Bounds on component spectra of multispectral images

A technique has been developed to estimate bounds on the spectra of major constituents of multispectral images. The bounds are two distinct sets of spectra, one in which the spectra are maximally independent from one another and another set in which the spectra are minimally independent. Both sets and their corresponding estimated abundance maps satisfy feasibility constraints for both spectral elements and fractional abundances. The actual spectra will have an independence measure between the minimal and maximum sets. An approach to mapping the feasibility region for all intermediate independence measures is described. In general, for a given level of independence there is an infinity of rotation axes about which small rotations of the spectra leads to another feasible set. In our approach, the selected rotation axes is the one which takes the maximally independent basis into the minimally independent basis. The effects of noise and low levels of additional components (impurities) are expected to have a larger effect on altering the spectra than the modifications due to small arbitrary rotations of feasible spectra. The technique is illustrated by application to a computer generated multispectral data array.