The student-t mixture as a natural image patch prior with application to image compression

Journal of Machine Learning Research

Volumn 15, Issue , 2014, Pages 2061-2086

  Van Den Oord, Aäron ^a   Schrauwen, Benjamin ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

Density modeling; GMM; Image compression; Mixture models; Unsupervised learning

Indexed keywords

ARTIFICIAL INTELLIGENCE; UNSUPERVISED LEARNING;

DEEP BELIEF NETWORKS; DENSITY MODELING; GAUSSIAN MIXTURE MODEL (GMMS); GMM; LOSSLESS IMAGE COMPRESSION; MIXTURE MODEL; REAL-VALUED DATA; UNSUPERVISED MACHINE LEARNING;

IMAGE COMPRESSION;

EID: 84904286258     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article

References (37)

1. Anuradha Aiyer, Kyungsuk Pyun, Ying-zong Huang, Deirdre B OBrien, and Robert M Gray. Lloyd clustering of Gauss mixture models for image compression and classification. Signal Processing: Image Communication, 20(5):459-485, 2005 (Pubitemid 40643796)
2. Yoshua Bengio. Learning deep architectures for AI. Foundations and Trends R in Machine Learning, 2(1):1-127, 2009
3. Richard P Brent. Algorithms for Minimization without Derivatives. Courier Dover Publications, 1973
4. Ori Bryt and Michael Elad. Compression of facial images using the k-svd algorithm. Journal of Visual Communication and Image Representation, 19(4):270-282, 2008
5. Arthur P Dempster, Nan M Laird, and Donald B Rubin. Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society. Series B (Methodological), pages 1-38, 1977
6. Michael Elad and Michal Aharon. Image denoising via sparse and redundant representations over learned dictionaries. Transactions on Image Processing, 15(12):3736-3745, 2006 (Pubitemid 44811686)
7. Dumitru Erhan, Yoshua Bengio, Aaron Courville, Pierre-Antoine Manzagol, Pascal Vincent, and Samy Bengio. Why does unsupervised pre-training help deep learning? The Journal of Machine Learning Research, 11:625-660, 2010
8. Vivek K Goyal. Theoretical foundations of transform coding. Signal Processing Magazine, 18(5):9-21, 2001 (Pubitemid 32932331)
9. Per Hedelin and Jan Skoglund. Vector quantization based on Gaussian mixture models. Transactions on Speech and Audio Processing, 8(4):385-401, 2000
10. Geoffrey E Hinton. Training products of experts by minimizing contrastive divergence. Neural Computation, 14(8):1771-1800, 2002
11. Wei Hong, John Wright, Kun Huang, and Yi Ma. A multiscale hybrid linear model for lossy image representation. In International Conference on Computer Vision, volume 1, pages 764-771. IEEE, 2005 (Pubitemid 44055032)
12. Inbal Horev, Ori Bryt, and Ron Rubinstein. Adaptive image compression using sparse dictionaries. In International Conference on Systems, Signals and Image Processing, pages 592-595. IEEE, 2012
13. Samuel Kotz and Saralees Nadarajah. Multivariate t-Distributions and their Applications. Cambridge University Press, 2004
14. Julien Mairal, Francis Bach, Jean Ponce, Guillermo Sapiro, and Andrew Zisserman. Nonlocal sparse models for image restoration. In International Conference on Computer Vision, pages 2272-2279. IEEE, 2009
15. David Martin, Charless Fowlkes, Doron Tal, and Jitendra Malik. A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In International Conference on Computer Vision, volume 2, pages 416-423, July 2001 (Pubitemid 32795086)
16. Bruno A Olshausen and David J Field. Sparse coding with an overcomplete basis set: A strategy employed by v1? Vision Research, 37(23):3311-3325, 1997 (Pubitemid 27493805)
17. William A Pearlman and Amir Said. Digital Signal Compression: Principles and Practice. Cambridge University Press, 2011
