For agricultural production and food safety, it is important to accurately and extensively estimate the heavy metal(loid) pollution contents in farmland soil. Remote sensing technology provides a feasible method for the rapid determination of heavy metal(loid) contents. In this study, the contents of Ni, Hg, Cr, Cu, and As in the agricultural soil of the Suzi River Basin in Liaoning Province were taken as an example. The spectral data, with Savitzky–Golay smoothing, were taken as the original spectra (OR), and the spectral transformation was achieved by continuum removal (CR), reciprocal (1/R), root means square ($\sqrt{\mathrm{R}}$), first-order differential (FDR), and second-order differential (SDR) methods. Then the spectral indices were calculated by the optimal band combination algorithm. The correlation between Ni, Hg, Cr, Cu, and As contents and spectral indices was analyzed, and the optimal spectral indices were selected. Then, multiple linear regression (MLR), partial least squares regression (PLSR), random forest regression (RFR), and adaptive neuro-fuzzy reasoning system (ANFIS) were used to establish the estimation model based on the combined optimal spectral indices method. The results show that the combined optimal spectral indices method improves the correlation between spectra and heavy metal(loid), the MLR model produces the best estimation effect for Ni and Cu (${\mathrm{R}}^2=0.713 \mathrm{and} 0.855$, RMSE = 5.053 and 8.113, RPD = 1.908 and 2.688, respectively), and the PLSR model produces the best effect for Hg, Cr, and As (${\mathrm{R}}^2=$ 0.653, 0.603, and 0.775, RMSE = 0.074, 23.777, and 1.923, RPD = 1.733, 1.621, and 2.154, respectively). Therefore, the combined optimal spectral indices method is feasible for heavy metal(loid) estimation in soils and could provide technical support for large-scale soil heavy metal(loid) content estimation and pollution assessment.

Portable X-ray fluorescence spectrometry (pXRF) is an analytical technique that can be used for rapid and non-destructive analysis in the field. However, the testing accuracy and precision for trace elements are significantly affected by the matrix effect, which comes mainly from major elements that constitute most of the matrix of a sample. To solve this problem, many methods based on linear regression models have been proposed, but when extreme values or outliers occur, the application of these methods will be greatly affected. In this study, 16 certified reference materials were collected for pXRF analysis, and the major elements most closely related to the elements to be measured were employed as correction indicators to calibrate the analysis results through the application of multiple linear regression analysis. Some statistical parameters were calculated to evaluate the correction results. Compared with the calibration data obtained from simple linear regression analysis without taking major elements into account, those corrected by the new method were of higher quality, especially for elements of Co, Zn, Mo, Ta, Tl, Pb, Cd and Sn. The results show that the new method can effectively suppress the influence of the matrix effect.