We introduce an adaptive graph normalized least mean pth power (GNLMP) algorithm that utilizes graph signal processing (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. Simulations show that the performance of the GNLMP algorithm in estimating steady-state and time-varying graph signals is faster than GLMP and is more robust in comparison to GLMS and GNLMS.

我们介绍了一种自适应图归一化最小平均 pth 功率 (GNLMP) 算法，该算法利用图信号处理 (GSP) 技术，包括带限滤波和节点采样，来估计脉冲噪声下的采样图信号。不同于基于最小二乘的算法，例如自适应 GSP 最小均方 (GLMS) 算法和归一化 GLMS (GNLMS) 算法，GNLMP 算法能够重建被非高斯噪声破坏的图信号重尾特征。与最近引入的自适应 GSP 最小平均 pth 功率 (GLMP) 算法相比，GNLMP 算法减少了迭代次数以收敛到稳定的图信号。推导出GNLMP算法的收敛条件，并证明了 GNLMP 算法处理具有多个特征的多维时变图信号的能力。仿真表明，GNLMP 算法在估计稳态和时变图形信号方面的性能比 GLMP 更快，并且与 GLMS 和 GNLMS 相比更稳健。