Simplex projection methods for selection of endmembers in hyperspectral imagery

It is well known that performance of subpixel target detection algorithms depends on the choice of endmembers used to characterize the background and the target in hyperspectral imagery. In this paper, we investigate how well a set of endmembers characterizes a given set of spectra. We are assuming a fully constrained linear mixing model, and analyze the resulting residuals. To facilitate geometric and intuitive interpretation, we formulate the resulting constrained least-squares estimation problem in terms of projections on low-dimensional simplexes. Consequently, we define a family of simplex projection methods (SPM) for endmember selection. We give numerical results for two known endmember-selection procedures -the pixel purity index (PPI) and the maximum distance (MaxD) methods. Then we compare these results to those for a simple version of SMP, called the Farthest Pixel Selection (FPS) method. This new class of techniques promises to give better descriptions of the target and background regions than do current methods, which in turn should lead to more precise detection (with lower false alarm rates) of low-visibility small (subpixel) targets