Optimization of endmembers for spectral mixture analysis

Linear spectral mixture analysis can be used to model the spectral variability in multi- or h yperspectral images and to relate the results to the physical abundance of surface constituents represented by the spectral endmembers. The most difficult step in. this analytical approach lies in the selection of spectral endmembers, which are chosen to represent surface components. A new approach to endhnember selection is presented here, which may be used to augment existing methods, in which the endmembers are derived -mathematically from the image data subject to a set of user-defined constraints. The constraints take the form of a starting -model and allowable deviations from that starting model, which incorporate any a priori knowledge of the data and physical properties of the scene. These constraints are applied to the basic mixing equations, which are then- solved iteratively to derive a set of spectral endmembers that t inintize the residual error. Because the input to the model is quantitative, the derivation. process is repeatable, and endmembers derived with different sets of constraints may be compared to each other directly. Three examples are presented, in which spectral endmembers are derived according to this nwdel for a series of images: a synthetic image cube whose endmembers are already known a natural terrestrial scene, and a natural lunar scene. Detailed analysis of the model inputs and results reveal that this modified approach to endinernber selection provides physically realistic spectral endmembers that in many cases represent purer components than could be found in any pixel in. the image scene.