DiffNMR: Advancing Inpainting of Randomly Sampled Nuclear Magnetic Resonance Signals

TL;DR

The paper addresses the challenge of long acquisition times in two-dimensional NMR by applying diffusion-based inpainting to non-uniformly sampled spectra. Using real Artina protein data, it compares four diffusion pipelines across time-time and time-frequency representations, demonstrating that time-frequency domain reconstructions with a conditioned or denoising diffusion approach most effectively preserve spectral integrity, measured by $MSE$, $R^2$, and $\frac{SNR_{rec}}{SNR_{ori}}$, while minimizing peak hallucinations. The proposed method consistently outperforms traditional baselines such as CS and LR across masking levels, with $D$-$T F$ often achieving the best overall performance. The work highlights the practical potential of diffusion models to accelerate NMR experiments and maintain high spectral fidelity, and suggests future exploration of Poisson-gap NUS and other realistic datasets.

Abstract

Nuclear Magnetic Resonance (NMR) spectroscopy leverages nuclear magnetization to probe molecules' chemical environment, structure, and dynamics, with applications spanning from pharmaceuticals to the petroleum industry. Despite its utility, the high cost of NMR instrumentation, operation and the lengthy duration of experiments necessitate the development of computational techniques to optimize acquisition times. Non-Uniform sampling (NUS) is widely employed as a sub-sampling method to address these challenges, but it often introduces artifacts and degrades spectral quality, offsetting the benefits of reduced acquisition times. In this work, we propose the use of deep learning techniques to enhance the reconstruction quality of NUS spectra. Specifically, we explore the application of diffusion models, a relatively untapped approach in this domain. Our methodology involves applying diffusion models to both time-time and time-frequency NUS data, yielding satisfactory reconstructions of challenging spectra from the benchmark Artina dataset. This approach demonstrates the potential of diffusion models to improve the efficiency and accuracy of NMR spectroscopy as well as the superiority of using a time-frequency domain data over the time-time one, opening new landscapes for future studies.

Figures (11)

• Figure 1: A 1D NMR experiment records the nuclei resonance in response to a radiofrequency pulse.
• Figure 2: A 2D NMR spectrum is obtained by applying a series of radiofrequency pulses and evolution time delays to a sample (here, five different values), and apply a 2D Fourier transform to obtain a 2D frequency spectrum.
• Figure 3: Non-Uniform Sampling: some of the evolution times (here: the second and fourth) are skipped.
• Figure 4: Diffusion steps: in the noising step (forward pass), the input is progressively corrupted. The Unet model is trained to predict the added noise (backward pass).
• Figure 5: UNet model for noise prediction.