Improving semisupervised hyperspectral unmixing using spatial correlation under a polynomial postnonlinear mixing model

Abstract

We present a semisupervised hyperspectral unmixing solution that incorporates the spatial information between neighbor pixels in the abundance estimation procedure. The proposed method is applied to a polynomial postnonlinear mixing model in which each pixel reflection is characterized by a nonlinear function of pure spectral signatures corrupted by additive white Gaussian noise. The image is partitioned into different classes containing similar materials with the same abundance vectors. We model the spatial correlation of pixels of each class by the Markov random field. A Bayesian framework is used to iteratively estimate each class and its corresponding abundance vector. Here, we propose the sparse Dirichlet prior for abundance vectors to demonstrate a semisupervised scenario. A Markov chain Monte Carlo algorithm is used to estimate abundance vectors. The major contribution of this work is based on combination of spatial correlation with nonlinear mixing models in a semisupervised scenario. The proposed approach is compared to linear mixing model, generalized bilinear mixing model, and the conventional polynomial postnonlinear mixing model algorithms. The results on both simulated and real data show the outperformance of the proposed algorithm by achieving lower errors in unmixing and reconstruction of hyperspectral images.