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.

光谱分解已经引起了人们对多光谱和高光谱数据处理的极大关注。在不同种类的光谱解混模型中，线性混合模型（LMM）由于其在光散射机制方面的简单性和在不同场景下的灵活性而得到了广泛应用。近来，已经开发了各种优化的LMM以增强分解能力。但是，仍然存在两个主要挑战：终端成员可变性和具有不等式约束的全局最优解。为了避免端元变异性的影响并扩展LMM的应用，提出了一种新的不等式约束加权线性混合模型（IWLMM）。基于变量误差（EIV）模型和加权总最小二乘（WTLS）理论，消除了端构件可变性和端构件以及混合像素的随机误差的问题。利用非负约束，还生成了一种简单的求解IWLMM的最佳算法。为了表明提出的IWLMM的优势，使用常规的完全约束最小二乘（FCLS），三个当前提出的基于LMM的模型（扰动LMM（PLMM），扩展LMM（ELMM）和增强LMM（ALMM））进行比较实验，以及在具有高光谱和多光谱数据集的四个合成和实际场景上，执行了三个基于物理学的非线性混合模型（双线性范模型（BFM），广义双线性模型（GBM）和多项式非线性后模型（PPNM））。实验结果表明，通过同时对频谱特征的摄动和缩放因子进行建模，在添加了对末端成员可变性的校正后，IWLMM的性能优于其他七个线性和非线性解混模型。它具有出色的分解和重建像素的能力。