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

Guoqiang Huan; Ying Li; Zhanjie Song

Applications of Mathematics (2016)

  • Volume: 61, Issue: 2, page 197-214
  • ISSN: 0862-7940

Abstract

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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 ℓ 1 -norm. However, the sparse noise has clustering effect in practice so using a certain ℓ 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.

How to cite

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Huan, Guoqiang, Li, Ying, and Song, Zhanjie. "A novel robust principal component analysis method for image and video processing." Applications of Mathematics 61.2 (2016): 197-214. <http://eudml.org/doc/276756>.

@article{Huan2016,
abstract = {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 $\ell _1$-norm. However, the sparse noise has clustering effect in practice so using a certain $\ell _p$-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.},
author = {Huan, Guoqiang, Li, Ying, Song, Zhanjie},
journal = {Applications of Mathematics},
keywords = {robust principal component analysis; sparse Bayesian learning; Markov random fields; matrix factorization; contiguity prior; robust principal component analysis; sparse Bayesian learning; Markov random fields; matrix factorization; contiguity prior},
language = {eng},
number = {2},
pages = {197-214},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A novel robust principal component analysis method for image and video processing},
url = {http://eudml.org/doc/276756},
volume = {61},
year = {2016},
}

TY - JOUR
AU - Huan, Guoqiang
AU - Li, Ying
AU - Song, Zhanjie
TI - A novel robust principal component analysis method for image and video processing
JO - Applications of Mathematics
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 2
SP - 197
EP - 214
AB - 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 $\ell _1$-norm. However, the sparse noise has clustering effect in practice so using a certain $\ell _p$-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.
LA - eng
KW - robust principal component analysis; sparse Bayesian learning; Markov random fields; matrix factorization; contiguity prior; robust principal component analysis; sparse Bayesian learning; Markov random fields; matrix factorization; contiguity prior
UR - http://eudml.org/doc/276756
ER -

References

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