Total Variation Regularized Tensor RPCA for Background Subtraction from Compressive Measurements

Wenfei Cao, Yao Wang*, Jian Sun, Deyu Meng, Can YANG, Andrzej Cichocki, Zongben Xu

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

146 Citations (Scopus)


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 principal component analysis (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 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. To characterize the correlations among the groups of similar 3D patches of video background, we further design a patch-group-based tensor RPCA model by joint tensor Tucker decompositions of 3D patch groups for modeling the video background. Efficient algorithms using the alternating direction method of multipliers 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.

Original languageEnglish
Article number7488247
Pages (from-to)4075-4090
Number of pages16
JournalIEEE Transactions on Image Processing
Issue number9
Publication statusPublished - Sept 2016

Scopus Subject Areas

  • Software
  • Computer Graphics and Computer-Aided Design

User-Defined Keywords

  • 3D total variation
  • Background subtraction
  • compressive imaging
  • nonlocal self-similarity
  • tensor robust principal component analysis
  • Tucker tensor decomposition
  • video surveillance


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