Hyperspectral Unmixing with Gaussian Mixture Model and Spatial Group Sparsity

Abstract

In recent years, endmember variability has received much attention in the field of hyperspectral unmixing. To solve the problem caused by the inaccuracy of the endmember signature, the endmembers are usually modeled to assume followed by a statistical distribution. However, those distribution-based methods only use the spectral information alone and do not fully exploit the possible local spatial correlation. When the pixels lie on the inhomogeneous region, the abundances of the neighboring pixels will not share the same prior constraints. Thus, in this paper, to achieve better abundance estimation performance, a method based on the Gaussian mixture model (GMM) and spatial group sparsity constraint is proposed. To fully exploit the group structure, we take the superpixel segmentation (SS) as preprocessing to generate the spatial groups. Then, we use GMM to model the endmember distribution, incorporating the spatial group sparsity as a mixed-norm regularization into the objective function. Finally, under the Bayesian framework, the conditional density function leads to a standard maximum a posteriori (MAP) problem, which can be solved using generalized expectation-maximization (GEM). Experiments on simulated and real hyperspectral data demonstrate that the proposed algorithm has higher unmixing precision compared with other state-of-the-art methods.