Estimating cadmium-lead concentrations in rice blades through fractional order derivatives of foliar spectra

Heavy metal pollution in farmland harms the environment and poses a potential risk to human health. Visible and near-infrared reflectance (VNIR) spectroscopy is a promising tool for estimating heavy metal concentrations in plants. Integer-order derivatives (including the first and second) are commonly used to pre-process VNIR data and successfully detect certain spectral signals. However, they fail to detect gradual tilts or curvatures and useful target variable information. In this study, a greenhouse experiment covering 16 pre-treatments of Cd–Pb (cadmium-lead) cross-contamination was designed to collect the VNIR data of rice blades during the late booting stage. A fractional order derivative (FOD) algorithm with increments of 0.1 was utilised to pre-process the spectra of the rice blades to explore the model performance in building relationships between Cd and Pb concentrations and leaf spectra. The results indicated that the inversion with pre-processing of integer-order derivatives was not as good as the optimal results with pre-processing of fractional-order derivatives. The R2 and RMSE of the Cd estimation reached 0.84 and 4.69 at 0.3rd order pre-processing, while the R2 and RMSE of Pb were 0.49 and 191.24 at 1.4th order pre-processing. These optimal results were better than those with pre-processing of 1st and 2nd derivatives, resulting in an increase of R2 and a decrease of RMSE. These results indicated that fractional-order derivatives outperformed integer-order derivatives for pre-processing the rice blades spectra to estimate Cd–Pb concentrations. Our results demonstrated that FOD is an effective spectral processing routine for heavy metal estimation for Cd–Pb cross-contamination.