Reducing statistical dependencies in natural signals using
 radial Gaussianization Siwei Lyu and Eero P. Simoncelli (W80)
source models

ICA PCA RG

radial Gaussianization (RG)
transformed
 radial density

Linearly transformed factorial

Elliptical

radial map original radial
 density

transformed density marginals
Factorial Gaussian Spherical

Note that Gaussians are the only elliptically symmetric 
 variables with independent components.

transformed original
0.5 0.4 0.3

original density

experiment with natural sounds
raw pca ica rg

bits
0.2 0.1 0 0.1

s(t)

s(t+0.1msec)

s(t+2.0msec)

s(t+3.5msec)

0.5 msec

1

1.5

2 2.5

3.5

pairwise joint densities of signal values with different separations

mutual information between signal 
 values as a function of separation