Nuclear Magnetic Resonance (NMR) spectroscopy is an important analytical tool in chemistry, biology, and life science, but it suffers from relatively low sensitivity and long acquisition time. Thus, improving the apparent signal-to-noise ratio and accelerating data acquisition become indispensable. In this review, we summarize the recent progress on low rank Hankel matrix and tensor methods, that exploit the exponential property of free induction decay signals, to enable effective denoising and spectra reconstruction. We also outline future developments that are likely to make NMR spectroscopy a far more powerful technique.

中文翻译：

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回顾与展望：使用低秩 Hankel 矩阵和张量进行 NMR 光谱去噪和重建

核磁共振 (NMR) 光谱是化学、生物学和生命科学中的重要分析工具，但它具有相对较低的灵敏度和较长的采集时间。因此，提高表观信噪比和加速数据采集变得不可或缺。在这篇综述中，我们总结了低秩 Hankel 矩阵和张量方法的最新进展，这些方法利用自由感应衰减信号的指数特性来实现有效的去噪和频谱重建。我们还概述了可能使 NMR 光谱成为一种更强大的技术的未来发展。