FURTHER RESULTS ON RELATIONSHIP BETWEEN SPECTRAL UNMIXING AND SUBSPACE PROJECTION

A recent short communication [1] showed that an orthogonal subspace pr ojection (OSP) classifier developed for hyperspectral image classifica tion in [2] was equivalent to a maximum likelihood estimator (MLE) res ulting from a standard method of linear unmixing. It further concluded that the MLE subsumed the OSP classifier in spite of a constant diffe rence in their magnitudes. Coincidentally the equivalence of the OSP a pproach to linear unmixing was also derive in [3] and [4] by using the least-squares estimation with the same abundance estimate given by th e MLE, In this communication, me show, on the contrary, that the MLE f an be viewed as an a posteriori version of the OSP classifier and, thu s, belongs to a family of OSP-based classifiers. More importantly, me further show that the constant produced by the MLE determines abundanc e estimation and has nothing to do with classification. As a result, i t only alters the abundance concentration of the classified pixels, bu t not classification results.