Multispectral and hyperspectral image analysis with convex cones

A new approach to multispectral and hyperspectral image analysis is present ed. This method, called convex cone analysis (CCA), is based on the fact th at some physical quantities such as radiance are nonnegative. The vectors f ormed by discrete radiance spectra are linear combinations of nonnegative c omponents, 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 end member spectra for unmixing or as target vectors for classification. To imp lement this concept, we find the eigenvectors of the sample spectral correl ation matrix of the image. Given the number of endmembers or classes, we se lect as many eigenvectors corresponding to the largest eigenvalues. These e igenvectors 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 m any zero elements as the number of eigenvectors minus one, Accordingly, a m ixed pixel can be decomposed by identifying the vertices that were used to form its spectrum. An algorithm for finding the convex cone boundaries is p resented, and applications to unsupervised unmixing and classification are demonstrated with simulated data as well as experimental data from the hype rspectral digital imagery collection experiment (HYDICE).