1,809 research outputs found
Total Variation Regularized Tensor RPCA for Background Subtraction from Compressive Measurements
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.Comment: To appear in IEEE TI
Robust PCA as Bilinear Decomposition with Outlier-Sparsity Regularization
Principal component analysis (PCA) is widely used for dimensionality
reduction, with well-documented merits in various applications involving
high-dimensional data, including computer vision, preference measurement, and
bioinformatics. In this context, the fresh look advocated here permeates
benefits from variable selection and compressive sampling, to robustify PCA
against outliers. A least-trimmed squares estimator of a low-rank bilinear
factor analysis model is shown closely related to that obtained from an
-(pseudo)norm-regularized criterion encouraging sparsity in a matrix
explicitly modeling the outliers. This connection suggests robust PCA schemes
based on convex relaxation, which lead naturally to a family of robust
estimators encompassing Huber's optimal M-class as a special case. Outliers are
identified by tuning a regularization parameter, which amounts to controlling
sparsity of the outlier matrix along the whole robustification path of (group)
least-absolute shrinkage and selection operator (Lasso) solutions. Beyond its
neat ties to robust statistics, the developed outlier-aware PCA framework is
versatile to accommodate novel and scalable algorithms to: i) track the
low-rank signal subspace robustly, as new data are acquired in real time; and
ii) determine principal components robustly in (possibly) infinite-dimensional
feature spaces. Synthetic and real data tests corroborate the effectiveness of
the proposed robust PCA schemes, when used to identify aberrant responses in
personality assessment surveys, as well as unveil communities in social
networks, and intruders from video surveillance data.Comment: 30 pages, submitted to IEEE Transactions on Signal Processin
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