Weighted abundance-constrained linear spectral mixture analysis

Linear spectral mixture analysis (LSMA) has been used in a wide range of applications. It is generally implemented without constraints due to mathematical tractability. However, it has been shown that constrained LSMA can improve unconstrained LSMA, specifically in quantification when accurate estimates of abundance fractions are necessary. As constrained LSMA is considered, two constraints are generally imposed on abundance fractions, abundance sum-to-one constraint (ASC) and abundance nonnegativity constraint (ANC), referred to as abundance-constrained LSMA (AC-LSMA). A general and common approach to solving AC-LSMA is to estimate abundance fractions in the sense of least squares error (LSE) while satisfying the imposed constraints. Since the LSE resulting from each individual band in abundance estimation is not weighted in accordance with significance of bands, the effect caused by the LSE is then assumed to be uniform over all the bands, which is generally not necessarily true. This paper extends the commonly used AC-LSMA to three types of weighted AC-LSMA resulting from three different signal processing perspectives, parameter estimation, pattern classification, and orthogonal subspace projection. As demonstrated by experiments, the weighted AC-LSMA generally performs better than unweighted AC-LSMA which can be considered as a special case of our proposed weighted AC-LSMA with the weighting matrix chosen to be the identity matrix.