Optimal linear spectral unmixing

Abstract

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 (CCPs) given the estimated EMS. For the EMS estimation problem, the authors propose a total least-squares (TLS) solution as an alternative to the conventional LS approach. The authors pose the CCP estimation problem as a constrained LS optimization problem. Then, they 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 (1993). Preliminary computer experiments indicated that the TLS-estimated EMS always leads to better estimates of CCP than that of the LS-estimated EMS.