A novel robust principal component analysis method for image and video processing

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• 作者：Guoqiang Huan ; Ying Li ; Zhanjie Song
• 关键词：robust principal component analysis ; sparse Bayesian learning ; Markov random fields ; matrix factorization ; contiguity prior
• 刊名：Applications of Mathematics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：61
• 期：2
• 页码：197-214
• 全文大小：859 KB
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• 作者单位：Guoqiang Huan (1) (2)
  Ying Li (3)
  Zhanjie Song (1) (2)
  
  1. School of Science, Tianjin University, Tianjin, 300072, China
  2. Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China
  3. State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin, 300072, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Applications of Mathematics
  Mechanics, Fluids and Thermodynamics
  Analysis
  Mathematical and Computational Physics
  Applied Mathematics and Computational Methods of Engineering
  Optimization
  
• 出版者：Springer Netherlands
• ISSN：1572-9109

文摘

The research on the robust principal component analysis has been attracting much attention recently. Generally, the model assumes sparse noise and characterizes the error term by the λ₁-norm. However, the sparse noise has clustering effect in practice so using a certain λ _p -norm simply is not appropriate for modeling. In this paper, we propose a novel method based on sparse Bayesian learning principles and Markov random fields. The method is proved to be very effective for low-rank matrix recovery and contiguous outliers detection, by enforcing the low-rank constraint in a matrix factorization formulation and incorporating the contiguity prior as a sparsity constraint. The experiments on both synthetic data and some practical computer vision applications show that the novel method proposed in this paper is competitive when compared with other state-of-the-art methods.