Incremental gradient on the Grassmannian for online foreground and background separation in subsampled video

It has recently been shown that only a small number of samples from a low-rank matrix are necessary to reconstruct the entire matrix. We bring this to bear on computer vision problems that utilize low-dimensional subspaces, demonstrating that subsampling can improve computation speed while still allowing for accurate subspace learning. We present GRASTA, Grassmannian Robust Adaptive Subspace Tracking Algorithm, an online algorithm for robust subspace estimation from randomly subsampled data. We consider the specific application of background and foreground separation in video, and we assess GRASTA on separation accuracy and computation time. In one benchmark video example [16], GRASTA achieves a separation rate of 46.3 frames per second, even when run in MATLAB on a personal laptop.