Graph Normalized-LMP Algorithm for Signal Estimation Under Impulsive Noise

TL;DR

This paper presents an adaptive graph normalized least mean pth power (GNLMP) algorithm for graph signal processing that effectively estimates signals corrupted by impulsive noise, outperforming existing algorithms in convergence speed and robustness.

Contribution

The paper introduces the GNLMP algorithm, a novel method that improves signal reconstruction under impulsive noise and reduces convergence time compared to prior algorithms.

Findings

GNLMP converges faster than GLMP.

GNLMP is more robust than GLMS and GNLMS.

Effective in processing multidimensional time-varying signals.

Abstract

In this paper, we introduce an adaptive graph normalized least mean pth power (GNLMP) algorithm for graph signal processing (GSP) that utilizes GSP techniques, including bandlimited filtering and node sampling, to estimate sampled graph signals under impulsive noise. Different from least-squares-based algorithms, such as the adaptive GSP Least Mean Squares (GLMS) algorithm and the normalized GLMS (GNLMS) algorithm, the GNLMP algorithm has the ability to reconstruct a graph signal that is corrupted by non-Gaussian noise with heavy-tailed characteristics. Compared to the recently introduced adaptive GSP least mean pth power (GLMP) algorithm, the GNLMP algorithm reduces the number of iterations to converge to a steady graph signal. The convergence condition of the GNLMP algorithm is derived, and the ability of the GNLMP algorithm to process multidimensional time-varying graph signals with multiple features is demonstrated as well. Simulations show the performance of the GNLMP algorithm in estimating steady-state and time-varying graph signals is faster than GLMP and more robust in comparison to GLMS and GNLMS.