A-POSTERIORI LEAST-SQUARES ORTHOGONAL SUBSPACE PROJECTION APPROACH TODESIRED SIGNATURE EXTRACTION AND DETECTION

One of the primary goals of imaging spectrometry in earth remote sensi ng applications is to determine identities and abundances of surface m aterials. In a recent study, an orthogonal subspace projection (OSP) w as proposed for image classification, :However, it was developed for a n a priori linear spectral mixture model which did not take advantage of a posteriori knowledge of observations. In this paper, an a posteri or least squares orthogonal subspace projection (LSOSP) derived from O SP is presented on the basis of an a posteriori model so that the abun dances of signatures can be estimated through observations rather than assumed to be known as in the a priori model. In order to evaluate th e OSP and LSOSP approaches, a Neyman-Pearson detection theory is devel oped where a receiver operating characteristic (ROC) curve is used for performance analysis, In particular, a locally optimal Neyman-Pearson 's detector is also designed for the case where the global abundance i s very small with energy close to zero a case to which both LSOSP and OSP cannot be applied. It is shown through computer simulations that t he presented LSOSP approach significantly improves the performance of OSP.