  Background subtraction has been a fundamental and widely studied task in
video analysis, with a wide range of applications in video surveillance,
teleconferencing and 3D modeling. Recently, motivated by compressive imaging,
background subtraction from compressive measurements (BSCM) is becoming an
active research task in video surveillance. In this paper, we propose a novel
tensor-based robust PCA (TenRPCA) approach for BSCM by decomposing video frames
into backgrounds with spatial-temporal correlations and foregrounds with
spatio-temporal continuity in a tensor framework. In this approach, we use 3D
total variation (TV) to enhance the spatio-temporal continuity of foregrounds,
and Tucker decomposition to model the spatio-temporal correlations of video
background. Based on this idea, we design a basic tensor RPCA model over the
video frames, dubbed as the holistic TenRPCA model (H-TenRPCA). To characterize
the correlations among the groups of similar 3D patches of video background, we
further design a patch-group-based tensor RPCA model (PG-TenRPCA) by joint
tensor Tucker decompositions of 3D patch groups for modeling the video
background. Efficient algorithms using alternating direction method of
multipliers (ADMM) are developed to solve the proposed models. Extensive
experiments on simulated and real-world videos demonstrate the superiority of
the proposed approaches over the existing state-of-the-art approaches.
