小麦条锈病具有流行性强，危害程度大等特点，严重影响了小麦的产量和质量。高光谱数据能够提供精细的地物光谱信息，被广泛应用于作物病害探测中。冠层高光谱数据容易受到背景和其它噪声信息的干扰，影响着小麦条锈病的遥感探测精度。对反射率光谱进行微分处理能够降低噪声干扰，突出光谱数据间细微差别，然而整数阶微分容易造成信号缺失，忽略掉部分有用的光谱信息。分数阶微分光谱能够呈现出原始光谱和整数阶微分光谱的“中间”光谱细节，平衡整数阶微分光谱的优缺点，在消除基线漂移、平缓背景干扰的同时可保留更多光谱信息。本文在利用Grunwald-Letnikov（GL）方法对条锈病胁迫下小麦冠层反射率光谱进行分数阶微分处理的基础上，利用相关系数、互信息等方法对分数阶微分光谱进行特征波段选择，以波段组合优化方法构建了两波段和三波段分数阶微分光谱指数，并将特征波段与分数阶微分光谱指数应用于小区控制实验和大田条件下的小麦条锈病遥感探测。

（1）通过GL方法对冠层原始光谱进行0~2阶分数阶微分处理（步长为0.1），采用相关系数和互信息分析了分数阶微分光谱对条锈病病情严重度的敏感性。结果表明，经过分数阶微分处理的光谱与条锈病病情严重度的敏感性得到增强，1.1~1.3阶微分光谱与病情严重度的最大相关系数和互信息均优于原始光谱和整数阶微分光谱，其中最大相关系数出现在1.2阶，对应波长为481nm，较原始光谱、一阶微分、二阶微分的最大相关系数分别提高了20.9%、3.9%和20.5%，最大互信息同样出现在1.2阶，对应波长为462nm，较原始光谱、一阶微分、二阶微分的最大互信息分别提高了72.9%、9.4%和10.8%。

（2）采用波段组合优化的方法构建了两波段分数阶微分光谱指数（FDI、FRI、FNDI）和三波段分数阶微分光谱指数（FIDI、FIRI、FPRI）。通过分析各指数与小麦条锈病严重度的相关性，利用最大相关系数确定了分数阶微分光谱指数的最优分数阶次及其对应波长，最终构建的两波段分数阶微分光谱指数为FDI^0.4(ρ₄₈₁, ρ₄₇₅)、FRI^1.3(ρ₄₇₈, ρ₆₂₂)、FNDI^1.2(ρ₄₈₁, ρ₆₇₃)，三波段分数阶微分光谱指数为FIDI^1.1(ρ₄₈₁, ρ₄₄₂, ρ₄₅₄)、FIRI^1.2(ρ₈₈₀, ρ₆₇₀, ρ₄₈₁)、FPRI^0.5(ρ₆₄₆, ρ₄₀₀, ρ₉₅₅)，三波段分数阶微分光谱指数与小麦条锈病严重度的相关性优于两波段分数阶微分光谱指数，其中FPRI^0.5(ρ₆₄₆, ρ₄₀₀, ρ₉₅₅)与小麦条锈病严重度的相关性最高。

（3）采用相关系数（CC）、互信息（MI）、相关系数结合遗传-支持向量回归（CGA-SVR）和互信息结合遗传-支持向量回归（MGA-SVR）对各阶次分数阶微分光谱进行波段优选，并应用偏最小二乘（PLS）和支持向量回归（SVR）进行模型构建。小区实验数据验证结果表明，以1.3阶微分光谱构建的MGA-SVR模型的预测性能最好，验证集预测病情指数（DI）和实测DI的R²为0.871，较原始光谱最优模型（CGA-SVR模型）、一阶微分光谱最优模型（MGA-SVR模型）、二阶微分光谱最优模型（MGA-SVR模型）分别提高了13.6%、7.5%和6.2%。大田实验数据验证结果表明1.3阶微分光谱构建的MGA-SVR模型对病情严重度的预测结果优于整数阶微分光谱的最佳模型。

（4）以本文构建的两波段和三波段分数阶微分光谱指数为输入特征构建小麦条锈病严重度估算的PLS模型和SVR模型，并将其与常用的反射率光谱指数、“三边”参数、吸收特征构建的模型进行对比。结果表明，相同的输入特征下，SVR模型的预测精度均优于PLS模型，利用分数阶微分光谱指数构建的PLS模型和SVR模型的预测精度均高于其它输入特征所建模型精度，其中SVR模型预测DI与实测DI的R²为0.901，较光谱指数、“三边”参数、吸收特征的SVR模型分别提高了11.4%、14.1%和15.2%，以大田样本对不同输入特征的SVR模型进行验证，分数阶微分光谱指数的SVR模型对大田样本DI的预测精度高于其它输入特征的SVR模型，证明分数阶微分光谱指数能够提高小麦条锈病的遥感探测精度。

