Most algorithms for hyperspectral image unmixing produce point estimates of fractional abundances of the materials to be separated. However, in the absence of reliable ground truth, the ability to perform abundance uncertainty quantification (UQ) should be an important feature of algorithms, e.g. to evaluate how hard the unmixing problem is and how much the results should be trusted. The usual modeling assumptions in Bayesian models for unmixing rely heavily on the Euclidean geometry of the simplex and typically disregard spatial information. In addition, to our knowledge, abundance UQ is close to nonexistent. In this paper, we propose to leverage Aitchinson geometry from the compositional data analysis literature to provide practitioners with alternative tools for modeling prior abundance distributions. In particular we show how to design simplex-valued Gaussian Process priors using this geometry. Then we link Aitchinson geometry to constrained sampling algorithms in the literature, and propose UQ diagnostics that comply with the constraints on abundance vectors. We illustrate these concepts on real and simulated data.

翻译：大多数高光谱图像解混算法仅生成待分离材料丰度分数的点估计。然而，在缺乏可靠地面真值的情况下，实现丰度不确定性量化应成为算法的重要特性，例如评估解混问题的难度以及结果的可信度。贝叶斯解混模型中的常规建模假设严重依赖于单纯形的欧几里得几何，且通常忽略空间信息。此外，据我们所知，丰度不确定性量化几乎不存在。本文提出利用成分数据分析文献中的艾奇逊几何，为实践者提供建模先验丰度分布的替代工具。我们特别展示了如何利用该几何设计单纯形值高斯过程先验，并将艾奇逊几何与文献中的约束采样算法相关联，进而提出符合丰度向量约束的不确定性量化诊断指标。最后，我们通过真实与模拟数据验证这些概念。