An Iterative Nonlinear Gaussianization Algorithm for Image Simulation and Synthesis

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 modi ed INGA is then proposed to nonlinearly transform ICA coe cients into statistically independent components. To quantify the performance of each algorithm: PCA, ICA, INGA, and modi ed 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 modi ed version) in situations where PCA and ICA poorly simulate the images of interest.