Parameter Estimation Of Generalized Gamma Mixture Model Based On MCMC And Its Applications

In recent years Bayesian approaches have found an increased interest in the image and signal processing community. An increasingly important topic in statistical signal and image processing is the modeling of non-Gaussian signals features and data. Finite mixture models provide a powerful, flexible and well principled statistical approach and have been commonly used to model complex data in many applications. Two important problems in mixture modeling are the choice of the components densities and parameters estimation methods. This thesis presents strong ability of description of the GFD (Generalized Gamma Distribution) as the mixture component of the finite mixture models, and the parameters are estimated using good flexibility MCMC (Markov chain Monte Carlo) algorithm, and then application to the modeling of SAR image.Firstly, the thesis simply analyzes the background and significance of the finite mixture models. In addition, the definition of the finite mixture models and the most common approaches for making inference on parameters in mixture models-ML(Maximum likelihood) method and the Bayesian techniques are introduced.Then, the MCMC algorithm is introduced in detailed. The theoretical derivations and simulations of based-MCMC algorithm for parameter estimation of the GMM (Gaussian Mixture Model) have been studied with fixed number of mixture components.After that, under the cases of known mixture size, we propose to simultaneously estimate the parameters of GFMM (Generalized Gamma Mixture Model) using the MCMC algorithm. Based on the full conditional distributions of the parameters are not in well known forms, the parameters are then sampled via Random Walk M-H (Metropolis-Hastings) algorithm, and choose an adaptive algorithm to find the right proposal distribution variance. A Monte Carlo simulation study of GFMM carried out with the synthetic data and the actual SAR image data is performed to demonstrate the feasibility and validity of MCMC algorithm.Finally, in order to address the problem of the number of mixture components for modeling the distributions is known of MCMC algorithm, presented RJMCMC (Reversible Jump Markov chain Monte Carlo) algorithm for researching parameters estimation of GFMM. The RJMCMC algorithm allows the sampling process to move across subspaces of the parameter of different dimensions, thus determines the number of mixture components. Experiments on the synthetic data and the actual SAR image data demonstrate the algorithm excellent performance on determining the model order.