提出新方法计算点到多面体的欧式距离，用于光谱图像非线性解混
Euclidean Distance to Convex Polyhedra and Application to Class Representation in Spectral Images
- 基于任意线性分类器构建空间密度函数，改进传统线性解混
- 精确求解多面体中最小范数点，算法高效且数学严谨
- 在萨姆森数据集和锂电池光谱图上表现优于现有方法，适用性强
为仅从观测数据估计丰度图，传统线性解混方法在波段过少或光谱高度相关时效果不佳。为此，本文提出一种新方法，基于任意线性分类器构建自适应的空间密度函数。给出了计算点到多面体集合欧氏距离的稳健数学公式，并设计了一种高效算法，可精确求出多面体中的最小范数点。在广泛使用的Samson高光谱数据集上的实证评估表明，该方法在重建丰度图方面优于现有最优方法。此外，其在不适用于线性解混模型的锂离子电池光谱图像上的应用，验证了该方法的通用性与有效性。
原文摘要 · Abstract (English)
With the aim of estimating the abundance map from observations only, linear unmixing approaches are not always suitable to spectral images, especially when the number of bands is too small or when the spectra of the observed data are too correlated. To address this issue in the general case, we present a novel approach which provides an adapted spatial density function based on any arbitrary linear classifier. A robust mathematical formulation for computing the Euclidean distance to polyhedral sets is presented, along with an efficient algorithm that provides the exact minimum-norm point in a polyhedron. An empirical evaluation on the widely-used Samson hyperspectral dataset demonstrates that the proposed method surpasses state-of-the-art approaches in reconstructing abundance maps. Furthermore, its application to spectral images of a Lithium-ion battery, incompatible with linear unmixing models, validates the method's generality and effectiveness.
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