Mapping target signatures via partial unmixing of AVIRIS data

A complete spectral unmixing of a complicated AVIRIS scene may not always be possible or even desired. High quality data of spectrally complex areas are very high dimensional and are consequently difficult to fully unravel. Partial unmixing provides a method of solving only that fraction of the data inversion problem that directly relates to the specific goals of the investigation. Many applications of imaging spectrometry can be cast in the form of the following question: 'Are my target signatures present in the scene, and if so, how much of each target material is present in each pixel?' This is a partial unmixing problem. The number of unmixing endmembers is one greater than the number of spectrally defined target materials. The one additional endmember can be thought of as the composite of all the other scene materials, or 'everything else'. Several workers have proposed partial unmixing schemes for imaging spectrometry data, but each has significant limitations for operational application. The low probability detection methods described by Farrand and Harsanyi and the foreground-background method of Smith et al are both examples of such partial unmixing strategies. The new method presented here builds on these innovative analysis concepts, combining their different positive attributes while attempting to circumvent their limitations. This new method partially unmixes AVIRIS data, mapping apparent target abundances, in the presence of an arbitrary and unknown spectrally mixed background. It permits the target materials to be present in abundances that drive significant portions of the scene covariance. Furthermore it does not require a priori knowledge of the background material spectral signatures. The challenge is to find the proper projection of the data that hides the background variance while simultaneously maximizing the variance amongst the targets.