Multispectral and hyperspectral image analysis with convex cones

A new approach to multispectral and hyperspectral image analysis is presented. This method, called convex cone analysis (CCA), is based on the fact that some physical quantities such as radiance are nonnegative. The vectors formed by discrete radiance spectra are linear combinations of nonnegative components, and they lie inside a nonnegative, convex region. The object of CCA is to find the boundary points of this region, which can be used as endmember spectra for unmixing or as target vectors for classification. To implement this concept, we find the eigenvectors of the sample spectral correlation matrix of the image. Given the number of endmembers or classes, we select as many eigenvectors corresponding to the largest eigenvalues. These eigenvectors are used as a basis to form linear combinations that have only nonnegative elements, and thus they lie inside a convex cone. The vertices of the convex cone will be those points whose spectral vector contains as many zero elements as the number of eigenvectors minus one. Accordingly, a mixed pixel can be decomposed by identifying the vertices that were used to form its spectrum. An algorithm for finding the convex cone boundaries is presented, and applications to unsupervised unmixing and classification are demonstrated with simulated data as well as experimental data from the hyperspectral digital imagery collection experiment (HYDICE).