Beyond traditional magnetic resonance processing with artificial intelligence

NMR spectroscopy provides atomic-level information about molecular structure, dynamics, and interactions, with data processing being critical to extract meaningful insights. Artificial intelligence, particularly deep learning, has emerged as a powerful alternative to traditional NMR processing methods. While early machine learning applications in NMR date to the 1970s, practical impact has expanded with advances in algorithms and hardware. Most DL applications have targeted established tasks such as spectral reconstruction, processing of non-uniformly sampled (NUS) time-domain signals, virtual homonuclear decoupling, pure shift spectra, denoising, and automated peak picking. This work asks whether DL can go beyond traditional problems to enable new processing and analysis capabilities. Specifically, the study introduces a Magnetic Resonance processing with AI (MR-AI) approach to: (1) recover high-quality pure absorptive spectra from incomplete Echo or Anti-Echo quadrature data that conventionally require both P- and N-type acquisitions, and (2) perform statistical analysis of spectra reconstructed by any method to predict per-point intensity uncertainty and define a reference-free spectrum quality score.

Prior studies have shown DL’s utility for accelerating and improving traditional NMR tasks, including reconstruction of NUS data, virtual decoupling, obtaining pure shift spectra, denoising, and peak picking. Early work from the 1970s introduced ML concepts for NMR spectral interpretation, and recent advances in deep architectures and computation have enabled practical deployments. Compressed sensing (CS) methods, such as iterative soft thresholding (CS-IST), have been widely used for NUS reconstruction and improved acquisition efficiency. Approaches like Virtual Echo processing and targeted acquisition strategies have further advanced reconstruction quality and speed. Despite these advances, conventional quadrature detection for Echo/Anti-Echo experiments has required both P- and N-type datasets to obtain pure absorptive spectra. No traditional method has been shown to convert single Echo or Anti-Echo phase-twisted spectra into pure absorptive form. Additionally, error estimation for nonlinear methods (including DNNs and CS) generally lacks robust per-point uncertainty measures and typically relies on reference-based metrics such as RMSD and R², which can be biased by imperfections in reference spectra. This study situates MR-AI within this context to address these gaps.

MR-AI leverages a deep neural network architecture (WNN-based) tailored to capture 2D spectral patterns in the frequency domain. For Echo (or Anti-Echo) reconstruction, where phase-twist lineshapes form distinctive 2D patterns, a 2D WNN architecture is employed. The MR-AI reconstruction pipeline comprises five sequentially trained WNNs. Each WNN takes as input the output of the previous network, with inputs and outputs normalized by the Euclidean norm of the input. The initial Echo (or Anti-Echo) spectrum with strong phase twist serves as the input to the first WNN. Subsequent WNNs progressively suppress artifacts and move the reconstruction toward a pure absorptive spectrum. A correction step combines the current Echo estimate with a transformed Anti-Echo estimate using a Fourier transform-based operation and a scaling factor to refine the reconstruction across iterations. For uncertainty prediction, MR-AI uses a probabilistic training objective based on the negative log-likelihood (NLL). Ground-truth synthetic spectra (y) are used to generate corrupted or incomplete inputs (e.g., Echo-only or NUS). A trained reconstruction method (e.g., MR-AI or CS) provides reconstructed spectra (μ). The network is trained to predict per-point uncertainty σ by minimizing NLL: NLL(y, μ) = −log(PDF(y|μ, σ)) = −log(√(2πσ²)) − (y − μ)²/(2σ²). During training, μ and y are known, and σ is learned. At inference, the trained WNN predicts σ for spectra reconstructed by the chosen method, enabling per-point confidence intervals and a reference-free quality metric. Baselines and processing: Compressed Sensing Iterative Soft Thresholding (CS-IST) with Virtual Echo was used as a comparator for Echo/Anti-Echo reconstruction and for 50% Poisson-gap NUS reconstruction. Evaluation metrics included traditional reference-based RMSD and R² (computed after normalizing spectra to the maximum peak and restricting calculations to points above 1% of the maximal intensity) and a reference-free predicted spectrum quality score (pSQ) derived from the distribution of normalized predicted uncertainties across spectral points above 1% intensity. Data: Synthetic 2D FIDs were generated across specified ranges of frequencies, decay times, amplitudes, and SNR (example parameters in Table 1). Experimental testing used previously published 2D spectra for several proteins (e.g., ubiquitin, azurin, MALT1, and Tau/HtaU). Fully sampled spectra S were subsampled with a fixed 50% Poisson-gap NUS schedule for NUS experiments. Training datasets for uncertainty estimation included: MR-AI reconstructions from Echo (or Anti-Echo) inputs referenced to S; CS reconstructions from Echo (or Anti-Echo) inputs referenced to S; and CS reconstructions from 50% NUS inputs referenced to S (Table 3). Cross-validation and training losses for both reconstruction and uncertainty models were monitored (Figs. 1, 5). Simulations assessed balanced and imbalanced P- and N-type data to probe reference bias (Fig. 6).

