Progresses on Low-Rank Reconstruction for Non-Uniformly Sampled NMR Spectra

Abstract

Multidimensional nuclear magnetic resonance (NMR) spectroscopy is frequently used to analyze molecular structures, and widely applied in researches in the fields of chemistry, biology and medicine. However, data acquisition time increases rapidly with increasing spectral dimension and number of sampling points. Non-uniformly sampling (NUS) can speed up data acquisition by reducing the amount of sampling data in the indirect dimensions, while obtaining a complete spectrum with proper reconstruction methods. How to achieve faster sampling and better reconstruction of a high-quality spectrum are important problems in multidimensional NMR. This article reviews the recent progresses on the low-rank NMR spectra reconstruction methods. First, the related mathematical basics of low-rank matrices are introduced. Then, the spectra reconstruction models are discussed from two perspectives:general low-rank matrix and structured low-rank Hankel matrix. Finally, the limitations and future trends of these methods are discussed.

Keywords

• nuclear magnetic resonance (nmr)
• non-uniformly sampling
• low-rank matrix
• spectra reconstruction
• review