Reducing statistical dependencies in natural signals using radial Gaussianization

Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference

Volumn , Issue , 2009, Pages 1009-1016

  Lyu, Siwei ^a   Simoncelli, Eero P ^b  

^a STATE UNIVERSITY OF NEW YORK   (United States)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BANDPASS FILTERS; GAUSSIAN DISTRIBUTION; GAUSSIAN NOISE (ELECTRONIC); SIGNAL PROCESSING;

FILTER RESPONSE; GAUSSIANIZATION; GAUSSIANS; INDEPENDENT COMPONENTS; LINEAR TRANSFORM; NON-GAUSSIAN; NON-GAUSSIAN SOURCES; SIMPLE++; STATISTICAL DEPENDENCIES; SYMMETRICS;

LINEAR TRANSFORMATIONS;

EID: 84858781961     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (30)

1. F Attneave. Some informational aspects of visual perception. Psych. Rev., 61:183-193, 1954.
2. H B Barlow. Possible principles underlying the transformation of sensory messages. In W A Rosenblith, editor, Sensory Communication, pages 217-234. MIT Press, Cambridge, MA, 1961.
3. B A Olshausen and D J Field. Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature, 381:607-609, 1996. (Pubitemid 26177476)
4. A van der Schaaf and J H van Hateren. Modelling the power spectra of natural images: Statistics and information. Vision Research, 28(17):2759-2770, 1996. (Pubitemid 26270905)
5. A J Bell and T J Sejnowski. The 'independent components' of natural scenes are edge filters. Vision Research, 37(23):3327-3338, 1997. (Pubitemid 27493806)
6. M S Lewicki. Efficient coding of natural sounds. Nature Neuroscience, 5(4):356-363, 2002. (Pubitemid 34279816)
7. R. Baddeley. Searching for filters with "interesting" output distributions: an uninteresting direction to explore. Network, 7:409-421, 1996. (Pubitemid 126714806)
8. Matthias Bethge. Factorial coding of natural images: how effective are linear models in removing higherorder dependencies? J. Opt. Soc. Am. A, 23(6):1253-1268, 2006.
9. B Wegmann and C Zetzsche. Statistical dependence between orientation filter outputs used in an human vision based image code. In Proc Visual Comm. and Image Processing, volume 1360, pages 909-922, Lausanne, Switzerland, 1990.
10. E P Simoncelli. Statisticalmodels for images: Compression, restoration and synthesis. In Proc 31st Asilomar Conf on Signals, Systems and Computers, volume 1, pages 673-678, Pacific Grove, CA, November 2-5 1997. IEEE Computer Society.
11. M J Wainwright and E P Simoncelli. Scale mixtures of Gaussians and the statistics of natural images. In S. A. Solla, T. K. Leen, and K.-R. Müller, editors, Adv. Neural Information Processing Systems (NIPS*99), volume 12, pages 855-861, Cambridge, MA, May 2000. MIT Press.
12. K.T. Fang, S. Kotz, and K.W. Ng. Symmetric Multivariate and Related Distributions. Chapman and Hall, London, 1990.
13. S. Lyu and E. P. Simoncelli. Nonlinear extraction of "independent components" of elliptically symmetric densities using radial Gaussianization. Technical Report TR2008-911, Computer Science Technical Report, Courant Inst. of Mathematical Sciences, New York University, April 2008.
14. D. Nash and M. S. Klamkin. A spherical characterization of the normal distribution. Journal of Multivariate Analysis, 55:56-158, 1976.
15. O Schwartz and E P Simoncelli. Natural signal statistics and sensory gain control. Nature Neuroscience, 4(8):819-825, August 2001. (Pubitemid 32702514)
16. William Feller. An Introduction to Probability Theory and Its Applications, volume 1. Wiley, January 1968.
17. C Zetzsche and G Krieger. The atoms of vision: Cartesian or polar? J. Opt. Soc. Am. A, 16(7), July 1999.
18. J. Huang and D. Mumford. Statistics of natural images and models. In IEEE International Conference on Computer Vision and Pattern Recognition (CVPR), 1999.
19. A Srivastava, X Liu, and U Grenander. Universal analytical forms for modeling image probability. IEEE Pat. Anal. Mach. Intell., 24(9):1200-1214, Sep 2002. (Pubitemid 35242581)
20. Y. Teh, M. Welling, and S. Osindero. Energy-based models for sparse overcomplete representations. Journal of Machine Learning Research, 4:1235-1260, 2003.
21. P IMJohannesma. The pre-response stimulus ensemble of neurons in the cochlear nucleus. In Symposium on Hearing Theory (IPO), pages 58-69, Eindhoven, Holland, 1972.
22. M. Studeny and J. Vejnarova. The multiinformation function as a tool for measuring stochastic dependence. In M. I. Jordan, editor, Learning in Graphical Models, pages 261-297. Dordrecht: Kluwer., 1998.
23. T. Cover and J. Thomas. Elements of Information Theory. Wiley-Interscience, 2nd edition, 2006.
24. A. Kraskov, H. Stögbauer, and P. Grassberger. Estimating mutual information. Phys. Rev. E, 69(6):66-82, Jun 2004.
25. E. G. Learned-Miller and J. W. Fisher. ICA using spacings estimates of entropy. Journal of Machine Learning Research, 4(1):1271-1295, 2000.
26. J H van Hateren and A van der Schaaf. Independent component filters of natural images compared with simple cells in primary visual cortex. Proc. R. Soc. Lond. B, 265:359-366, 1998. (Pubitemid 28111919)
27. A. Hyvärinen. Fast and robust fixed-point algorithms for independent component analysis. IEEE Transactions on Neural Networks, 10(3):626-634, 1999.
28. Scott Saobing Chen and Ramesh A. Gopinath. Gaussianization. In Advances in Neural Computation Systems (NIPS), pages 423-429, 2000.
29. S. Roth and M. Black. Fields of experts: A framework for learning image priors. In IEEE Conference on Computer Vision and Patten Recognition (CVPR), volume 2, pages 860-867, 2005.
30. S Lyu and E P Simoncelli. Statistical modeling of images with fields of Gaussian scale mixtures. In B Schölkopf, J Platt, and T Hofmann, editors, Adv. Neural Information Processing Systems 19, volume 19, Cambridge, MA, May 2007. MIT Press.