Nonlinear extraction of 'Independent Components' of natural images using radial Gaussianization

S Lyu and E P Simoncelli

Published in Neural Computation, vol.21(6), pp. 1485--1519, Jun 2009.

DOI: 10.1162/neco.2009.04-08-773

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  • We consider the problem of efficiently encoding a signal by transforming it to a new representation whose components are statistically independent. A widely studied linear solution, known as independent components analysis (ICA), exists for the case when the signal is generated as a linear transformation of independent non-Gaussian sources. Here, we examine a complementary case, in which the source is non-Gaussian and elliptically symmetric. In this case, no invertible linear transform suffices to decompose the signal into independent components, but we show that a simple nonlinear transformation, which we call radial Gaussianization (RG), is able to remove all dependencies. We then examine this methodology in the context of natural image statistics. We first show that distributions of spatially proximal bandpass filter responses are better described as elliptical than as linearly transformed independent sources. Consistent with this, we demonstrate that the reduction in dependency achieved by applying RG to either nearby pairs or blocks of bandpass filter responses is significantly greater than that achieved by ICA. Finally, we show that the RG transformation may be closely approximated by divisive normalization, which has been used to model the nonlinear response properties of visual neurons.
  • Superseded Publications: Lyu08d
  • nips*08 paper (includes sound statistics): Lyu08d
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