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Bayesian robust principal component analysis.

Publication ,  Journal Article
Ding, X; He, L; Carin, L
Published in: IEEE transactions on image processing : a publication of the IEEE Signal Processing Society
December 2011

A hierarchical Bayesian model is considered for decomposing a matrix into low-rank and sparse components, assuming the observed matrix is a superposition of the two. The matrix is assumed noisy, with unknown and possibly non-stationary noise statistics. The Bayesian framework infers an approximate representation for the noise statistics while simultaneously inferring the low-rank and sparse-outlier contributions; the model is robust to a broad range of noise levels, without having to change model hyperparameter settings. In addition, the Bayesian framework allows exploitation of additional structure in the matrix. For example, in video applications each row (or column) corresponds to a video frame, and we introduce a Markov dependency between consecutive rows in the matrix (corresponding to consecutive frames in the video). The properties of this Markov process are also inferred based on the observed matrix, while simultaneously denoising and recovering the low-rank and sparse components. We compare the Bayesian model to a state-of-the-art optimization-based implementation of robust PCA; considering several examples, we demonstrate competitive performance of the proposed model.

Duke Scholars

Published In

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society

DOI

EISSN

1941-0042

ISSN

1057-7149

Publication Date

December 2011

Volume

20

Issue

12

Start / End Page

3419 / 3430

Related Subject Headings

  • Artificial Intelligence & Image Processing
  • 4607 Graphics, augmented reality and games
  • 4603 Computer vision and multimedia computation
  • 1702 Cognitive Sciences
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing
 

Citation

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Ding, X., He, L., & Carin, L. (2011). Bayesian robust principal component analysis. IEEE Transactions on Image Processing : A Publication of the IEEE Signal Processing Society, 20(12), 3419–3430. https://doi.org/10.1109/tip.2011.2156801
Ding, Xinghao, Lihan He, and Lawrence Carin. “Bayesian robust principal component analysis.IEEE Transactions on Image Processing : A Publication of the IEEE Signal Processing Society 20, no. 12 (December 2011): 3419–30. https://doi.org/10.1109/tip.2011.2156801.
Ding X, He L, Carin L. Bayesian robust principal component analysis. IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. 2011 Dec;20(12):3419–30.
Ding, Xinghao, et al. “Bayesian robust principal component analysis.IEEE Transactions on Image Processing : A Publication of the IEEE Signal Processing Society, vol. 20, no. 12, Dec. 2011, pp. 3419–30. Epmc, doi:10.1109/tip.2011.2156801.
Ding X, He L, Carin L. Bayesian robust principal component analysis. IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. 2011 Dec;20(12):3419–3430.

Published In

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society

DOI

EISSN

1941-0042

ISSN

1057-7149

Publication Date

December 2011

Volume

20

Issue

12

Start / End Page

3419 / 3430

Related Subject Headings

  • Artificial Intelligence & Image Processing
  • 4607 Graphics, augmented reality and games
  • 4603 Computer vision and multimedia computation
  • 1702 Cognitive Sciences
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing