A robust online subspace estimation and tracking algorithm

Abstract

In this paper, we present a robust online subspace estimation and tracking algorithm (ROSETA) that is capable of identifying and tracking a time-varying low dimensional subspace from incomplete measurements and in the presence of sparse outliers. Our algorithm minimizes a robust ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm cost function between the observed measurements and their projection onto the estimated subspace. The projection coefficients and sparse outliers are computed using ADMM solver and the subspace estimate is updated using a proximal point iteration with adaptive parameter selection. We demonstrate using simulated experiments and a video background subtraction example that ROSETA succeeds in identifying and tracking low dimensional subspaces using fewer iterations than other state of art algorithms.