Hyperspectral unmixing while considering endmember variability is usually
performed by the normal compositional model (NCM), where the endmembers for
each pixel are assumed to be sampled from unimodal Gaussian distributions.
However, in real applications, the distribution of a material is often not
Gaussian. In this paper, we use Gaussian mixture models (GMM) to represent the
endmember variability. We show, given the GMM starting premise, that the
distribution of the mixed pixel (under the linear mixing model) is also a GMM
(and this is shown from two perspectives). The first perspective originates
from the random variable transformation and gives a conditional density
function of the pixels given the abundances and GMM parameters. With proper
smoothness and sparsity prior constraints on the abundances, the conditional
density function leads to a standard maximum a posteriori (MAP) problem which
can be solved using generalized expectation maximization. The second
perspective originates from marginalizing over the endmembers in the GMM, which
provides us with a foundation to solve for the endmembers at each pixel. Hence,
our model can not only estimate the abundances and distribution parameters, but
also the distinct endmember set for each pixel. We tested the proposed GMM on
several synthetic and real datasets, and showed its potential by comparing it
to current popular methods.

考虑端元变化的高光谱解混存在现实应用中物质分布通常不是高斯分布，本文提出使用高斯混合模型表示端元变化，通过两种视角验证了使用高斯混合模型与线性混合模型推导混合像素分布的关系，基于此给出了一种用于估计混合像素分布和端元的方法，并在合成数据和真实数据上验证其效果。

高斯混合模型用于高光谱分离成分中的端元变异表示

A Gaussian mixture model representation of endmember variability in  hyperspectral unmixing

When considering the problem of unmixing hyperspectral images, most of the
literature in the geoscience and image processing areas relies on the widely
used linear mixing model (LMM). However, the LMM may be not valid and other
nonlinear models need to be considered, for instance, when there are
multi-scattering effects or intimate interactions. Consequently, over the last
few years, several significant contributions have been proposed to overcome the
limitations inherent in the LMM. In this paper, we present an overview of
recent advances in nonlinear unmixing modeling.

本文综述了非线性解混模型在高光谱遥感图像中的应用和发展。

高光谱影像的非线性解混模型与算法

Nonlinear unmixing of hyperspectral images: models and algorithms

In this paper, we study the nonnegative matrix factorization problem under
the separability assumption (that is, there exists a cone spanned by a small
subset of the columns of the input nonnegative data matrix containing all
columns), which is equivalent to the hyperspectral unmixing problem under the
linear mixing model and the pure-pixel assumption. We present a family of fast
recursive algorithms, and prove they are robust under any small perturbations
of the input data matrix. This family generalizes several existing
hyperspectral unmixing algorithms and hence provides for the first time a
theoretical justification of their better practical performance.

本文研究了非负矩阵分解问题，该问题在可分离性假设下等同于高光谱分离问题。我们提出了一族快速递归算法，并证明了它们对输入数据矩阵的任意小干扰都具有鲁棒性。这一族算法扩展了现有的几种高光谱分离算法，并首次提供了其更好的实际表现的理论证明。