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

TL;DR

This review discusses recent advances in NMR spectroscopy denoising and reconstruction using low rank Hankel matrices and tensors, highlighting methods that exploit signal properties to improve data quality and acquisition speed.

Contribution

It summarizes recent progress in low rank Hankel matrix and tensor methods for NMR denoising and reconstruction, and outlines future research directions.

Findings

Enhanced denoising and reconstruction techniques for NMR signals.

Exploitation of exponential properties of free induction decay signals.

Potential for significantly improved NMR data quality and acquisition efficiency.

Abstract

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.