18. David Peel and Geoffrey J McLachlan. Robust mixture modelling using the t distribution. Statistics and Computing, 10(4):339-348, 2000
19. Stefan Roth and Michael J Black. Fields of experts: A framework for learning image priors. In Computer Vision and Pattern Recognition, 2005., volume 2, pages 860-867. IEEE, 2005
20. Gerald Schaefer and Michal Stich. UCID: an uncompressed color image database. In Electronic Imaging 2004, pages 472-480. International Society for Optics and Photonics, 2003
21. Athanassios Skodras, Charilaos Christopoulos, and Touradj Ebrahimi. The JPEG 2000 still image compression standard. Signal Processing Magazine, 18(5):36-58, 2001 (Pubitemid 32932333)
22. Yichuan Tang, Ruslan Salakhutdinov, and Geoffrey Hinton. Deep mixtures of factor analysers. In International Conference on Machine Learning, pages 505-512, 2012
23. Yichuan Tang, Ruslan Salakhutdinov, and Geoffrey Hinton. Tensor analyzers. In Interna- tional Conference on Machine Learning, 2013
24. Lucas Theis, Sebastian Gerwinn, Fabian Sinz, and Matthias Bethge. In all likelihood, deep belief is not enough. The Journal of Machine Learning Research, 12:3071-3096, 2011
25. Lucas Theis, Reshad Hosseini, and Matthias Bethge. Mixtures of conditional Gaussian scale mixtures applied to multiscale image representations. PLoS ONE, 7(7), Jul 2012. doi: 10.1371/journal.pone.0039857
26. D Michael Titterington, Adrian FM Smith, Udi E Makov, et al. Statistical Analysis of Finite Mixture Distributions, volume 7. Wiley New York, 1985
27. Benigno Uria, Iain Murray, and Hugo Larochelle. A deep and tractable density estimator. arXiv preprint arXiv:1310.1757, 2013a
28. Benigno Uria, Iain Murray, and Hugo Larochelle. Nade: The real-valued neural autoregressive density-estimator. arXiv preprint arXiv:1306.0186, 2013b
29. Aäron van den Oord, Sander Dieleman, and Benjamin Schrauwen. Learning a piecewise linear transform coding scheme for images. In 2012 International Conference on Graphic and Image Processing, pages 876844-876844. International Society for Optics and Photonics, 2013
30. Gregory K Wallace. The JPEG still picture compression standard. Communications of the ACM, 34(4):30-44, 1991
31. Yair Weiss and William T Freeman. What makes a good model of natural images? In Computer Vision and Pattern Recognition, 2007., pages 1-8. IEEE, 2007
32. Max Welling, Simon Osindero, and Geoffrey E Hinton. Learning sparse topographic representations with products of Student-t distributions. In Advances in Neural Information Processing Systems, pages 1359-1366, 2002
33. John Wright, Yi Ma, Julien Mairal, Guillermo Sapiro, Thomas S Huang, and Shuicheng Yan. Sparse representation for computer vision and pattern recognition. Proceedings of the IEEE, 98(6):1031-1044, 2010
34. Guoshen Yu, Guillermo Sapiro, and Stéphane Mallat. Solving inverse problems with piecewise linear estimators: from Gaussian mixture models to structured sparsity. Transactions on Image Processing, 21(5):2481-2499, 2012
35. Joaquin Zepeda, Christine Guillemot, and Ewa Kijak. Image compression using sparse representations and the iteration-tuned and aligned dictionary. Journal of Selected Topics in Signal Processing, 5(5):1061-1073, 2011
36. Daniel Zoran and Yair Weiss. From learning models of natural image patches to whole image restoration. In International Conference on Computer Vision, pages 479-486. IEEE, 2011
37. Daniel Zoran and Yair Weiss. Natural images, Gaussian mixtures and dead leaves. In Advances in Neural Information Processing Systems, volume 25, pages 1745-1753, 2012