| This dissertation focuses on the development of methods and algorithms to analyze imaging spectrometry data with a minimum of assumptions and/or prior knowledge about the scene. Two existing statistical techniques never before applied to hyperspectral imaging were implemented and studied: Convex Cone Analysis (CCA) and Projection Pursuit (PP). The purpose of CCA is to unmix an image pixel into its individual endmembers without knowledge of the endmembers' identity. Only the number of endmembers is required. CCA is based on the fact that some physical quantities such as radiance or reflectance are non-negative. The vectors formed by the pixel spectra are linear combinations of non-negative components, and lie inside a non-negative, convex region. The boundary points of this region can be used as endmembers for unmixing or image segmentation. Projection Pursuit is a technique that aids in the visual analysis of high-dimensional data by computing linear projections that are interesting in some sense. By using an information-theoretic criterion, we are able to compute projections of the image cube that separate spectrally distinct objects from both the background and each other without the need for ground truth information or target spectra. This approach is superior to anomaly detection because it does not rely simply on second-order statistics, but rather exploits the non-Gaussian aspects of the data. An orthonormal transform is computed which maximizes a relative entropy-based projection index for each projection. This transform operates in the same way as the Principal Components Analysis (PCA) or the Minimum Noise Fraction (MNF) transforms, but with different, typically more informative, results. It is also demonstrated that, when combined with an interference suppression algorithm, PP can serve as a powerful unsupervised target detector. |
