Optimization of Endmembers Mixture Analysis for Spectral

L i n e a r spectral mixture analysis can be used to model the .spectral variability in multior hyperspectral images and to relate the results to the physical abundance of surface constituents represented by the spectral endmembets. The nmst difficult ,step in this analytical approach lies in the ,selectimt of ,spectral endmembers, which are chosen to represent .surface components. A new approach to endmember selection is presented here, which may be used to augment existing methods, in which the endmemhens are derived mathematically from the image data subject to a set of user-defined constraints. The eon.straints take the titan of a starting model and allowable deviations from that starting model, which irtcorporate any a priori knowledge of the data and physical properties of the scene. These constraints are applied to the basic mixing equation.s', which are the~ solved iteratively to derive a .set of spectral endmembens' that minimize the residual error. Because the input to the model i,s qua~titative, the derivation process is repeatable, and endmembecs derived with different sets of constraints may be compared to each other directly. Three examples are presented, in which spectral endmembens are derived according to this model fi~r a .series of images: a sy~thetic image cube whose endmembecs" are already km~wn, a natural terrestrial scene, and a natural lunar .scene. Detailed analysis of the model inputs and results reveal that this modified approach to end~wmber selection provides physically realistic spectral endmembens" that in many cases represent purer components that~ could be fl)und it~ any pixel in the image scene. ©Elsevier Science Inc., 1997