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Compressive sensing by learning a Gaussian mixture model from measurements.

Publication ,  Journal Article
Yang, J; Liao, X; Yuan, X; Llull, P; Brady, DJ; Sapiro, G; Carin, L
Published in: IEEE transactions on image processing : a publication of the IEEE Signal Processing Society
January 2015

Compressive sensing of signals drawn from a Gaussian mixture model (GMM) admits closed-form minimum mean squared error reconstruction from incomplete linear measurements. An accurate GMM signal model is usually not available a priori, because it is difficult to obtain training signals that match the statistics of the signals being sensed. We propose to solve that problem by learning the signal model in situ, based directly on the compressive measurements of the signals, without resorting to other signals to train a model. A key feature of our method is that the signals being sensed are treated as random variables and are integrated out in the likelihood. We derive a maximum marginal likelihood estimator (MMLE) that maximizes the likelihood of the GMM of the underlying signals given only their linear compressive measurements. We extend the MMLE to a GMM with dominantly low-rank covariance matrices, to gain computational speedup. We report extensive experimental results on image inpainting, compressive sensing of high-speed video, and compressive hyperspectral imaging (the latter two based on real compressive cameras). The results demonstrate that the proposed methods outperform state-of-the-art methods by significant margins.

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Published In

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

DOI

EISSN

1941-0042

ISSN

1057-7149

Publication Date

January 2015

Volume

24

Issue

1

Start / End Page

106 / 119

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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Yang, J., Liao, X., Yuan, X., Llull, P., Brady, D. J., Sapiro, G., & Carin, L. (2015). Compressive sensing by learning a Gaussian mixture model from measurements. IEEE Transactions on Image Processing : A Publication of the IEEE Signal Processing Society, 24(1), 106–119. https://doi.org/10.1109/tip.2014.2365720
Yang, Jianbo, Xuejun Liao, Xin Yuan, Patrick Llull, David J. Brady, Guillermo Sapiro, and Lawrence Carin. “Compressive sensing by learning a Gaussian mixture model from measurements.IEEE Transactions on Image Processing : A Publication of the IEEE Signal Processing Society 24, no. 1 (January 2015): 106–19. https://doi.org/10.1109/tip.2014.2365720.
Yang J, Liao X, Yuan X, Llull P, Brady DJ, Sapiro G, et al. Compressive sensing by learning a Gaussian mixture model from measurements. IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. 2015 Jan;24(1):106–19.
Yang, Jianbo, et al. “Compressive sensing by learning a Gaussian mixture model from measurements.IEEE Transactions on Image Processing : A Publication of the IEEE Signal Processing Society, vol. 24, no. 1, Jan. 2015, pp. 106–19. Epmc, doi:10.1109/tip.2014.2365720.
Yang J, Liao X, Yuan X, Llull P, Brady DJ, Sapiro G, Carin L. Compressive sensing by learning a Gaussian mixture model from measurements. IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. 2015 Jan;24(1):106–119.

Published In

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

DOI

EISSN

1941-0042

ISSN

1057-7149

Publication Date

January 2015

Volume

24

Issue

1

Start / End Page

106 / 119

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