Review and prospect: NMR spectroscopy denoising and reconstruction with low‐rank Hankel matrices and tensors
Tianyu Qiu, Zi Wang, Huiting Liu, Di Guo, Xiaobo Qu
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 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.
Topics & Concepts
Hankel matrixChemistryNuclear magnetic resonance spectroscopyTensor (intrinsic definition)Rank (graph theory)SpectroscopyNoise reductionMatrix (chemical analysis)Sensitivity (control systems)Noise (video)Nuclear magnetic resonanceBiological systemStatistical physicsAnalytical Chemistry (journal)PhysicsComputer scienceArtificial intelligenceOrganic chemistryMathematicsQuantum mechanicsChromatographyPure mathematicsElectronic engineeringEngineeringBiologyImage (mathematics)CombinatoricsAdvanced NMR Techniques and ApplicationsSparse and Compressive Sensing TechniquesNMR spectroscopy and applications