Automatic baseline correction of 1D NMR spectra using a spline-constrained neural network

Baseline distortion remains a persistent source of error in NMR spectroscopy, compromising lineshape fidelity, weak-peak detection, and quantitative peak integration. Automatic baseline correction is particularly challenging for spectra with densely overlapped resonances, limited signal-free regions, or complex low-frequency distortions. Here, we propose a structurally model-constrained deep learning framework, named SplineNet, for automatic baseline correction of 1D NMR spectra. Instead of directly mapping a distorted spectrum to a corrected spectrum or an unconstrained point-wise baseline, the network predicts the coefficients of a cubic B-spline basis, from which the baseline is reconstructed. This output-space constraint incorporates the smooth and slowly varying nature of NMR baselines and reduces the tendency of the model to absorb narrow resonance peaks into the baseline estimate. The method was evaluated using simulated spectra with known baselines, water-suppressed ¹H NMR spectra, and ¹³C DEPT-135 spectra, and was compared with conventional baseline-correction algorithms and unconstrained deep learning models. The spline-constrained model reduced baseline estimation errors, improved stability in peak-crowded regions, and yielded peak integrals closer to reference values than direct point-wise regression. These results suggest that constraining neural-network outputs to a spline-defined smooth function space provides a robust and physically interpretable strategy for automated NMR baseline correction.