Robust Subspace Tracking with Missing Data and Outliers via ADMM

Robust subspace tracking is crucial when dealing with data in the presence of both outliers and missing observations. In this paper, we propose a new algorithm, namely PETRELS-ADMM, to improve performance of subspace tracking in such scenarios. Outliers residing in the observed data are first detected in an efficient way and removed by the alternating direction method of multipliers (ADMM) solver. The underlying subspace is then updated by the algorithm of parallel estimation and tracking by recursive least squares (PETRELS) in which each row of the subspace matrix was estimated in parallel. Based on PETRELS-ADMM, we also derive an efficient way for robust matrix completion. Performance studies show the superiority of PETRELS-ADMM as compared to the state-of-the-art algorithms. We also illustrate its effectiveness for the application of background-foreground separation.