Optimal linear spectral unmixing

In this paper, the optimal estimate of ground cover components of a linearly mixed spectral pixel in remote-sensing imagery is investigated. The problem is formulated as two consecutive constrained least-squares (LS) problems: the first problem concerns the estimation of the end-member spectra (EMS), and the second concerns the estimate,,within each mixed pixel, of ground cover class proportions (CCP's) given the estimated EMS. For the EMS estimation problem, we propose a total least-squares (TLS) solution as an alternative to the conventional LS approach. We pose the CCP estimation problem as a constrained LS optimization problem. Then, we solve for exact solution using a quadratic programming (QP) method, as opposed to the Lagrange multiplier (LM)-based approximated solution proposed by Settle and Drake [16]. Preliminary computer experiments indicated that the TLS-estimated EMS always leads to better estimates of CCP than that of the LS-estimated EMS.