A novel robust principal component analysis method for image and video processing
Applications of Mathematics, Tome 61 (2016) no. 2, pp. 197-214
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.
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.
DOI :
10.1007/s10492-016-0128-8
Classification :
60J20, 62H25, 68Q87
Keywords: robust principal component analysis; sparse Bayesian learning; Markov random fields; matrix factorization; contiguity prior
Keywords: robust principal component analysis; sparse Bayesian learning; Markov random fields; matrix factorization; contiguity prior
@article{10_1007_s10492_016_0128_8,
author = {Huan, Guoqiang and Li, Ying and Song, Zhanjie},
title = {A novel robust principal component analysis method for image and video processing},
journal = {Applications of Mathematics},
pages = {197--214},
year = {2016},
volume = {61},
number = {2},
doi = {10.1007/s10492-016-0128-8},
mrnumber = {3470773},
zbl = {06562153},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-016-0128-8/}
}
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 SP - 197 EP - 214 VL - 61 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.1007/s10492-016-0128-8/ DO - 10.1007/s10492-016-0128-8 LA - en ID - 10_1007_s10492_016_0128_8 ER -
%0 Journal Article %A Huan, Guoqiang %A Li, Ying %A Song, Zhanjie %T A novel robust principal component analysis method for image and video processing %J Applications of Mathematics %D 2016 %P 197-214 %V 61 %N 2 %U http://geodesic.mathdoc.fr/articles/10.1007/s10492-016-0128-8/ %R 10.1007/s10492-016-0128-8 %G en %F 10_1007_s10492_016_0128_8
Huan, Guoqiang; Li, Ying; Song, Zhanjie. A novel robust principal component analysis method for image and video processing. Applications of Mathematics, Tome 61 (2016) no. 2, pp. 197-214. doi: 10.1007/s10492-016-0128-8
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