高光谱遥感技术具有强大的地物探测能力.然而,其空间分辨率低的特点导致光谱图像中存在大量的混合像元,该现象阻碍了高光谱技术的应用和发展.针对米级以下的高光谱图像,线性混合模型能够很好地为混合像元建模.由于其物理上的可释性以及数学上的可操作性,作为光谱解混基础的线性混合模型受到了广泛关注,为高光谱图像的混合像元解混问题提供了重要的解决思路.然而,由于观测噪声、环境条件、端元变异性和数据集大小等情况的存在,线性解混依然是一个具有挑战性的不适定的逆问题.通过整理近五年的文献资料,分别从非负矩阵分解、原型分析、贝叶斯方法以及稀疏解混四个方面介绍线性解混数学模型的发展现状以及面临的问题.

Hyperspectral imaging acquires precise spectral information about the scene radiance that is exploited from efficient earth exploration in remote sensing. However, because of the limited spatial resolution, mixed pixels widely exist in the obtained hyperspectral data. It severely hinders the application of hyperspectral data. Hence, hyperspectral unmixing (HU) has become an essential task for HSI analysis. The most commonly model used for the mixture formation is a linear process or non-linear process. As linear mixing model (LMM) has clear physical meaning and is amenable to mathematical treatment, it has received widespread attention. To tackle the unmixing challenge, a number of linear algorithms have been proposed effectively. However, unmixing is a challenging, ill-posed inverse problem because of observation noise, environmental conditions, endmember variability, and data set size. The paper provided a comprehensive review of the state-of-the-art model in spectral unmixing. These models are discussed according to the following four categories: matrix decomposition, archetype analysis, bayesian method and sparse regression. In addition, both advantages and defects of these models are presented. Finally, a perspective on future research directions for advancing spectral unmixing methods is offered.