  This work presents a new robust PCA method for foreground-background
separation on freely moving camera video with possible dense and sparse
corruptions. Our proposed method registers the frames of the corrupted video
and then encodes the varying perspective arising from camera motion as missing
data in a global model. This formulation allows our algorithm to produce a
panoramic background component that automatically stitches together corrupted
data from partially overlapping frames to reconstruct the full field of view.
We model the registered video as the sum of a low-rank component that captures
the background, a smooth component that captures the dynamic foreground of the
scene, and a sparse component that isolates possible outliers and other sparse
corruptions in the video. The low-rank portion of our model is based on a
recent low-rank matrix estimator (OptShrink) that has been shown to yield
superior low-rank subspace estimates in practice. To estimate the smooth
foreground component of our model, we use a weighted total variation framework
that enables our method to reliably decouple the true foreground of the video
from sparse corruptions. We perform extensive numerical experiments on both
static and moving camera video subject to a variety of dense and sparse
corruptions. Our experiments demonstrate the state-of-the-art performance of
our proposed method compared to existing methods both in terms of foreground
and background estimation accuracy.
