  In this paper, we consider the compressed video background subtraction
problem that separates the background and foreground of a video from its
compressed measurements. The background of a video usually lies in a low
dimensional space and the foreground is usually sparse. More importantly, each
video frame is a natural image that has textural patterns. By exploiting these
properties, we develop a message passing algorithm termed offline
denoising-based turbo message passing (DTMP). We show that these structural
properties can be efficiently handled by the existing denoising techniques
under the turbo message passing framework. We further extend the DTMP algorithm
to the online scenario where the video data is collected in an online manner.
The extension is based on the similarity/continuity between adjacent video
frames. We adopt the optical flow method to refine the estimation of the
foreground. We also adopt the sliding window based background estimation to
reduce complexity. By exploiting the Gaussianity of messages, we develop the
state evolution to characterize the per-iteration performance of offline and
online DTMP. Comparing to the existing algorithms, DTMP can work at much lower
compression rates, and can subtract the background successfully with a lower
mean squared error and better visual quality for both offline and online
compressed video background subtraction.
