Gaussian mixture parameter estimation with known means and unknown class-dependent variances

This paper develops a recursive, convergent estimator for some parameters of Gaussian mixtures. The M class conditional (component) densities of the mixture random variable are Gaussian with known and distinct means and unknown and possibly different variances. A joint estimator of M prior (mixing) probabilities and M class conditional variances is derived. Sufficient conditions on the data and control parameters are derived for the estimator to converge. Convergence of the estimator follows from the use of a stochastic approximation theorem. Techniques to extend the estimators for the case of Successive class labels forming a Markov chain are mentioned. The estimator has applications in blind parameter estimation in digital communication with symbol dependent noise variance and in image compression. (C) 2002 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.