Chinese Journal of Magnetic Resonance >

2020 , Vol. 37 >Issue 3: 255 - 272

DOI: https://doi.org/10.11938/cjmr20202816

Review Articles

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

  • ZHAN Jia-ying ,
  • TU Zhang-ren ,
  • DU Xiao-feng ,
  • YUAN Bin ,
  • GUO Di ,
  • QU Xiao-bo
Expand
  • 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 date: 2020-03-11

  Online published: 2020-04-20

Fold

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

Cite this article

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 . DOI: 10.11938/cjmr20202816

References

[1] BORGIA A, BORGIA M B, BUGGE K, et al. Extreme disorder in an ultrahigh-affinity protein complex[J]. Nature, 2018, 555(7694):61-66.
[2] LIU G, LEVIEN M, KARSCHIN N, et al. One-thousand-fold enhancement of high field liquid nuclear magnetic resonance signals at room temperature[J]. Nat Chem, 2017, 9(7):676-680.
[3] NGUYEN H M, PENG X, DO M N, et al. Denoising MR spectroscopic imaging data with low-rank approximations[J]. IEEE T Bio-Med Eng, 2013, 60(1):78-89.
[4] HUANG Y, CAO S H, YANG Y, et al. Ultrahigh-resolution NMR spectroscopy for rapid chemical and biological applications in inhomogeneous magnetic fields[J]. Anal Chem, 2017, 89(13):7115-7122.
[5] GUO D, LU H, QU X B. A fast low rank Hankel matrix factorization reconstruction method for non-uniformly sampled magnetic resonance spectroscopy[J]. IEEE Access, 2017, 5:16033-16039.
[6] GUO D, QU X B. Improved reconstruction of low intensity magnetic resonance spectroscopy with weighted low rank Hankel matrix completion[J]. IEEE Access, 2018, 6:4933-4940.
[7] HILLER S, GARCES R G, MALIA T J, et al. Solution structure of the integral human membrane protein VDAC-1 in detergent micelles[J]. Science, 2008, 321(5893):1206-1210.
[8] GAO D L, SUN P, WANG Q W, et al. Interactions between albumin and fatty acids studied by NMR spectroscopy[J]. Chinese J Magn Reson, 2018, 35(3):338-344. 高东莉, 孙鹏, 王倩文, 等. 运用NMR研究白蛋白与脂肪酸的相互作用[J]. 波谱学杂志, 2018, 35(3):338-344.
[9] MOBLI M, HOCH J C. Nonuniform sampling and non-Fourier signal processing methods in multidimensional NMR[J]. Prog Nucl Magn Reson Spectrosc, 2014, 83:21-41.
[10] YUAN B, DING Y, KAMAL G M, et al. Reconstructing diffusion ordered NMR spectroscopy by simultaneous inversion of Laplace transform[J]. J Magn Reson, 2017, 278:1-7.
[11] QU X B, CAO X, GUO D, et al. Compressed sensing for sparse magnetic resonance spectroscopy[C]//18th Sci. Meeting Int Soc Magn Reson Med (ISMRM), Stockholm, Sweden. 2010, 10:3371.
[12] HOLLAND D J, BOSTOCK M J, GLADDEN L F, et al. Fast multidimensional NMR spectroscopy using compressed sensing[J]. Angew Chem Int Ed, 2011, 50(29):6548-6551.
[13] KAZIMIERCZUK K, OREKHOV V Y. Accelerated NMR spectroscopy by using compressed sensing[J]. Angew Chem Int Ed, 2011, 123(24):5670-5673.
[14] QU X B, GUO D, CAO X, et al. Reconstruction of self-sparse 2D NMR spectra from undersampled data in the indirect dimension[J]. Sensors, 2011, 11(9):8888-8909.
[15] QU X B, MAYZEL M, CAI J F, et al. Accelerated NMR spectroscopy with low-rank reconstruction[J]. Angew Chem Int Ed, 2015, 54(3):852-854.
[16] QU X B, HUANG Y H, LU H F, et al. Accelerated nuclear magnetic resonance spectroscopy with deep learning[J]. Angew Chem Int Ed, 2020, 132(26):10383-10386.
[17] SIBISI S, SKILLING J, BRERETON R G, et al. Maximum entropy signal processing in practical NMR spectroscopy[J]. Nature, 1984, 311(5985):446-447.
[18] BARNA C J, TAN S M, LADE E D. Use of CLEAN in conjunction with selective data sampling for 2D NMR experiments[J]. J Magn Reson, 1988, 78(2):327-332.
[19] COGGINS B E, ZHOU P. High resolution 4-D spectroscopy with sparse concentric shell sampling and FFT-CLEAN[J]. J Biomol NMR, 2008, 42(4):225-239.
[20] JARAVINE V, IBRAGHIMOV I, OREKHOV V Y. Removal of a time barrier for high-resolution multidimensional NMR spectroscopy[J]. Nat Methods, 2006, 3(8):605-607.
[21] DRORI I. Fast minimization by iterative thresholding for multidimensional NMR spectroscopy[J]. Eurasip J Adv Sig Pr, 2007, 2007(1):020248.
[22] YING J F, DELAGLIO F, TORCHIA D A, et al. Sparse multidimensional iterative lineshape-enhanced (SMILE) reconstruction of both non-uniformly sampled and conventional NMR data[J]. J Biomol NMR, 2017, 68(2):101-118.
