Linear unmixing using endmember subspaces and physics based modeling

One of the biggest issues with the Linear Mixing Model (LMM) is that it is implicitly assumed that each of the individual material components throughout the scene may be described using a single dimension (e.g. an endmember vector). In reality, individual pixels corresponding to the same general material class can exhibit a large degree of variation within a given scene. This is especially true in broad background classes such as forests, where the single dimension assumption clearly fails. In practice, the only way to account for the multidimensionality of the class is to choose multiple (very similar) endmembers, each of which represents some part of the class. To address these issues, we introduce the endmember subgroup model, which generalizes the notion of an 'endmember vector' to an 'endmember subspace'. In this model, spectra in a given hyperspectral scene are decomposed as a sum of constituent materials; however, each material is represented by some multidimensional subspace (instead of a single vector). The dimensionality of the subspace will depend on the within-class variation seen in the image. The endmember subgroups can be determined automatically from the data, or can use physics-based modeling techniques to include 'signature subspaces', which are included in the endmember subgroups. In this paper, we give an overview of the subgroup model; discuss methods for determining the endmember subgroups for a given image, and present results showing how the subgroup model improves upon traditional single endmember linear mixing. We also include results that use the 'signature subspace' approach to identifying mixed-pixel targets in HYDICE imagery.