Graph Normalized-LMP Algorithm for Signal Estimation Under Impulsive Noise

• Published in: Journal of signal processing systems Vol. 95; no. 1; pp. 25 - 36
• Main Authors: Yan, Yi, Adel, Radwa, Kuruoglu, Ercan Engin
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.01.2023; Springer Nature B.V
• Subjects: Algorithms; Circuits and Systems; Computer Imaging; Deep learning; Eigenvectors; Electrical Engineering; Engineering; Estimation; Experiments; Fourier transforms; Graphs; Image Processing and Computer Vision; Least mean squares; Least mean squares algorithm; Neural networks; Noise; Optimization; Pattern Recognition; Pattern Recognition and Graphics; Random noise; Signal processing; Signal,Image and Speech Processing; Vision; Wavelet transforms; Impulsive noise; Multidimensional graph signal; Alpha-stable noise; Graph signal processing; Normalized least mean pth power algorithm
• ISSN: 1939-8018; 1939-8115
• DOI: 10.1007/s11265-022-01802-2

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.