Minimum Mean Square Error Estimation Under Gaussian Mixture Statistics
Statistics Theory
2011-08-18 v1 Statistics Theory
Abstract
This paper investigates the minimum mean square error (MMSE) estimation of x, given the observation y = Hx+n, when x and n are independent and Gaussian Mixture (GM) distributed. The introduction of GM distributions, represents a generalization of the more familiar and simpler Gaussian signal and Gaussian noise instance. We present the necessary theoretical foundation and derive the MMSE estimator for x in a closed form. Furthermore, we provide upper and lower bounds for its mean square error (MSE). These bounds are validated through Monte Carlo simulations.
Cite
@article{arxiv.1108.3410,
title = {Minimum Mean Square Error Estimation Under Gaussian Mixture Statistics},
author = {John T. Flam and Saikat Chatterjee and Kimmo Kansanen and Torbjorn Ekman},
journal= {arXiv preprint arXiv:1108.3410},
year = {2011}
}