Sparse-Sample Reconstruction of Crop Vigor Using Sentinel-2 NDVI: A Preliminary Benchmark of IDW and Kriging for Precision Agriculture

Sparse field measurements and frequent cloud cover continue to limit the availability of complete NDVI observations for precision agriculture. To address this constraint, this study evaluates how effectively both classical geostatistical interpolation and modern artificial intelligence‑based predictors can reconstruct full NDVI surfaces from limited point samples. A Sentinel‑2 NDVI composite (10 m, June–July 2024) over a digitised 98.1 ha arable parcel in Uckermark, Brandenburg, Germany, serves as the reference dataset, with 9,811 in‑field pixels retained after masking. Fifty sparse samples were generated by drawing points from the reference raster with added Gaussian sensor noise, and the sampling process was repeated 50 times to ensure robust evaluation. Two established geostatistical methods—inverse distance weighting and ordinary kriging—were benchmarked alongside five learning‑based approaches: random forest, gradient boosting, Gaussian process regression, a coordinate‑based neural network with random Fourier positional encoding, and a residual‑kriging hybrid. The AI models were applied directly to the sparse NDVI samples to learn the relationship between spatial coordinates and NDVI values, enabling full‑parcel predictions without relying on manually defined spatial structures. The neural network used Fourier features to encode spatial position, while the residual‑kriging hybrid combined machine learning predictions with kriging of residuals to capture the remaining spatial dependence. This dual‑framework design provides a scientifically grounded comparison between manually parameterised geostatistical interpolators and data‑driven AI models, addressing a central question in remote‑sensing‑based surface reconstruction: whether learned predictors can outperform classical methods under sparse‑sampling constraints. All hyperparameters—including IDW power, neighbourhood size, variogram model, kernel choice, and encoding bandwidth—were selected within each repetition using training data only. The exponential variogram consistently outperformed spherical, Gaussian, and linear alternatives. Ordinary kriging achieved the lowest mean error (held‑out RMSE 0.089 ± 0.035; full‑field RMSE 0.092 ± 0.011; R² 0.586 ± 0.104), although its performance was statistically indistinguishable from inverse distance weighting (paired p = 0.38). Both geostatistical methods significantly outperformed all five AI‑based predictors across sampling densities from 20 to 200 points. Kriging prediction variance demonstrated good calibration (RMSSE 0.88), and management‑zone delineation using k‑means clustering reproduced 81.4% of reference‑raster zones. The results indicate that, under sparse‑sampling conditions, classical geostatistical interpolation remains more reliable than current AI‑based predictors for NDVI surface reconstruction. Broader multi‑parcel validation will be required to generalise performance across crop types, seasons, and sampling densities