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

arXiv: https://arxiv.org/abs/2007.12646 · HTML: https://mlsanity.com/paper/2007.12646/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jul 2020.

## Built on by (most cited first, 3 of 3)

- [TVCondNet: A Conditional Denoising Neural Network for NMR Spectroscopy](https://mlsanity.com/paper/2405.11064/) (2024)
- [Magnetic Resonance Spectroscopy Deep Learning Denoising Using Few In Vivo Data](https://mlsanity.com/paper/2101.11442/) (2021)
- [Convex Dual Theory Analysis of Two-Layer Convolutional Neural Networks with Soft-Thresholding](https://mlsanity.com/paper/2304.06959/) (2023)

## Abstract (arXiv)

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.