Analysis of Spatial-Spectral Relationships in Real Hyperspectral Imaging to use for Hyperspectral Unmixing

Abstract

The basic statement on the linear unmixing model apply to hyperspectral images, is that the pixels are in the convex hull of the cone with the endmembers at its vertices. Hyperspectral data, in general, does not follow this structure. Here we use data exploration to analyze how spatial information can be used to extract uniform regions in the image. Several spectral unmixing algorithms look for a single convex region to depict a hyperspectral scene for a particular set of endmembers. A convex region can be defined in Euclidian space as if for every pair of points within the data cloud, every point on the straight-line segment that joins the pair of points is also within the data cloud. For instance, a solid cube is convex data cloud. This research proposes a methodology to perform unsupervised unmixing establishing how the spatial information help to capture the relationship between the grade of uniformity of the clusters, and the convex regions in the image data set. The effect of splitting the image helps us to obtain homogeneous regions. To achieve the localization of the endmember, principal component analysis is used, and the first three of them containing about 96% of the total information of hyperspectral image and then they are plotted for visualization their behavior. This analysis help us to understand the relation between the spatial domain information and data cloud structure. We saw experimentally that by partitioning the image in homogeneous regions we can decompose the data cloud in piece wise convex regions. We can then apply linear unmixing to these regions and easily extract endmembers for different homogeneous tiles in the image and shows how to perform hyperspectral unmixing using local information and merge them at a global level to develop an accurate description of the scene under study.