A Robust Proportionate Graph Recursive Least Squares Algorithm for Adaptive Graph Signal Recovery

In this brief, we propose a robust proportionate Recursive Least Square (RLS) algorithm to address the problem of adaptive graph signal recovery in the presence of impulsive noise. In this problem, a graph signal should be recovered from only a subset of sampled graph signal in an adaptive manner. To this end, first, the classical graph RLS algorithm in the literature is written in a standard way, which is represented by an error correction term. Second, the proportionate graph RLS is formulated by adding a gain matrix in the recursion. Then, to calculate the gain matrix, an optimization problem with non-negative and scaling constraints is suggested. The active-set approach is utilized to handle these constraints. To enhance robustness against impulsive noise, we utilize optimized coefficients derived from the minimum disturbance principle. Moreover, an analytical lower bound for the minimum disturbance and the computational complexity analysis are given. Simulation results show the advantages of the proposed proportionate-based RLS algorithm over other approaches in terms of the rate of convergence in presence of impulsive noise.