[23] CHEN D C, WANG Z, GUO D, et al. Review and prospect:deep learning in nuclear magnetic resonance spectroscopy[J]. Chem-Eur J, 2020, doi:doi.org/10.1002/chem.202000246.
[24] ZHENG H, HAN M Y, HU B W, et al. Comparison of different sampling schemes in compressed sensing reconstruction for DQ-SQ experiments[J]. Chinese J Magn Reson, 2014, 31(4):535-547. 郑慧, 韩明月, 胡炳文等. 不同采样模式的固体DQ-SQ实验的压缩感知重建比较[J]. 波谱学杂志, 2014, 31(4):535-547.
[25] ZHANG Z Y, QU X B, LIN Y Q, et al. Sparse reconstruction algorithm of NMR spectrum based on minimizing approximate L0 norm[J]. Chinese J Magn Reson, 2013, 30(4):528-540. 张正炎, 屈小波, 林雁勤等. 基于近似L0范数最小化的NMR波谱稀疏重建算法[J]. 波谱学杂志, 2013, 30(4):528-540.
[26] NIE L S, JIANG B, ZHANG X, et al. A compressed sensing and resampling based noise suppression method for NMR[J]. Chinese J Magn Reson, 2016, 33(2):244-256. 聂莉莎, 蒋滨, 张许, 等. 基于压缩感知/重采样的NMR噪声抑制新方法[J]. 波谱学杂志, 2016, 33(2):244-256.
[27] SHCHUKINA A, KASPRZAK P, DASS R, et al. Pitfalls in compressed sensing reconstruction and how to avoid them[J]. J Biomol NMR, 2016, 68(2):79-98.
[28] CANDÈS E J, WAKIN M B. An introduction to compressive sampling[J]. IEEE Signal Proc Mag, 2008, 25(2):21-30.
[29] 张贤达. 矩阵分析及应用[M]. 北京:清华大学出版社, 2015.
[30] CANDÈS E J, RECHT B. Exact matrix completion via convex optimization[J]. Found Comput Math, 2009, 9(6):717-772.
[31] CAI J F, CANDÈS E J, SHEN Z. A singular value thresholding algorithm for matrix completion[J]. SIAM J Optimiz, 2010, 20(4):1956-1982.
[32] YING J X, LU H, WEI Q. Hankel matrix nuclear norm regularized tensor completion for N-dimensional exponential signals[J]. IEEE T Signal Proce, 2017, 65(14):3702-3717.
[33] KOEHL P. Linear prediction spectral analysis of NMR data[J]. Prog Nucl Magn Reson Spectrosc, 1999, 34(3,4):257-299.
[34] MAN P P, BONHOMME C, BABONNEAU F. Denoising NMR time-domain signal by singular-value decomposition accelerated by graphics processing units[J]. Solid State Nucl Mag, 2014, 61:28-34.
[35] QIU T Y, LIAO W J, GUO D, et al. Gaussian noise removal with exponential functions and spectral norm of weighted Hankel matrices[J]. arXiv:2001.11815, 2020.
[36] MAYZEL M, KAZIMIERCZUK K, OREKHOV V Y. The causality principle in the reconstruction of sparse NMR spectra[J]. Chem Commun, 2014, 50(64):8947-8950.
[37] RECHT B, FAZEL M, PARRILO P A. Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization[J]. SIAM Rev, 2010, 52(3):471-501.
[38] FAZEL M, PONG T K, SUN D F, et al. Hankel matrix rank minimization with applications to system identification and realization[J]. SIAM J Matrix Anal A, 2013, 34(3):946-977.
[39] LU H F, ZHANG X L, QIU T Y, et al. Low rank enhanced matrix recovery of hybrid time and frequency data in fast magnetic resonance spectroscopy[J]. IEEE T Bio-Med Eng, 2018, 65(4):809-820.
[40] HAHN E L. Spin echoes[J]. Phys Rev, 1950, 80:580-594.
[41] MORRIS K F, JOHNSON C S. Diffusion-ordered two-dimensional nuclear magnetic resonance spectroscopy[J]. J Am Chem Soc, 1992, 114(8):3139-3141.
[42] HUANG J L, YU Y H. Effects of digital resolution on diffusional dimension in DOSY experiments[J]. Chinese J Magn Reson, 2018, 35(3):287-293. 黄俊霖, 余亦华. 扩散序谱(DOSY)实验中扩散系数维数字分辨率的影响[J]. 波谱学杂志, 2018, 35(3):287-293.
[43] URBAŃCZYK M, KOŹMIŃSKI W, KAZIMIERCZUK K. Accelerating diffusion-ordered NMR spectroscopy by joint sparse sampling of diffusion and time dimensions[J]. Angew Chem Int Ed, 2014, 53(25):6464-6467.
[44] URBAŃCZYK M, BERNIN D, KOŹMIŃSKI W, et al. Iterative thresholding algorithm for multiexponential decay applied to PGSE NMR data[J]. Anal Chem, 2013, 85(3):1828-1833.
[45] 张自飞. 联合稀疏与低秩特性的磁共振扩散谱重建[D]. 厦门:厦门大学, 2019.
[46] 陈忠, 张自飞, 郭迪, 等. 结合稀疏和低秩特性的欠采样磁共振扩散谱的重建方法:中国, 10874832.4[P]. 2018-11-16.
[47] LIN E P, YANG Y, HUANG Y Q, et al. High-resolution reconstruction for diffusion-ordered NMR spectroscopy[J]. Anal Chem, 2020, 92(1):634-639.
[48] COLBOURNE A A, MORRIS G A, NILSSON M. Local covariance order diffusion-ordered spectroscopy:a powerful tool for mixture analysis[J]. J Am Chem Soc, 2011, 133(20):7640-7643.
Options
Outlines

/

〈 〉

Copyright © 2017 Editorial Board of Chinese Journal of Magnetic Resonance
Powered by Beijing Magtech Co. Ltd