基于低秩矩阵的非均匀采样NMR波谱重建进展

doi:10.11938/cjmr20202816

波谱学杂志 ›› 2020, Vol. 37 ›› Issue (3): 255-272.doi: 10.11938/cjmr20202816

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基于低秩矩阵的非均匀采样NMR波谱重建进展

詹嘉莹¹, 涂章仁^1,2, 杜晓凤¹, 袁斌³, 郭迪¹, 屈小波⁴

1. 厦门理工学院计算机与信息工程学院, 福建厦门 361024;
2. 厦门理工学院光电与通信工程学院, 福建厦门 361024;
3. 波谱与原子分子物理国家重点实验室, 武汉磁共振中心(中国科学院武汉物理与数学研究所), 湖北武汉 430071;
4. 厦门大学电子科学系, 福建省等离子体与磁共振重点实验室, 福建厦门 361005

收稿日期:2020-03-11 出版日期:2020-09-05 发布日期:2020-04-20
通讯作者: 郭迪,Tel:15396288685,E-mail:guodi@xmut.edu.cn. E-mail:guodi@xmut.edu.cn
基金资助:
国家自然科学基金资助项目（61871341，61672335，61971361）；厦门市产学研协同创新及科技合作项目（3502Z20183053）.

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

ZHAN Jia-ying¹, TU Zhang-ren^1,2, DU Xiao-feng¹, YUAN Bin³, GUO Di¹, QU Xiao-bo⁴

1. School of Computer and Information Engineering, Xiamen University of Technology, Xiamen 361024, China;
2. School of Opto-Electronic and Communication Engineering, Xiamen University of Technology, Xiamen 361024, China;
3. State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, National Center for Magnetic Resonance in Wuhan(Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences), Wuhan 430071, China;
4. Department of Electronic Science, Xiamen University, Fujian Provincial Key Laboratory of Plasma and Magnetic Resonance, Xiamen 361005, China

Received:2020-03-11 Online:2020-09-05 Published:2020-04-20

摘要/Abstract

摘要： 多维核磁共振（Nuclear Magnetic Resonance，NMR）利用多维波谱来分析分子结构，被广泛用于化学、生物学和医学等领域，但信号采样时间随波谱维度和采样点数增加而迅速增长．非均匀采样通过降低间接维采样点数来加速数据采集，并引入合理的重建方法获得完整的NMR波谱．如何快速重建高质量的波谱，是NMR信号处理研究的前沿．本文主要综述近年来基于低秩矩阵的NMR波谱重建方法的发展．首先介绍了低秩矩阵的相关数学基础；然后从一般低秩矩阵和结构化低秩汉克尔矩阵两个角度来论述重建模型，并讨论相关的NMR波谱应用；最后分析了该技术存在的不足，并展望其未来发展的趋势．

关键词: 核磁共振, 非均匀采样, 低秩矩阵, 波谱重建, 综述

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.

Key words: nuclear magnetic resonance (NMR), non-uniformly sampling, low-rank matrix, spectra reconstruction, review

中图分类号:

詹嘉莹, 涂章仁, 杜晓凤, 袁斌, 郭迪, 屈小波. 基于低秩矩阵的非均匀采样NMR波谱重建进展[J]. 波谱学杂志, 2020, 37(3): 255-272.

ZHAN Jia-ying, TU Zhang-ren, DU Xiao-feng, YUAN Bin, GUO Di, QU Xiao-bo. Progresses on Low-Rank Reconstruction for Non-Uniformly Sampled NMR Spectra[J]. Chinese Journal of Magnetic Resonance, 2020, 37(3): 255-272.

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基于低秩矩阵的非均匀采样NMR波谱重建进展

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

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