An iterative nonlinear Gaussianization algorithm for image simulation and synthesis, (with J.-J. Lin and R. A. Levine), submitted for publication, 2001.
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 INGA is
to extend principal component analysis (PCA), which transforms a set
of correlated random variables into uncorrelated (independent up to
second order) random variables, and Independent Component Analysis
(ICA), which linearly transforms random variables into variates that
are "as independent as possible." A modified INGA is then proposed
to nonlinearly transform ICA coefficients into statistically
independent components. To quantify the performance of each
algorithm: PCA, ICA, INGA, and modified INGA, we study the Edgeworth
Kullback-Leibler Distance (EKLD) which serves to measure the
"distance" between two distributions in multi-dimensions.
Several examples are presented to demonstrate the superior performance of INGA
(and its modified version) in situations where PCA and ICA poorly simulate the
images of interest.
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