Online Robust Subspace Tracking from Partial Information

TL;DR

GRASTA is an efficient online algorithm that robustly tracks subspaces from incomplete and corrupted data, enabling real-time applications like background separation in videos with high speed and accuracy.

Contribution

This paper introduces GRASTA, a novel robust online subspace tracking algorithm using $l^1$-norm minimization on the Grassmannian, effective for incomplete and corrupted streaming data.

Findings

GRASTA successfully tracks non-stationary subspaces with outliers.

It achieves real-time background-foreground separation in videos.

Operates at 57 frames per second on standard hardware.

Abstract

This paper presents GRASTA (Grassmannian Robust Adaptive Subspace Tracking Algorithm), an efficient and robust online algorithm for tracking subspaces from highly incomplete information. The algorithm uses a robust $l^1$-norm cost function in order to estimate and track non-stationary subspaces when the streaming data vectors are corrupted with outliers. We apply GRASTA to the problems of robust matrix completion and real-time separation of background from foreground in video. In this second application, we show that GRASTA performs high-quality separation of moving objects from background at exceptional speeds: In one popular benchmark video example, GRASTA achieves a rate of 57 frames per second, even when run in MATLAB on a personal laptop.