Further results on relationship between spectral unmixing and subspace projection

A recent short communication, J. J. Settle (1996), showed that an orthogonal subspace projection (OSP) classifier developed for hyperspectral image classification in J. Harsanyi et al. (1994) was equivalent to a maximum likelihood estimator (MLE) resulting from a standard method of linear unmixing. It further concluded that the MLE subsumed the OSP classifier in spite of a constant difference in their magnitudes. Coincidentally, the equivalence of the OSP approach to linear unmixing was also derived in J. Harsanyi (1993) and T. M. Tu et al. (1997) by using the least-squares estimation with the same abundance estimate given by the MLE. In this communication, the author shows, on the contrary, that the MLE can be viewed as an a posteriori version of the OSP classifier and, thus, belongs to a family of OSP-based classifiers. More importantly, the author further shows that the constant produced by the MLE determines abundance estimation and has nothing to do with classification. As a result, it only alters the abundance concentration of the classified pixels, but not classification results.