A1117
Title: Low-rank and sparse decomposition on graphs with non-convex smoothness regularization
Authors: Chee-Ming Ting - Monash University, Malaysia (Malaysia) [presenting]
Hernando Ombao - King Abdullah University of Science and Technology (KAUST) (Saudi Arabia)
Fuad Noman - Monash University Malaysia (Malaysia)
Abstract: The challenge of recovering graph-structured signals from noisy and corrupted measurements, where the signals exhibit a piecewise smooth structure with varying levels of smoothness across different node clusters. A robust signal recovery method based on low-rank plus sparse (L+S) decomposition with non-convex smoothness regularization is proposed. In this model, the observed measurements are decomposed into a sum of correlated graph signals (approximately low-rank), sparse outliers, and small noise. Low-rank and sparse components are induced via nuclear norm and L1 norm minimization, respectively. Additionally, a fusion penalty that promotes smoothness is incorporated by penalizing differences in signals between connected nodes. Joint use of low-rank and smoothness regularization effectively captures both global and local smooth structures of the graph signal. A family of non-convex smoothness regularizers is employed, including the smoothly clipped absolute deviation (SCAD) and minimax concave penalty (MCP). To solve the resulting optimization problem, an efficient accelerated proximal gradient algorithm is developed. Simulations demonstrate the superior recovery performance of the method compared to existing graph signal recovery techniques and convex smoothness regularizers. Applied to naturalistic fMRI data, the approach reveals consistent brain connectivity profiles within groups of subjects sharing similar traits and behavior in a population graph.
