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.

中文翻译：

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非迭代高斯化

在这项工作中，我们提出了一种基于 copula 函数的非迭代高斯变换策略，它不需要以前研究中常见的限制性假设，例如椭圆对称分布假设和线性独立分量分析假设。理论特性保证了所提出的策略可以将具有连续多元分布的任何随机变量向量精确地转换为遵循多元高斯分布的变量向量。仿真研究还表明，与 Box-Cox 高斯化和径向高斯化等其他一些方法相比，这种策略的性能优于其他方法。还显示了用于图像合成的概率密度估计的应用。