Denoising with Infinite Mixture of Gaussians

We show in this paper how an Infinite Mixture of Gaussians model can be used to estimate/denoise non-Gaussian data with local linear estimators based on the Wiener filter. The decomposition of the data in Gaussian components is straightforwardly computed with the Gaussian Transform, previously derived in [2]. The estimation is based on a two-step procedure, the first step consisting in variance estimation, and the second step in data estimation through Wiener filtering. We propose new generic variance estimators based on the Infinite Gaussian Mixture prior such as the cumulative estimator or the local-global estimator, as well as more classical Bayesian estimators. Results are presented in terms of distortion for the case of Generalized Gaussian data.