Nuclear Magnetic Resonance (NMR) spectroscopy is a crucial technique for obtaining atomic-level information about molecular structure, dynamics, and interactions. Effective data processing is essential for extracting meaningful insights from NMR data. Traditional NMR processing methods often face limitations in speed, accuracy, and the types of problems they can solve. Artificial intelligence (AI), particularly deep learning (DL), offers a promising alternative, potentially overcoming these limitations. While early applications of machine learning in NMR date back to the 1970s, recent advancements in algorithms and computational power have significantly enhanced their practical utility. Most DL applications in NMR focus on improving existing techniques, such as spectral reconstruction, handling non-uniformly sampled (NUS) data, virtual homo-decoupling, obtaining pure shift spectra, denoising, and automated peak picking. This research explores whether DL can address entirely new challenges in NMR data processing and analysis, potentially leading to innovative signal processing algorithms. The study investigates if AI can go beyond solving traditional problems and introduce novel approaches to spectral processing and analysis.

The literature extensively covers the application of deep learning in NMR spectroscopy for improving existing processing techniques. Studies have demonstrated the use of deep neural networks for tasks such as spectral reconstruction from non-uniformly sampled data (Hansen, 2019; Qu et al., 2020; Karunathilaka & Hansen, 2023), virtual decoupling (Karunathilaka et al., 2021), pure shift spectral generation (Kazimierczuk et al., 2021; Towse et al., 2022; Zhan et al., 2024; Zheng et al., 2024), denoising (Lee & Kim, 2019; Chen et al., 2023), and automated peak picking (Kukkonen et al., 2018; Li et al., 2023). Early work by Reilly and Kowalski (1971) demonstrated the potential of pattern recognition in NMR spectral interpretation. However, this study focuses on tasks previously considered impossible using traditional methods, demonstrating AI's potential to expand the scope of NMR analysis beyond established techniques.

The researchers developed and trained artificial neural networks, specifically a modified version of their previously introduced Wavelet Neural Network (WNN) architecture, to address three novel challenges in NMR processing. The core of the methodology is the Magnetic Resonance processing with Artificial Intelligence (MR-AI) toolbox. This toolbox utilizes a deep neural network (DNN) architecture to tackle three key problems: 1. **Quadrature Detection from Incomplete Data:** Traditionally, quadrature detection in multidimensional NMR experiments requires acquiring two datasets (cosine and sine modulated). This study demonstrates that MR-AI can reconstruct a high-quality spectrum from a single dataset (either echo or anti-echo), overcoming the limitation of needing both datasets. This is achieved by treating the phase-twisted lineshapes in the incomplete data as a pattern recognition problem, which the WNN is trained to solve. The architecture consists of five WNNs working sequentially, with each WNN refining the output of the previous one. The initial input is the echo (or anti-echo) spectrum, and each subsequent WNN aims to progressively remove artifacts and generate a spectrum closer to the true absorptive form. A correction step is incorporated, using a combination of the echo and anti-echo data (or estimations thereof) to further enhance accuracy. 2. **Uncertainty Estimation of Signal Intensities:** Traditional methods struggle to accurately estimate the uncertainty associated with signal intensities, particularly when using non-linear processing techniques. This study uses a DNN to directly predict the uncertainty at each point in a reconstructed spectrum. The network is trained using a negative log-likelihood (NLL) loss function, learning the uncertainty (σ) while the reconstructed value (μ) and ground truth (y) are known. This approach enables the assessment of confidence in signal intensity values. 3. **Reference-free Spectrum Quality Score:** A reference-free metric (pSQ) was developed to quantitatively assess spectrum quality without relying on a reference spectrum, unlike traditional methods which rely on metrics like RMSD and R². This metric utilizes the predicted uncertainty from the previous step, normalizing these uncertainties and then using them to score the overall quality. The performance of MR-AI was evaluated using both synthetic and experimental data. Synthetic data allowed for controlled experiments and comparisons with traditional methods like Compressed Sensing Iterative Soft Thresholding (CS-IST). Experimental data from various proteins (Ubiquitin, Azurin, MALT1, Tau) were used to validate the performance of MR-AI on real-world NMR data. Various metrics, including RMSD, R², and the novel pSQ, were used for the evaluation.

The key findings of this study demonstrate the significant advantages of the proposed MR-AI approach for solving previously intractable problems in NMR processing: 1. **Successful Quadrature Detection from Incomplete Data:** MR-AI successfully reconstructed high-quality 2D NMR spectra using only echo or anti-echo data, which is impossible with traditional methods. This is a substantial advancement, as it can significantly reduce experimental time by eliminating the need to acquire two complete datasets for quadrature detection. 2. **Accurate Uncertainty Estimation:** The DNN model effectively predicted the uncertainty of signal intensities, providing a crucial measure of confidence in quantitative analysis. This is particularly valuable when using non-linear processing methods where traditional error estimation techniques are inadequate. The predicted uncertainty visualized in the spectra allows for direct visual assessment of the reliability of each point in the reconstructed spectra. 3. **Robust Reference-free Spectrum Quality Assessment:** The pSQ metric provided a reliable and reference-free way to assess NMR spectrum quality. This metric correlated well with traditional reference-based scores (RMSD and R²) but was less susceptible to biases associated with imperfections in the reference spectra, as shown in experiments with imbalanced echo and anti-echo data. This is a crucial step for more objective evaluation of the quality of NMR spectra generated with different processing methodologies, without the need for ground truth data. The researchers compared MR-AI to compressed sensing (CS) using both synthetic and experimental data. In general, MR-AI demonstrated superior performance, particularly in cases with imbalanced echo/anti-echo data, where traditional reference-based quality metrics fail to accurately reflect the actual spectrum quality. The ability to process incomplete or unbalanced data is of significant practical importance, allowing for faster data acquisition and more robust analysis even under less than ideal experimental conditions. The superior performance of MR-AI was consistently observed in experiments with different proteins and experimental parameters, further demonstrating the robustness of the approach.

This study's findings significantly advance NMR spectroscopy by presenting AI-based solutions to previously unsolvable processing challenges. The ability to reconstruct spectra from incomplete data dramatically reduces experimental time and cost. The capacity to accurately quantify uncertainty associated with signal intensities is crucial for reliable quantitative analysis. Finally, the development of a reference-free spectrum quality score eliminates the need for ground truth data, streamlining the evaluation of NMR processing methods. The superior performance of MR-AI compared to established methods like CS underscores the potential of AI in transforming NMR data analysis. These innovations have implications for various fields, including structural biology, metabolomics, and materials science. Future research could focus on expanding MR-AI's capabilities to handle higher dimensional NMR data and incorporating more advanced DL architectures to further improve accuracy and efficiency.

This work introduces the MR-AI toolbox, a powerful new tool for NMR processing. It successfully addresses three significant challenges: reconstructing spectra from incomplete data, providing uncertainty estimates for signal intensities, and developing a reference-free spectrum quality score. The superior performance of MR-AI compared to existing methods highlights AI's transformative potential in NMR spectroscopy. Future work should explore the application of MR-AI to more complex NMR experiments and the development of even more sophisticated AI models for NMR data processing.

While the study demonstrates the significant potential of MR-AI, several limitations should be acknowledged. The training data used to develop the models influences their performance, and the generalizability to datasets significantly different from the training data remains to be fully assessed. Furthermore, the computational cost of running the deep learning models may be higher compared to traditional NMR processing methods. More research is needed to optimize the algorithms for faster execution and reduced computational resources.