Improved analysis and modelling of soil diffuse reflectance spectra using wavelets

Diffuse reflectance spectroscopy using visible (vis), near-infrared (NIR) and mid-infrared (mid-IR) energy can be a powerful tool to assess and monitor soil quality and function. Mathematical pre-processing techniques and multivariate calibrations are commonly used to develop spectroscopic models to predict soil properties. These models contain many predictor variables that are collinear and redundant by nature. Partial least squares regression (PLSR) is often used for their analysis. Wavelets can be used to smooth signals and to reduce large data sets to parsimonious representations for more efficient data storage, computation and transmission. Our aim was to investigate their potential for the analyses of soil diffuse reflectance spectra. Specifically we wished to: (i) show how wavelets can be used to represent the multi-scale nature of soil diffuse reflectance spectra, (ii) produce parsimonious representations of the spectra using selected wavelet coefficients and (iii) improve the regression analysis for prediction of soil organic carbon (SOC) and clay content. We decomposed soil vis-NIR and mid-IR spectra using the discrete wavelet transform (DWT) using a Daubechies's wavelet with two vanishing moments. A multiresolution analysis (MRA) revealed their multi-scale nature. The MRA identified local features in the spectra that contain information on soil composition. We illustrated a technique for the selection of wavelet coefficients, which were used to produce parsimonious multivariate calibrations for SOC and clay content. Both vis-NIR and mid-IR data were reduced to less than 7% of their original size. The selected coefficients were also back-transformed. Multivariate calibrations were performed by PLSR, multiple linear regression (MLR) and MLR with quadratic polynomials (MLR-QP) using the spectra, all wavelet coefficients, the selected coefficients and their back transformations. Calibrations by MLR-QP using the selected wavelet coefficients produced the best predictions of SOC and clay content. MLR-QP accounted for any nonlinearity in the data. Transforming soil spectra into the wavelet domain and producing a smaller representation of the data improved the efficiency of the calibrations. The models were computed with reduced, parsimonious data sets using simpler regressions.