Linear Spectral Mixture Analysis Based Approaches to Estimation of Virtual Dimensionality in Hyperspectral Imagery

Virtual dimensionality (VD) is a new concept which was originally developed for estimating the number of spectrally distinct signatures present in hyperspectral data. The effectiveness of the VD is determined by the technique used for VD estimation. This paper develops an orthogonal subspace projection (OSP) technique to estimate the VD. The idea is derived from linear spectral mixture analysis where a data sample vector is modeled as a linear mixture of a finite set of what is called as virtual endmembers in this paper. A similar idea was also previously investigated by the signal subspace estimate (SSE) and was later improved by hyperspectral signal subspace identification by minimum error (HySime), where the minimum mean squared error is used as a criterion to determine the VD. Interestingly, with an appropriate interpretation, the proposed OSP technique includes the SSE/HySime as its special case. In order to demonstrate its utility, experiments using synthetic images and real image data sets are conducted for performance analysis.