Multidimensional nuclear magnetic resonance (NMR) spectroscopy is one of the most crucial detection tools for molecular structure analysis and has been widely used in biomedicine and chemistry. However, the development of NMR spectroscopy is hampered by long data collection time. Non-uniform sampling empowers rapid signal acquisition by collecting a small subset of data. Since the sampling rate is lower than that of the Nyquist sampling ratio, undersampling artifacts arise in reconstructed spectra. To obtain a high-quality spectrum, it is necessary to apply reasonable prior constraints in spectrum reconstruction models. The self-learning subspace method has been shown to possess superior advantages than that of the state-of-the-art low-rank Hankel matrix method when adopting high acceleration in data sampling. However, the self-learning subspace method is time-consuming due to the singular value decomposition in iterations. In this paper, we propose a fast self-learning subspace method to enable fast and high-quality reconstructions. Aided by parallel computing, the experiment results show that the proposed method can reconstruct high-fidelity spectra but spend less than 10% of the time required by the non-parallel self-learning subspace method.

中文翻译：

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非均匀采样核磁共振谱的快速自学习子空间重构方法

多维核磁共振（NMR）光谱是用于分子结构分析的最关键的检测工具之一，已广泛用于生物医学和化学领域。但是，较长的数据收集时间阻碍了NMR光谱学的发展。非均匀采样通过收集一小部分数据来实现快速信号采集。由于采样率低于奈奎斯特采样率，因此在重构频谱中会出现欠采样伪像。为了获得高质量的频谱，有必要在频谱重建模型中应用合理的先验约束。当在数据采样中采用高加速度时，自学习子空间方法已显示出比最新的低秩汉克尔矩阵方法优越的优势。然而，自学习子空间方法由于迭代中的奇异值分解而非常耗时。在本文中，我们提出了一种快速的自学习子空间方法，以实现快速，高质量的重建。在并行计算的帮助下，实验结果表明，该方法可以重构高保真频谱，但花费的时间少于非并行自学习子空间方法的10％。