Sub-sampling of NMR Correlation and Exchange Experiments
This work addresses signal processing challenges in NMR experiments, offering incremental improvements for researchers in spectroscopy and computational physics.
The study evaluated sub-sampling techniques for NMR signals, comparing inversion algorithms like Tikhonov regularization, MTGV regularization, and deep learning. Results showed deep learning outperforms regularization methods with fully sampled signals, while MTGV regularization is better with significantly sub-sampled signals, and fully random sampling was the best overall scheme.
Sub-sampling is applied to simulated $T_1$-$D$ NMR signals and its influence on inversion performance is evaluated. For this different levels of sub-sampling were employed ranging from the fully sampled signal down to only less than two percent of the original data points. This was combined with multiple sample schemes including fully random sampling, truncation and a combination of both. To compare the performance of different inversion algorithms, the so-generated sub-sampled signals were inverted using Tikhonov regularization, modified total generalized variation (MTGV) regularization, deep learning and a combination of deep learning and Tikhonov regularization. Further, the influence of the chosen cost function on the relative inversion performance was investigated. Overall, it could be shown that for a vast majority of instances, deep learning clearly outperforms regularization based inversion methods, if the signal is fully or close to fully sampled. However, in the case of significantly sub-sampled signals regularization yields better inversion performance than its deep learning counterpart with MTGV clearly prevailing over Tikhonov. Additionally, fully random sampling could be identified as the best overall sampling scheme independent of the inversion method. Finally, it could also be shown that the choice of cost function does vastly influence the relative rankings of the tested inversion algorithms highlighting the importance of choosing the cost function accordingly to experimental intentions.