Improving the results of spectral unmixing of Landsat Thematic Mapper imagery by enhancing the orthogonality of end-members

Spectral unmixing is a technique that has been developed to derive fractions of spectrally pure materials that contribute to observed spectral reflectance characteristics of a mixture through a inverse least-squares deconvolution using end-member spectra. This technique has been shown to be very successful when applied to high spectral resolution imaging or non-imaging data where subtle diagnostic absorption features largely determine the spectral characteristics of the data. A large and vastly growing number of papers where spectral unmixing is applied to analyse low resolution image data (e.g. Landsat Thematic Mapper (TM), NOAA AVHRR, etc.) often to derive abundances of different materials as input parameters for models (i.e. land degradation models, crop growth models, hydrologic models, etc.) has evolved throughout recent years. This justifies efforts put into the quality assessment of these abundance estimates. In this paper we evaluate the effect of end-member redundancy on the deconvolution of spectral mixtures in unconstrained unmixing using simulated, one-dimensional spectral mixtures of three end-members that we unmix with two out of three of these components. Our analysis shows a relationship between the unmixing error and the difference between the true and estimated abundance with an index which combines (1) the weighted correlation of end-members in the mixture, (2) the correlation between the end-members used in unmixing this mixture, and (3) the amount of 'information' mapped in the end-members. Given this result we investigate the reduction of correlation in the spectral unmixing process and present an application of unmixing to decorrelated Landsat TM data using the minimum noise fraction transformation. The statistical evaluation of this experiment shows that over-and undershooting rather than the error in the unmixed spectrum can be significantly improved when decorrelating the data.