Robust multivariate density estimation under Gaussian noise

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.