Genetic algorithm and expectation maximization for parameter estimation of mixture Gaussian model phantom

Abstract

We present a new approach for estimating parameters of Gaussian mixture model by Genetic Algorithms (Gas) and Expectation Maximization (EM). It has been shown that Gas is independent of initialization parameters. In this work we propose combination of Gas and EM algorithms (GA-EM) for learning Gaussian mixture components to achieve accurate parameter estimation independent of initial values. To assess the performance of the proposed method, a series of Gaussian phantoms, based on modified Shepp-Logan method, were created. In this phantom, each tissue segment presents a Gaussian density function that its mean and variance can be controlled. EM, Gas and GAs-EM were employed to estimate the tissue parameters in each phantom. The results indicate that EM algorithm, as expected is heavily impacted by the initial values. Coupling Gas with EM not only improves the overall accuracy, it also provides estimates that are independent of initial seed values. The proposed method offers a solution for accurate and stable solution for parameter estimation in for Gaussian mixture models, with higher likelihood 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.