A novel inequality-constrained weighted linear mixture model for endmember variability

Spectral unmixing has trigged considerable attention to both multispectral and hyperspectral data processing. Among different kinds of spectral unmixing models, the linear mixture model (LMM) has been widely applied with its simplicity in light scattering mechanisms and flexibility in different scenarios. Recently, a variety of optimized LMMs have been developed to enhance the decomposing ability. However, two major challenges still exist: endmember variability and global optimum solution with the inequality constraint. In this study, aiming to avoid the influence of endmember variability and to extend the application of LMM, a novel inequality-constrained weighted linear mixture model (IWLMM) is proposed. Based on the errors-in-variables (EIV) model and the theory of weighted total least squares (WTLS), the issue of endmember variability and stochastic errors of both endmembers and mixed pixels are eliminated. With the non-negativity constraint, a brief optimal algorithm to solve the IWLMM is generated as well. In order to indicate the advantages of proposed IWLMM, comparative experiments with the conventional fully constrained least squares (FCLS), three currently proposed LMM-based models (perturbed LMM (PLMM), extended LMM (ELMM) and augmented LMM (ALMM)) and three physics-based nonlinear mixture models (bilinear-Fan model (BFM), generalized bilinear model (GBM) and polynomial post-nonlinear model (PPNM)) on four synthetic and real scenarios with hyperspectral and multispectral datasets were performed. The experimental results suggest the IWLMM outperforms the other seven linear and nonlinear unmixing models after adding the correction for endmember variability by modeling the perturbation and scaling factors of spectral features simultaneously. It has an impressive ability for decomposing and reconstructing pixels.