the advantages of the graph normalized LMS and graph normalized sign algorithms, possessing the former's convergence speed and the latter's robustness. Stochastic analysis of the proposed updating rule is provided, while two time-varying algorithmic improvements are suggested. Finally, computer simulation results demonstrate the performance superiority of the developed approach over state-of-the-art schemes.