非负和完全可加性约束下的光谱源贝叶斯分离
Bayesian separation of spectral sources under non-negativity and full additivity constraints
摘要：
本文研究了未知比例线性混合光谱源的分离问题。问题的主要难点是保证混合系数的完全可加性（和为一）以及源和混合系数的非负性。最近提出了一种基于Gamma先验的贝叶斯估计方法来处理线性混合模型中的非负约束。然而，纳入完整的可加性约束需要进一步的发展。本文研究了一种新的多层贝叶斯模型，该模型适用于线性混合物的回归变量和回归系数的非负性和和对一约束。该模型的未知参数的估计是使用适当的吉布斯采样器生成的样本进行的。所提出的算法的性能进行评估，通过模拟结果进行合成混合模型。所提出的方法也适用于处理多组分化学混合物产生的拉曼光谱。
英文摘要：
This paper addresses the problem of separating spectral sources which are linearly mixed with unknown proportions. The main difficulty of the problem is to ensure the full additivity (sum-to-one) of the mixing coefficients and non-negativity of sources and mixing coefficients. A Bayesian estimation approach based on Gamma priors was recently proposed to handle the non-negativity constraints in a linear mixture model. However, incorporating the full additivity constraint requires further developments. This paper studies a new hierarchical Bayesian model appropriate to the non-negativity and sum-to-one constraints associated to the regressors and regression coefficients of linear mixtures. The estimation of the unknown parameters of this model is performed using samples generated using an appropriate Gibbs sampler. The performance of the proposed algorithm is evaluated through simulation results conducted on synthetic mixture models. The proposed approach is also applied to the processing of multicomponent chemical mixtures resulting from Raman spectroscopy.
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