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. Sucient 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. Keywords: Symbol-dependent variances, Class-dependent additive Gaussian noise, Blind parameter estimation, Adaptive receivers, Nonuniform image quantization. 3 I Introduction Estimation of..