We propose an Iterative Nonlinear Gaussianization Algorithm (INGA),
which seeks a nonlinear map from a set of dependent random variables
to independent Gaussian random variables.
A direct motivation of the INGA is to extend the principal component
analysis (PCA) which transforms a set of correlated random variables into
uncorrelated (independent up to second order) random variables.
An obvious advantage of deriving independent components is that we can simulate
a stochastic process of dependent multivariate variables by sampling univariate
independent variables. The quality of the transformation is evaluated by
statistical tests on the Kullback-Leibler (KL) distance between the
distribution of the transformed variables the standard multivariate Gaussian
distribution N(0,I).
The quality of the simulations is evaluated quantitatively
by the statistics of the KL distances between the sample mean distribution of
the original samples and that of the simulated samples.
Several numerical examples including synthetic and real-life image databases
show the capabilities and limitations of INGA.
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