Feature-constrained conditional generative data augmentation for hyperspectral retrieval of nitrogen and phosphorus in inland waters under small-sample conditions

Abstract

Hyperspectral retrieval of total nitrogen (TN) and total phosphorus (TP) is constrained by the scarcity of field spectra paired with laboratory measurements. We developed a feature-constrained conditional generative adversarial network (F-CGAN) for a 46-site inland-river dataset. Its generator maps noise and target concentration to a 651-band spectrum, while a frozen partial least-squares regression (PLSR) supervisor applies a feature-consistency penalty within target-specific windows identified from Pearson and Spearman correlations. A 36-site development set was used for feature selection, model fitting, and tuning, and 10 sites were held out for final evaluation. Synthetic-spectral fidelity was assessed using t-distributed stochastic neighbor embedding (t-SNE), maximum mean discrepancy (MMD), and a principal-component-based Fréchet distance (PCA-FD); predictive utility was compared across five regression models. The hybrid one-dimensional convolutional neural network–Transformer (Hybrid) increased \(R^2\) and reduced root mean square error (RMSE) at every augmentation ratio relative to the unaugmented baseline. Across 100–400%, RMSE reductions ranged from 6.19 to 13.68% for TN and from 2.80 to 16.94% for TP. At 400%, Hybrid achieved TN/TP \(R^2\) values of 0.8726/0.8800 and RMSEs of 2.6820/0.0600 mg L\(^{-1}\). In 10,000 paired Bootstrap resamples, the proportions favoring lower RMSE ranged from 83.47 to 98.83% for TN and from 92.79 to 99.61% for TP. After Holm correction across the eight target–ratio comparisons, only TP at 400% remained below 0.05; the other comparisons, including TN at 400%, were not statistically significant. The results indicate a broadly favorable but non-monotonic and architecture-dependent augmentation response, while uncertainty remains because of the small independent test set.