面向土壤与矿物的大光谱库下采用迭代、稀疏与集成方法的高光谱解混
Hyperspectral Unmixing using Iterative, Sparse and Ensambling Approaches for Large Spectral Libraries Applied to Soils and Minerals
AI总结：
针对大光谱库下高光谱解混的不适定问题，对比了LASSO、ElasticNet及结合二者的迭代特征选择、BMA、BMA-Q等稀疏回归变体，通过分子组成异同评估各方法识别混合物质的准确率。
摘要：
解混是高光谱图像处理中的基础流程，该过程基于候选物质的光谱与像素光谱，确定混合像素中存在的物质类别。要实现实用且通用的解混，需要大型光谱库，库中需包含覆盖每种候选物质全部变异的样本测量值，以及种类足够丰富的潜在物质集合。然而，当光谱数量多于波段数量时，使用基于经典最小二乘回归的解混方法会导致反演问题不适定。此外，出于数值计算和维度方面的原因，包含超过10或20条光谱的光谱库在计算上会表现出不适定特性。在当前实践中，图像解混通常使用人工选择的物质或图像端元来完成。要利用大型光谱库对未知物质的光谱进行通用解混，需要某种形式的稀疏回归——即仅少量系数非零的回归方法，这需要在拟合优度与模型规模之间进行权衡。本研究对比了两种稀疏回归技术的多种变体，重点关注物质的结构与化学性质之间的关系，以及各类模型识别混合像素中正确物质组合的准确率。具体而言，我们研究了LASSO回归和ElasticNet，并将其与迭代特征选择的多种变体、贝叶斯模型平均（Bayesian Model Averaging, BMA）以及二次贝叶斯模型平均（quadratic BMA, BMA-Q）进行对比，后两种方法以LASSO回归和ElasticNet作为基础模型。为评估这些方法的有效性，我们对比了模型中选出的物质与真值之间的分子组成异同。
英文摘要：
Unmixing is a fundamental process in hyperspectral image processing in which the materials present in a mixed pixel are determined based on the spectra of candidate materials and the pixel spectrum. Practical and general utility requires a large spectral library with sample measurements covering the full variation in each candidate material as well as a sufficiently varied collection of potential materials. However, any spectral library with more spectra than bands will lead to an ill-posed inversion problem when using classical least-squares regression-based unmixing methods. Moreover, for numerical and dimensionality reasons, libraries with over 10 or 20 spectra behave computationally as though they are ill-posed. In current practice, unmixing is often applied to imagery using manually-selected materials or image endmembers. General unmixing of a spectrum from an unknown material with a large spectral library requires some form of sparse regression; regression where only a small number of coefficients are nonzero. This requires a trade-off between goodness-of-fit and model size. In this study we compare variations of two sparse regression techniques, focusing on the relationship between structure and chemistry of materials and the accuracy of the various models for identifying the correct mixture of materials present. Specifically, we examine LASSO regression and ElasticNet in contrast with variations of iterative feature selection, Bayesian Model Averaging (BMA), and quadratic BMA (BMA-Q) -- incorporating LASSO regression and ElasticNet as their base model. To evaluate the the effectiveness of these methods, we consider the molecular composition similarities and differences of substances selected in the models compared to the ground truth.
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