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Nuclear Magnetic Resonance (NMR) spectroscopy is an important analytical toolin chemistry, biology, and life science, but it suffers from relatively lowsensitivity and long acquisition time. Thus, improving the apparentsignal-to-noise ratio and accelerating data acquisition become indispensable.In this review, we summarize the recent progress on low rank Hankel matrix andtensor methods, that exploit the exponential property of free induction decaysignals, to enable effective denoising and spectra reconstruction. We alsooutline future developments that are likely to make NMR spectroscopy a far morepowerful technique.

Review and Prospect: NMR Spectroscopy Denoising & Reconstruction with Low Rank Hankel Matrices and Tensors