A set theoretic approach to target detection using spectral signature statistics

Pixels in hyperspectral images usually contain spectra from several classifiable objects, so that the recorded pixel is a mixture of the classes. Current methods estimate the proportion of each class using a set of spectral signatures describing only the class means. Since the means are known only by estimation methods, we introduce an approach that also incorporates the variation inherent in this estimation. The total least squares approach using projections onto convex sets (POCS) produces improved performance over simple maximum likelihood methods, even one that also uses the constraint sets and POCS.