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Non-iterative Gaussianization

In this work, we propose a non-iterative Gaussian transformation strategy based on copula function, which doesn't require some commonly seen restrictive assumptions in the previous studies such as the elliptically symmetric distribution assumption and the linear independent component analysis assumption. Theoretical properties guarantee the proposed strategy can exactly transfer any random variable vector with a continuous multivariate distribution to a variable vector that follows a multivariate Gaussian distribution. Simulation studies also demonstrate the outperformance of such a strategy compared to some other methods like Box-Cox Gaussianization and radial Gaussianization. An application for probability density estimation for image synthesis is also shown.