Finding virtual signatures for linear spectral mixture analysis

A new concept of virtual signature (VS) is introduced for linear spectral mixture analysis (LSMA) that can be used to form a linear mixture model (LMM) to perform data unmixing. A VS is defined as a spectrally distinct signature and different from an endmember as a pure signature in the sense that a VS must be extracted directly from the data and can be a mixed signature. It is also different from virtual endmembers (VEs) introduced in nonlinear spectral mixture analysis according to a bilinear model. By virtue of VS, this paper investigates three least squares (LSs)-based criteria, LS error (LSE), orthogonal subspace projection (OSP) residual, and maximal likelihood estimation (MLE) error, and further designs of their respective recursive algorithms to find VSs for LSMA to unmix data. In the mean time, a binary composite hypothesis testing-based Neyman Pearson detector is also developed in conjunction with the developed recursive algorithms to determine if their produced signatures are indeed desired VSs. Finally, an experiment-based comparative analysis is also conducted to demonstrate the proposed approaches.