arXiv:2503.17118eess.IV2025-03

比较稀疏、迭代与混合整数规划模型在高光谱解混中的表现。

Spectral Unmixing Comparison with Sparse, Iterative and Mixed Integer Programming Models

  • 对比稀疏回归、迭代搜索与混合整数规划解混方法
  • 新方法HySUDeB在平均误差和精度上优于传统方法
  • 适合高光谱图像分析与矿物识别研究者参考

高光谱解混是通过分析混合像素光谱,识别其中包含的纯物质及其比例的过程。本文深入探讨了普通最小二乘法(OLS)在高光谱图像分析中线性混合模型应用时所隐含的假设。同时,研究了基于稀疏回归、迭代特征搜索策略以及数学规划等高效解混方法的变体,并与一种新型解混方法HySUDeB进行比较。通过计算各模型的平均误差与精度评估性能。此外,还构建了矿物分子结构的分类体系,以深化对目标物质检测的理解。

原文摘要 · Abstract (English)

Hyperspectral unmixing is the analytical process of determining the pure materials and estimating the proportions of such materials composed within an observed mixed pixel spectrum. We can unmix mixed pixel spectra using linear and nonlinear mixture models. Ordinary least squares (OLS) regression serves as the foundation for many linear mixture models employed in Hyperspectral Image analysis. Though variations of OLS are implemented, studies rarely address the underlying assumptions that affect results. This paper provides an in depth discussion on the assumptions inherently endorsed by the application of OLS regression. We also examine variations of OLS models stemming from highly effective approaches in spectral unmixing -- sparse regression, iterative feature search strategies and Mathematical programming. These variations are compared to a novel unmixing approach called HySUDeB. We evaluated each approach's performance by computing the average error and precision of each model. Additionally, we provide a taxonomy of the molecular structure of each mineral to derive further understanding into the detection of the target materials.

高光谱解混稀疏回归数学规划矿物识别

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