TY - JOUR
T1 - Node-Adaptive Regularization for Graph Signal Reconstruction
AU - Yang, Maosheng
AU - Coutino, Mario
AU - Leus, Geert
AU - Isufi, Elvin
PY - 2021
Y1 - 2021
N2 - A critical task in graph signal processing is to estimate the true signal from noisy observations over a subset of nodes, also known as the reconstruction problem. In this paper, we propose a node-adaptive regularization for graph signal reconstruction, which surmounts the conventional Tikhonov regularization, giving rise to more degrees of freedom; hence, an improved performance. We formulate the node-adaptive graph signal denoising problem, study its bias-variance trade-off, and identify conditions under which a lower mean squared error and variance can be obtained with respect to Tikhonov regularization. Compared with existing approaches, the node-adaptive regularization enjoys more general priors on the local signal variation, which can be obtained by optimally designing the regularization weights based on Prony's method or semidefinite programming. As these approaches require additional prior knowledge, we also propose a minimax (worst-case) strategy to address instances where this extra information is unavailable. Numerical experiments with synthetic and real data corroborate the proposed regularization strategy for graph signal denoising and interpolation, and show its improved performance compared with competing alternatives.
AB - A critical task in graph signal processing is to estimate the true signal from noisy observations over a subset of nodes, also known as the reconstruction problem. In this paper, we propose a node-adaptive regularization for graph signal reconstruction, which surmounts the conventional Tikhonov regularization, giving rise to more degrees of freedom; hence, an improved performance. We formulate the node-adaptive graph signal denoising problem, study its bias-variance trade-off, and identify conditions under which a lower mean squared error and variance can be obtained with respect to Tikhonov regularization. Compared with existing approaches, the node-adaptive regularization enjoys more general priors on the local signal variation, which can be obtained by optimally designing the regularization weights based on Prony's method or semidefinite programming. As these approaches require additional prior knowledge, we also propose a minimax (worst-case) strategy to address instances where this extra information is unavailable. Numerical experiments with synthetic and real data corroborate the proposed regularization strategy for graph signal denoising and interpolation, and show its improved performance compared with competing alternatives.
UR - http://www.scopus.com/inward/record.url?scp=85126715474&partnerID=8YFLogxK
U2 - 10.1109/OJSP.2021.3056897
DO - 10.1109/OJSP.2021.3056897
M3 - Article
SN - 2644-1322
VL - 2
SP - 85
EP - 98
JO - IEEE Open Journal of Signal Processing
JF - IEEE Open Journal of Signal Processing
M1 - 9346013
ER -