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

摘要

We present new approaches based on Genetic Algorithms (GAs), Simulated Annealing (SA) and Expectation Maximization (EM) for determining parameters of the mixture 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 efficiently optimize functions in large search spaces while the solution obtained by EM is a function of initial parameters. Hence there is a relatively high likelihood of achieving sub-optimal solution, due to trapping in local maxima. In this work, we propose a combination of Genetic Algorithm with EM (Interlaced GA-EM) to improve estimation of Gaussian mixture parameters. The method uses population of mixture models, rather than a single mixture, iteratively 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 the 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 affected by the initial values. The best result in terms of computational time and accuracy was obtained from Interlaced GA-EM. The proposed method offers an accurate and stable solution for parameter estimation on Gaussian mixture models, with higher likelihood of achieving global optimal minima. Obtaining such accurate parameter estimation is a key requirement for several image segmentation approaches, which rely on a priori knowledge of tissue distribution.