Least squares subspace projection approach to mixed pixel classification for hyperspectral images

Abstract

An orthogonal subspace projection (OSP) method using linear mixture modeling was recently explored in hyperspectral image classification and has shown promise in signature detection, discrimination, and classification. In this paper, the OSP is revisited and extended by three unconstrained least squares subspace projection approaches, called signature space OSP, target signature space OSP, and oblique subspace projection, where the abundances of spectral signatures are not known a priori but need to be estimated, a situation to which the OSP cannot be directly applied. The proposed three subspace projection methods can be used not only to estimate signature abundance, but also to classify a target signature at subpixel scale so as to achieve subpixel detection. As a result, they can be viewed as a posteriori OSP as opposed to OSP, which can be thought of as a priori OSP. In order to evaluate these three approaches, their associated least squares estimation errors are cast as a signal detection problem ill the framework of the Neyman-Pearson detection theory so that the effectiveness of their generated classifiers can be measured by receiver operating characteristics (ROC) analysis. All results are demonstrated by computer simulations and Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data.