Review and prospect: NMR spectroscopy denoising and reconstruction with low-rank Hankel matrices and tensors.

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 became indispensable. In this review, we summarize the recent progress on low-rank Hankel matrix and tensor methods, which 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.