Hyperspectral Images Classification using Gaussian Mixture Model and Gibbs Sampler Algorithm

Hyperspectral image contains hundreds of narrow and contiguous spectral bands. Because of this high spectral resolution, hyperspectral images provide valuable information from the earth surface materials and objects. By advances in remote sensing technology and production of hyper spectral data with high spatial and spectral information, using such data for a detailed study of the phenomenon is spreading quickly. One of the most important applications of hyperspectral data analysis is either supervised or unsupervised classification for land cover mapping. Among different unsupervised methods, Gaussian mixture model has attracted a lot of attention, due to its performance and efficient computational time. Gaussian Mixture Models (GMMs) have been frequently applied in hyperspectral image classification tasks. The problem of estimating the parameters in a Gaussian mixture model has been studied in the literature. Gibbs sampler is one of the methods that can be applied for this problem. Another method for estimation the parameters of a Gaussian mixture model is Expectation-Maximization (EM) algorithm. EM is a general method for optimizing likelihood functions and is useful in situations where data might be missing or simpler optimization methods fail .On the other hand, the large number of bands in a hyperspectral images leads into estimation of a large number of parameters. In the other point of view, the enormous amount of information provided by hyperspectral images increases the computational burden as well as the correlation among spectral bands. Thus, dimensionality reduction is often conducted as one of the most important steps before target detection to both maximize the detection performance and minimize the computational burden. In this paper, we use PCA and Random Projection (RP) for solving the high dimensionality of the data. In order to evaluate the proposed algorithm in real analysis scenarios, we used two benchmark hyperspectral data sets collected by AVIRIS and Reflective Optics System Spectrographic Imaging System (ROSIS). In order to evaluate the effectiveness of the proposed method which is based on the using GMMS and its parameter are estimated using Gibbs sampler method we used two well-known dataset ROSIS and AVIRIS hyperspectral images which they are acquired from a urban and agricultural area, respectively. Moreover, for better evaluation we used a simulated data which is attained using a toolbox which is known as HYDRA project. Investigations on the simulated dataset and two real hyperspectral data showed that the case in which the number of bands has been reduced in the pre-processing stage using either RP or PCA in the feature space, can result the highest accuracy and efficiency for thematic mapping. We also demonstrated that the superiority of the Gibbs sampler in comparison with EM algorithm for estimating the GMM parameters. For instance, in Pavia university dataset, the overall accuracy and Kappa coefficient was 88.80 and 0.84, respectively for GMM-Gibbs-RP method and for GMM-EM-RP method the overall accuracy and kappa coefficient was 84.21 and 0.80, respectively. In other view point, in urban area (Pavia university dataset) with small structures, the amount of improvement in by Gibbs sampler in comparison with EM algorithm was more than the AVIRIS dataset which is related to agricultural area with bigger regions. This shows the capability of Gibbs sampler in confronting with singularities.