Observation of random variables is often corrupted by additive Gaussian noise. Noise-reducing data processing is time-consuming and may introduce unwanted artifacts. In this paper, a novel approach to description of random variables insensitive with respect to Gaussian noise is presented. The proposed quantities represent the probability density function of the variable to be observed, while noise estimation, deconvolution or denoising are avoided. Projection operators are constructed, that divide the probability density function into a non-Gaussian and a Gaussian part. The Gaussian part is subsequently removed by modifying the characteristic function to ensure the invariance. The descriptors are based on the moments of the probability density function of the noisy random variable. The invariance property and the performance of the proposed method are demonstrated on real image data.

中文翻译：

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高斯噪声下的鲁棒多元密度估计

随机变量的观察经常被加性高斯噪声破坏。降噪数据处理非常耗时，并且可能会引入不需要的伪像。在本文中，提出了一种描述对高斯噪声不敏感的随机变量的新方法。建议的数量表示要观察的变量的概率密度函数，同时避免了噪声估计、去卷积或去噪。构建投影算子，将概率密度函数分为非高斯部分和高斯部分。随后通过修改特征函数去除高斯部分以确保不变性。描述符基于噪声随机变量的概率密度函数的矩。