Reducing statistical dependencies in natural signals using radial Gaussianization

Siwei Lyu, Eero Simoncelli

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider the problem of transforming a signal to a representation in which the components are statistically independent. When the signal is generated as a linear transformation of independent Gaussian or non-Gaussian sources, the solution may be computed using a linear transformation (PCA or ICA, respectively). Here, we consider a complementary case, in which the source is non-Gaussian but elliptically symmetric. Such a source cannot be decomposed into independent components using a linear transform, but we show that a simple nonlinear transformation, which we call radial Gaussianization (RG), is able to remove all dependencies. We apply this methodology to natural signals, demonstrating that the joint distributions of nearby bandpass filter responses, for both sounds and images, are closer to being elliptically symmetric than linearly transformed factorial sources. Consistent with this, we demonstrate that the reduction in dependency achieved by applying RG to either pairs or blocks of bandpass filter responses is significantly greater than that achieved by PCA or ICA.

Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference
Pages1009-1016
Number of pages8
StatePublished - 2009
Event22nd Annual Conference on Neural Information Processing Systems, NIPS 2008 - Vancouver, BC, Canada
Duration: Dec 8 2008Dec 11 2008

Other

Other22nd Annual Conference on Neural Information Processing Systems, NIPS 2008
CountryCanada
CityVancouver, BC
Period12/8/0812/11/08

Fingerprint

Linear transformations
Independent component analysis
Bandpass filters
Acoustic waves

ASJC Scopus subject areas

  • Information Systems

Cite this

Lyu, S., & Simoncelli, E. (2009). Reducing statistical dependencies in natural signals using radial Gaussianization. In Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference (pp. 1009-1016)

Reducing statistical dependencies in natural signals using radial Gaussianization. / Lyu, Siwei; Simoncelli, Eero.

Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference. 2009. p. 1009-1016.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Lyu, S & Simoncelli, E 2009, Reducing statistical dependencies in natural signals using radial Gaussianization. in Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference. pp. 1009-1016, 22nd Annual Conference on Neural Information Processing Systems, NIPS 2008, Vancouver, BC, Canada, 12/8/08.
Lyu S, Simoncelli E. Reducing statistical dependencies in natural signals using radial Gaussianization. In Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference. 2009. p. 1009-1016
Lyu, Siwei ; Simoncelli, Eero. / Reducing statistical dependencies in natural signals using radial Gaussianization. Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference. 2009. pp. 1009-1016
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