Resolution in NMR is defined as the ability to distinguish and accurately determine signal positions while mitigating overlap. In the pursuit of ultimate resolution, we introduce peak probability presentations ( P 3 ), a statistical spectral representation that assigns a probability to each spectral point, indicating the likelihood that a peak maximum occurs at that location. The mapping between the traditional spectrum and P 3 is achieved using MR-Ai, a physics-inspired and computationally efficient deep-learning neural network. P 3 is validated on 60 database proteins and showcased on the challenging Tau and MATL1 proteins. Using synthetic spectra, we show that the achieved peak-localization precision closely approaches the theoretical limits set by the Cramér-Rao lower bound and Bayesian Monte Carlo estimates. Furthermore, MR-Ai enables the coprocessing of multiple spectra, facilitating direct information exchange between datasets to enhance spectral quality, particularly in cases of highly sparse sampling.
Jahangiri et al. (Fri,) studied this question.