Constrained Nonnegative Matrix Factorization for Hyperspectral Unmixing and Its Applications

Abstract

Hyperspectral remote sensing imagery, containing both spatial and spectral information captured by imaging sensors, has been widely used for ground information extraction. Due to the long distance of the imaging sensors to the targets of monitoring and the intrinsic property of sensors, hyperspectral images normally do not have high spatial resolution, which causes mixed responses of various types of ground objects in the images. Therefore, hyperspectral unmixing has become an important technique to decompose mixed pixels into a collection of spectral signatures, or endmembers, and their corresponding proportions, i.e., abundance. Hyperspectral unmixing methods can be mainly divided into three categories: geometric based, statistics based, and sparse regression based. Among these methods, nonnegative matrix factorization (NMF), as one of the statistical methods, has attracted much attention. It treats unmixing as a blind source separation problem, and decomposes image data into endmember and abundance ma- trices simultaneously. However, the NMF algorithm may fall into local minima because the objective function of NMF is a non-convex function. Adding adequate constraint to NMF has become one solution to solve this problem. In this thesis, we introduce three different constraints for the NMF based hyperspe tral unmixing method. The first constraint is a partial prior knowledge of endmember constraint. It assumes that some endmembers could be treated as known endmembers before unmixing. The proposed model minimizes the differences between the spectral signatures of endmembers being estimated in the image data and the standard signa- tures of known endmembers extracted from a library or detected from the ground. The benefit of this method is that it not only uses the prior knowledge on the unmixing tasks, but also considers the distribution of the real data in the hyperspectral dataset, so that the discrepancy between the prior knowledge and the data can be compromised. Furthermore, the proposed method is general in nature, and can be easily extended to other NMF based hyperspectral unmixing algorithms.