Reducing statistical dependencies in natural signals using radial Gaussianization

S Lyu and E P Simoncelli

Presented at:
Neural Information Processing Systems (NIPS*08)

Published in Adv. Neural Information Processing Systems 21, vol.21 pp. 1009--1016, May 2009. Presented at NIPS, Dec 2008.

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    • 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.
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  • Courant Inst. technical report: TR-lyu-08Nonlinear extraction of 'Independent Components' of elliptically symmetric densities using radial Gaussianization
    by S Lyu and E P Simoncelli
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