TVCondNet: A Conditional Denoising Neural Network for NMR Spectroscopy

TL;DR

This work tackles denoising in NMR spectroscopy, where low SNR and costly Hankel-based approaches hinder real-time analysis. The authors propose TVCondNet, a conditional denoising network that uses the TV denoising result as a conditioning input to a residual 1D U-Net, learning to recover the noise component via a loss on the residual ${\bm{Y}}-{\bm{X}}$ with ${\bm{c}}$ guiding the network. The method is trained across four input SNRs $\{3,5,10,15\}$ dB and evaluated on experimentally collected NMR data, demonstrating superior denoising performance (higher SNR, lower RMSE) and faster inference than traditional TV, Wavelet Thresholding, CHORD, and standard DL models. The approach offers practical benefits for real-time or near-real-time NMR analysis by improving peak fidelity while reducing computational burden, suggesting wide applicability in spectral analysis workflows. The denoising problem is framed as recovering ${\bm{X}}^*$ from ${\bm{Y}} = \Re({\bm{F}}{\bm{N}}({\bm{x}}+{\bm{e}}))$ by minimizing a data-fidelity term plus a regularizer, with TV regularization defined as $\rho_{TV}({\bm{X}}) = \sum_{i=1}^{n-1} |{\bm{X}}_{i+1}-{\bm{X}}_i|$, and TVCondNet leverages this by conditioning the network on the TV solution to refine noise estimates.

Abstract

Nuclear Magnetic Resonance (NMR) spectroscopy is a widely-used technique in the fields of bio-medicine, chemistry, and biology for the analysis of chemicals and proteins. The signals from NMR spectroscopy often have low signal-to-noise ratio (SNR) due to acquisition noise, which poses significant challenges for subsequent analysis. Recent work has explored the potential of deep learning (DL) for NMR denoising, showing significant performance gains over traditional methods such as total variation (TV) denoising. This paper shows that the performance of DL denoising for NMR can be further improved by combining data-driven training with traditional TV denoising. The proposed TVCondNet method outperforms both traditional TV and DL methods by including the TV solution as a condition during DL training. Our validation on experimentally collected NMR data shows the superior denoising performance and faster inference speed of TVCondNet compared to existing methods.

Figures (3)

• Figure 1: Illustration of the TVCondNet pipeline. Noisy spectra for training are obtained by adding white Gaussian noise to the FID of the NMR signal, followed by Fourier transformation and normalization. TV denoising solution, concatenated with noisy spectra, condition the model's training to enhance its noise removal performance. TVCondNet is trained to predict the noise pattern from the noisy spectra with the loss calculated between the predicted and actual noise.
• Figure 2: The visual comparison of NMR spectra denoising for TVCondNet and selected benchmarks. Peak intensity is visualized against data index and the performance is reported in terms of SNR and RMSE. Note the superior performance of TVCondNet in denoising, visible in the denoised spectrum (top), the zoomed-in section of the spectrum, and error visualization (bottom).
• Figure 3: The visual comparison of NMR spectra denoising for TVCondNet and CHORD for cropped FID signal (2048 data points). Peak intensity is visualized against data index and the performance is reported in terms of SNR and RMSE. Note the superior denoising performance of TVCondNet.