Proportionate Adaptive Graph Signal Recovery

TL;DR

This paper introduces two new proportionate-type adaptive algorithms for graph signal recovery, which converge faster than traditional LMS methods by optimizing gain matrices and incorporating previous signal information.

Contribution

The paper proposes two novel proportionate-type adaptive graph signal recovery algorithms with closed-form gain matrices and stability analysis, improving convergence speed over existing methods.

Findings

The proposed algorithms converge faster than standard LMS.

Simulation results validate the effectiveness of the new algorithms.

The algorithms incorporate previous signals for improved recovery.

Abstract

This paper generalizes the proportionate-type adaptive algorithm to the graph signal processing and proposes two proportionate-type adaptive graph signal recovery algorithms. The gain matrix of the proportionate algorithm leads to faster convergence than least mean squares (LMS) algorithm. In this paper, the gain matrix is obtained in a closed-form by minimizing the gradient of the mean-square deviation (GMSD). The first algorithm is the Proportionate-type Graph LMS (Pt-GLMS) algorithm which simply uses a gain matrix in the recursion process of the LMS algorithm and accelerates the convergence of the Pt-GLMS algorithm compared to the LMS algorithm. The second algorithm is the Proportionate-type Graph Extended LMS (Pt-GELMS) algorithm, which uses the previous signal vectors alongside the signal of the current iteration. The Pt-GELMS algorithm utilizes two gain matrices to control the effect of the signal of the previous iterations. The stability analyses of the algorithms are also provided. Simulation results demonstrate the efficacy of the two proposed proportionate-type LMS algorithms.