In this paper, we present a novel approach for the reconstruction of sparse graph signals using a distributed adaptive thresholding recursive least squares algorithm. Our proposed scheme leverages signal measurements across multiple time steps to estimate the underlying graph signal. To achieve this, we define a cost function that combines a weighted least squares term and an \(L_0\) norm. The cost function is then minimized using a surrogate minimization scheme and the recursive least squares technique. The resulting algorithm is an adaptive thresholding recursive least squares scheme that effectively recovers sparse graph signals. Additionally, we apply a consensus-based method to enable distributed recovery, and derive recursive updating relations to speed up the algorithm. Our approach offers a significant novelty in the field of graph signal recovery, providing an efficient and accurate solution for reconstructing sparse graph signals. The numerical simulations show the superiority of the proposed algorithm over the other state-of-the-art algorithms from the point of view of the convergence rate and the mean square deviation (MSD) criterion.
