We have evaluated and combined the features of three different methods to develop an algorithm for rapidly processing hyperspectral images. The hyperspectra were initially processed with Principal Component Analysis to find the appropriate number of independent components and abstract spectral representations (loadings). Key Set Factor Analysis and SIMPLISMA (SIMPle-to-use Interactive Self- modeling Mixture Analysis) methods were combined to find `pure' wavelengths for the components from the loadings. These `pure' wavelengths were used to product initial guesses for the relative concentrations of the components, and these concentrations were used to predict the pure component spectra. The spectra were further refined by using the method of Alternating Least Squares. The methodology is demonstrated on infrared spectra of a simple, three- component chemical mixture and on a hyperspectral infrared image of cartilage tissue.