Improved methods for parameter estimation of mixture Gaussian model using genetic and maximum-likelihood algorithms

Abstract

We present new approaches based on Genetic Algorithms (GAs), Simulated Annealing (SA) and Expectation Maximization (EM) for learning parameters of the mixture of Gaussian model. GAs are adaptive search techniques designed to search for near optimal solutions of large-scale optimization problems with multiple local maxima. It has been shown that GAs are independent of initialization parameters and can provide an efficient technique to optimize functions in large search spaces while the solution obtained by EM is a function of initial parameters, hence relatively high likelihood of achieving sub-optimal solution, due to trapping in local maxima. In this work we propose a new incorporate genetic algorithm with EM (Interactive GA-EM) to improve estimation of Gaussian mixture parameters. The method uses a population of mixture models, rather than a single mixture, interactively in both GA and EM to determine Gaussian mixture parameters. To assess the performance of the proposed methods, a series of Gaussian phantoms, based on modified Shepp-Logan method, were created. All proposed methods were employed to estimate the tissue parameters in each phantom. The results indicate that the EM algorithm, as expected, is heavily impacted by the initial values. The best result on both computational time and accuracy was obtained from Interactive GA-EM. The proposed method offers an accurate and stable solution for parameter estimation on Gaussian mixture models, with higher chance of achieving global optimal. Obtaining such accurate parameter estimation is a key requirement for several image segmentation approaches, which rely on a priori knowledge of tissue distribution.