Wheat stripe rust has the characteristics of strong epidemic and serious damage, which seriously affects the yield and quality of wheat. Hyperspectral data is widely used in crop disease detection because it can provide fine spectral information of ground features. Canopy hyperspectral data is easily disturbed by background and other noise information, which affects the remote sensing detection accuracy of wheat stripe rust. Differential processing of reflectance spectrum can reduce noise interference and highlight the subtle differences between spectral data. However, integer order differential is easy to cause signal loss and ignore part of useful spectral information. The fractional differential spectrum can present the "intermediate" spectral details of the original spectrum and the integer differential spectrum, balancing the advantages and disadvantages of the integer differential spectrum, more spectral information can be retained while eliminating baseline drift and smoothing background interference. In this paper, the Grunwald-Letnikov (GL) method was used to perform fractional differential processing on wheat canopy reflectance spectra under stripe rust stress. Then, correlation coefficients, mutual information and other methods were used to select the characteristic bands of the fractional differential spectra, the two-band and three-band fractional differential spectral indices were constructed by the band combination optimization method. Finally, the characteristic band and fractional differential spectral index were applied to the remote sensing detection of Wheat Stripe Rust under plot control experiment and field condition.

(1) The original spectrum of the canopy was processed with 0~2 order fractional differentiation (step length is 0.1) by the GL method, and the sensitivity of the fractional differential spectrum to the severity of stripe rust was analyzed using correlation coefficients and mutual information. The results showed that the sensitivity of the spectrum to the severity of stripe rust disease has been enhanced after fractional differential processing. The maximum correlation coefficient and mutual information between the 1.1~1.3 order differential spectrum and the severity of the disease were better than the original spectrum and the integer-order differential spectrum. The maximum correlation coefficient appeared at order 1.2 and the corresponding wavelength was 481nm, which was 20.9%, 3.9% and 20.5% higher than that of the original spectrum, the first order differential spectrum and the second order differential spectrum, respectively. The maximum mutual information also appeared at order 1.2, corresponding wavelength was 462nm, which was 72.9%, 9.4% and 10.8% higher than the maximum mutual information of original spectrum, first-order differential and second-order differential, respectively.

(2) The two-band fractional differential spectral indices (FDI, FRI, FNDI) and the three-band fractional differential spectral indices (FIDI, FIRI, FPRI) were constructed using the method of band combination optimization. By analyzing the correlation between each index and the severity of wheat stripe rust, using the maximum correlation coefficient to determine the optimal fractional order of the fractional differential spectral indices and its corresponding wavelength, the final two-band fractional differential spectral indices were FDI^0.4(ρ₄₈₁, ρ₄₇₅), FRI^1.3(ρ₄₇₈, ρ₆₂₂), FNDI^1.2(ρ₄₈₁, ρ₆₇₃), the three-band fractional differential spectral indices were FIDI^1.1(ρ₄₈₁, ρ₄₄₂, ρ₄₅₄), FIRI^1.2(ρ₈₈₀, ρ₆₇₀, ρ₄₈₁), FPRI^0.5(ρ₆₄₆, ρ₄₀₀, ρ₉₅₅). The correlation between the three-band fractional differential spectral indices and the severity of wheat stripe rust was better than that of the two-band fractional differential spectral indices, and FPRI^0.5(ρ₆₄₆, ρ₄₀₀, ρ₉₅₅) had the highest correlation with the severity of wheat stripe rust.

(3) Correlation coefficient (CC), mutual information (MI), correlation coefficient combined with genetic support vector regression (CGA-SVR) and mutual information combined with genetic support vector regression (MGA-SVR) were used to optimize the bands of each order fractional differential spectrum. Partial least squares (PLS) and support vector regression (SVR) were used for model construction. The experimental data verification results of the cell showed that the MGA-SVR model constructed with the 1.3-order differential spectrum had the best predictive performance. The R² between the predicted disease index (DI) of the validation set and the measured DI was 0.871, which were 13.6%, 7.5%, and 6.2% higher than the optimal model of the original spectrum (CGA-SVR model), the optimal model of the first-order differential spectrum (MGA-SVR model), and the optimal model of the second-order differential spectrum (MGA-SVR model), respectively. The Field experimental data verification results showed that the MGA-SVR model constructed by 1.3-order differential spectrum was better than the best model of integer-order differential spectrum in predicting the severity of the disease.

(4) The two-band and three-band fractional differential spectral indices constructed in this paper were used as input features to construct the PLS model and SVR model for estimating the severity of wheat stripe rust. And compared it with the commonly used models constructed by reflectance spectral index, "trilateral" parameters, and absorption characteristics. The results showed that under the same input characteristics, the prediction accuracy of the SVR model was better than that of the PLS model. Regardless of the modeling method adopted, the prediction accuracy of the PLS model and SVR model constructed using the fractional differential spectral index were higher than the accuracy of the models constructed with other input features. The R² of the SVR model predicted DI and the measured DI was 0.901, which was 11.4%, 14.1% and 15.2% higher than the SVR model of spectral index, "trilateral" parameters, and absorption characteristics, respectively. The field samples were used to verify SVR models with different input characteristics. The SVR model of fractional differential spectral index had a higher prediction accuracy for the DI of field samples than SVR models with other input characteristics. It is proved that the fractional differential spectral index can improve the remote sensing detection accuracy of wheat stripe rust.

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