高光谱成像技术在实现低成本大范围的土壤重金属快速监测方面独具潜力。针对高光谱图像反演中突出的小样本问题，本文基于分数阶微分(Fractional Order Derivative, FOD)提出一种面向高光谱图像的土壤重金属反演方法。首先，利用土壤采样点的邻近像元进行样本扩充，增加样本的光谱差异性；其次，采用FOD突出光谱特征同时保留微分光谱的渐变信息；进而通过竞争自适应重加权采样(Competitive Adaptive Reweighted Sampling，CARS)优选波段，采用偏最小二乘方法（PLSR）建立反演模型。以新疆哈密黄山南矿区获取的72个土壤样本和航空高光谱图像为研究数据，对铅(Pb)、锌(Zn)、镍(Ni)三种重金属进行反演，结果表明：样本扩充不仅缓和了模型的过拟合现象，还提升了重金属反演精度；最佳阶数的分数阶微分能有效增强光谱特征，提高反演精度；CARS相对于相关系数法(Correlation Coefficient, CC) 、遗传算法(Genetic Algorithm，GA)选出的波段组合反演精度更优，对研究区重金属Pb、Zn、Ni的反演精度R2分别为0.7974、0.8690和0.8303，反演方法具有较好的鲁棒性。

Objective: Hyperspectral imaging technology has the unique potential to rapidly monitor soil heavy metals at a low cost and large scale. For hyperspectral images, the number of soil image elements differs greatly from the number of soil samples, so the problem of small samples is prominent. In this study, we proposed a soil heavy metal estimation method based on fractional order derivative (FOD) for hyperspectral images. Method: Firstly, we extracted the neighboring pixels of soil samples to expand the samples and increase the spectral variability; secondly, FOD was used to highlight the spectral features; then we selected the bands by Competitive Adaptive Reweighted Sampling (CARS) and used partial least squares (PLSR) to construct the model. Seventy-two soil samples and aerial hyperspectral images obtained from the Huangshan South mine in Hami, Xinjiang were used to estimate three heavy metals, namely, lead (Pb), zinc (Zn), and nickel (Ni). Result: After the sample expansion, the estimation accuracy of the test set was improved for three heavy metals, the test set R2 improved from 0.6128 to 0.7974 for Pb, from 0.8178 to 0.8690 for Zn, and from 0.6969 to 0.8303 for Ni, while the R2 of the training set was above 0.8. The accuracy of estimation model for three heavy metals with the best fractional order differentiation was better than that using integer order differentiation. CARS+PLSR obtained higher estimation accuracy than the modeling approaches of GA+PLSR and CC+PLSR, the estimation accuracies R2 were 0.7974, 0.8690, and 0.8303 for Pb, Zn, and Ni. Conclusion: The sample expansion alleviated the overfitting phenomenon and improved the estimation accuracy. The FOD of the optimal order could effectively enhance the spectral features and improve the estimation accuracy. The CARS was more accurate than the Correlation Coefficient (CC) and Genetic Algorithm (GA), and the estimation method of this study has good robustness.