Multi-scale Gaussian pyramid preprocessing of Vis–NIR and XRF spectra for heavy metal estimation in agricultural soils

Monitoring heavy metal concentrations in agricultural soils is essential to assess risks to crop quality and food safety, but conventional laboratory analyses are slow, expensive, and unsuitable for large-scale surveys. Visible, near-infrared (Vis–NIR) and X-ray fluorescence (XRF) spectroscopy offer rapid, non-destructive alternatives, but their high-dimensional, noisy, and collinear spectra require careful preprocessing procedure. This study evaluates the Gaussian pyramid scale-space, a multi-resolution preprocessing framework originally developed for image processing, as a unified approach for denoising and dimensionality reduction of Vis–NIR and XRF spectra of 100 soil samples collected from the DEMMIN agricultural site (northeastern Germany) and analyzed for heavy metals (Cr, Mn, Fe, Cu, Zn, and Pb) concentrations. Eight Gaussian pyramid octaves were generated from each spectrum, together with first- and second-derivative variants, and Cubist regression models were trained for each combination of metal, sensor, octave, and derivative. Single-sensor XRF models achieved strong performance in the independent test set for Mn, Fe, Cu, Zn, and Pb ( R 2 = 0.92–0.97; RPD = 3.77–6.72) and moderate performance for Cr ( R 2 = 0.4). Single-sensor Vis–NIR models were uninformative in all metals, consistent with the background-level concentrations and low organic carbon of the site. The optimal predictive resolution for XRF was systematically found in intermediate octaves (0.08–0.32 keV), corresponding to a 4- to 16-fold reduction of the original sampling interval. The low-level fusion of Vis–NIR and XRF did not improve with XRF alone. The Cubist feature-importance analysis recovered the characteristic K α and L-series emission energies of each element, confirming that the models exploit physically meaningful spectral information. The Gaussian pyramid scale-space is therefore proposed as a principled and computationally efficient preprocessing strategy for the evaluation of heavy metals in soil based on XRF spectra.