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。