- MR-AI reconstructs pure absorptive spectra from single Echo or single Anti-Echo datasets, a task previously considered infeasible with traditional methods, by recognizing and correcting phase-twisted 2D patterns. - On real 2D 15N-TROSY data (e.g., MALT1) and additional proteins, both MR-AI and CS-IST adequately reconstruct spectra, but MR-AI yields lower RMSD and higher R² versus the complete reference, indicating superior fidelity. - Reconstructions from equivalent 50% NUS acquisitions show even better quality than Echo-only or Anti-Echo-only reconstructions, suggesting that a well-trained MR-AI strategy can outperform acquiring only P- or N-type data in practice. - Reference-based metrics (RMSD, R²) favored Anti-Echo over Echo in multiple datasets, a surprising result explained by practical imbalances between P- and N-type acquisitions leading to biased reference spectra. Simulations with amplitude-imbalanced P/N pairs reproduced this effect. - MR-AI trained with an NLL objective predicts per-point intensity uncertainties for spectra reconstructed by MR-AI or CS. The uncertainty overlays (e.g., pink 95% CI) qualitatively match true error patterns (red difference to reference), enabling localized confidence estimation. - The reference-free predicted spectrum quality score (pSQ), computed from the distribution of normalized uncertainties above the 1% intensity threshold, correlates with traditional reference-based metrics across methods and datasets but avoids bias from imperfect references. In balanced vs imbalanced simulations, pSQ reports equal Echo/Anti-Echo quality where traditional metrics are skewed by reference imperfections. - Overall, MR-AI expands NMR processing by enabling reconstruction from incomplete quadrature data, providing uncertainty quantification, and offering a robust, reference-free quality metric.

The study addresses whether deep learning can extend beyond traditional NMR processing tasks by demonstrating three advances: Echo/Anti-Echo single-channel reconstruction to pure absorptive spectra, per-point uncertainty prediction for nonlinear reconstructions, and a reference-free quality metric (pSQ). The ability to reconstruct from incomplete quadrature data challenges the long-held assumption that both P- and N-type datasets are required for pure absorptive spectra, offering a practical route when only one component is reliably acquired or when experimental imbalances occur. The per-point uncertainty estimates supply actionable confidence information absent in conventional pipelines, particularly important for nonlinear methods (DNNs, CS) where baseline noise does not reflect reconstruction error. The pSQ metric allows objective comparison across methods and acquisitions without dependence on potentially biased references, as highlighted by the Echo/Anti-Echo imbalance case. Together, these capabilities can guide acquisition strategies (e.g., targeted or time-saving protocols), inform algorithmic development, and increase the robustness of spectral interpretation in challenging conditions.

The MR-AI toolbox introduces intelligent NMR processing beyond traditional methods by: (1) reconstructing pure absorptive spectra from single Echo or Anti-Echo inputs, (2) predicting per-point intensity uncertainties for nonlinear reconstructions, and (3) defining a reference-free spectrum quality score (pSQ). These advances demonstrate that AI can both solve previously intractable processing problems and provide quantitative, reference-independent quality assessment. The approach may reduce experimental time when balanced quadrature acquisition is impractical and can inform targeted acquisition strategies. Future research could broaden MR-AI to additional NMR experiment types and dimensionalities, explore domain adaptation for diverse spectrometers and sample types, and integrate uncertainty-aware reconstruction directly into acquisition optimization.

- Generalization depends on the training data distribution and network design; performance on experiment types or conditions not represented in training remains to be established. - Experimental validation focused on a limited set of 2D protein spectra and specific reconstruction scenarios (single Echo/Anti-Echo, 50% NUS). Broader benchmarking across more samples, pulse sequences, fields, and noise conditions would strengthen conclusions. - Reference-based metrics can be biased by acquisition imbalances; while pSQ mitigates this, further calibration and statistical validation of uncertainty predictions across diverse datasets are warranted. - Detailed hyperparameters, training regimes, and ablation analyses are not fully elaborated in the main text; reproducibility relies on provided code and models. - Real-time or on-instrument deployment and computational performance were not the focus and require further study.