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

Abstract

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.