Kernel-Based Weighted Abundance Constrained Linear Spectral Mixture Analysis for Remotely Sensed Images

Linear spectral mixture analysis (LSMA) is a theory that can be used to perform spectral unmixing where three major LSMA techniques, least squares orthogonal subspace projection (LSOSP), non-negativity constrained least squares (NCLS) and fully constrained least squares (FCLS) have been developed for this purpose. Subsequently, these three techniques were further extended to Fisher´s LSMA (FLSMA), weighted abundance constrained LSMA (WAC-LSMA) and kernel-based LSMA (K-LSMA). This paper combines both approaches of KLSMA and WAC-LSMA to derive a most general version of LSMA, kernel-based WACLSMA (KWAC-LSMA), which includes all the above-mentioned LSMA as its special cases. In particular, a new version of kernelizing FLSMA, referred to as kernel FLSMA (K-FLSMA) can be also developed to enhance the FLSMA performance by replacing the weighting matrix used in WAC-LSMA with a matrix specified by the within-class scatter matrix. The utility of the KWAC-LSMA is further demonstrated by multispectral and hyperspectral experiments for performance analysis.