标题： 利用深度学习实现终极核磁共振分辨率 显示英文标题

标题： Towards Ultimate NMR Resolution with Deep Learning

摘要： 在多维核磁共振光谱中，实际分辨率被定义为在重叠峰、热噪声和光谱伪影的背景下区分并准确确定信号位置的能力。为了追求极限分辨率，我们引入了峰概率表示法（$P^3$）——一种统计光谱表示方法，它为每个光谱点分配一个概率，表明峰值最大值出现在该位置的可能性。 光谱与$P^3$之间的映射是通过 MR-Ai 实现的，MR-Ai 是一种受物理启发的深度学习神经网络架构，旨在处理多维核磁共振光谱。 此外，我们证明了 MR-Ai 能够实现多个光谱的同时处理，促进了数据集之间的直接信息交换。 这一功能显著提高了光谱质量，特别是在高度稀疏采样的情况下。 MR-Ai 的性能以及$P^3$的高值在合成数据和Tau蛋白、MATL1、钙调蛋白以及其他几种蛋白质的光谱中得到了验证。 显示英文摘要

摘要： In multidimensional NMR spectroscopy, practical resolution is defined as the ability to distinguish and accurately determine signal positions against a background of overlapping peaks, thermal noise, and spectral artifacts. 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 of a peak maximum occurring at that location. The mapping between the spectrum and $P^3$ is achieved using MR-Ai, a physics-inspired deep learning neural network architecture, designed to handle multidimensional NMR spectra. Furthermore, we demonstrate that MR-Ai enables coprocessing of multiple spectra, facilitating direct information exchange between datasets. This feature significantly enhances spectral quality, particularly in cases of highly sparse sampling. Performance of MR-Ai and high value of the $P^3$ are demonstrated on the synthetic data and spectra of Tau, MATL1, Calmodulin, and several other proteins.