Non-uniform and sparse sampling of multi-dimensional NMR spectra has over the last decade become an important tool to allow for fast acquisition of multi-dimensional NMR spectra with high resolution. The success of non-uniform sampling NMR hinge on both the development of algorithms to accurately reconstruct the sparsely sampled spectra and the design of sampling schedules that maximise the information contained in the sampled data. Traditionally, the reconstruction tools and algorithms have aimed at reconstructing the full spectrum and thus ‘fill out the missing points’ in the time-domain spectrum, although other techniques are based on multi-dimensional decomposition and extraction of multi-dimensional shapes. Also over the last decade, machine learning, deep neural networks, and artificial intelligence have seen new applications in an enormous range of sciences, including analysis of MRI spectra. As a proof-of-principle, it is shown here that simple deep neural networks can be trained to reconstruct sparsely sampled NMR spectra. For the reconstruction of two-dimensional NMR spectra, reconstruction using a deep neural network performs as well, if not better than, the currently and widely used techniques. It is therefore anticipated that deep neural networks provide a very valuable tool for the reconstruction of sparsely sampled NMR spectra in the future to come.

中文翻译：

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使用深度神经网络重建非均匀采样的 NMR 谱

多维 NMR 谱的非均匀稀疏采样在过去十年中已成为快速采集高分辨率多维 NMR 谱的重要工具。非均匀采样核磁共振的成功取决于精确重建稀疏采样光谱的算法的开发以及最大化采样数据中包含的信息的采样计划的设计。传统上，重建工具和算法的目标是重建全频谱，从而“填补时域频谱中的缺失点”，尽管其他技术是基于多维分解和多维形状提取。同样在过去十年中，机器学习、深度神经网络和人工智能在众多科学领域得到了新的应用，包括 MRI 光谱分析。作为原理验证，这里表明可以训练简单的深度神经网络来重建稀疏采样的 NMR 谱。对于二维核磁共振谱的重建，使用深度神经网络的重建效果与当前广泛使用的技术一样好，甚至更好。因此，预计深度神经网络将在未来为稀疏采样核磁共振谱的重建提供非常有价值的工具。