Laplace NMR谱图重建——从经典正则化到深度学习

杨钰; 陈博; 吴柳滨; 林恩平; 黄玉清; 陈忠

doi:10.11938/cjmr20233079

波谱学杂志 >

2024 , Vol. 41 >Issue 2: 191 - 208

DOI: https://doi.org/10.11938/cjmr20233079

综述评论

Laplace NMR谱图重建——从经典正则化到深度学习

杨钰 ,
陈博 ,
吴柳滨 ,
林恩平 ,
黄玉清 ,
陈忠

展开

厦门大学电子科学系，福建厦门 361005

*Tel: +86 18250756791, E-mail: yuyang15@xmu.edu.cn.

收稿日期: 2023-08-29

网络出版日期: 2023-10-10

基金资助

厦门市自然科学基金(3502Z202373005);国家自然科学基金资助项目(12175189)

收起

Spectrum Reconstruction for Laplace NMR: From Handcraft Regularization to Deep Learning

YANG Yu ,
CHEN Bo ,
WU Liubin ,
LIN Enping ,
HUANG Yuqing ,
CHEN Zhong

Expand

Department of Electronic Science, Xiamen University, Xiamen 361005, China

Received date: 2023-08-29

Online published: 2023-10-10

Fold

摘要

拉普拉斯核磁共振（Laplace NMR）可以提供待测样品的扩散系数或弛豫时间等物理参数信息，是用于研究分子化学结构、动力学和相互作用的强大工具．Laplace NMR的适用性很大程度上取决于拉普拉斯逆变换相关的信号处理算法的性能．在本文中，我们首先讨论了Laplace NMR谱图重建问题的不适定性，接着回顾了经典的基于正则化约束的重建算法，并介绍了目前前沿的深度学习算法在处理Laplace反演问题方面的应用，最后总结了这些算法的优缺点，并对Laplace NMR信号处理方法未来改进方向进行了展望．

关键词： 拉普拉斯核磁共振; 扩散核磁共振; 扩散排序谱; 拉普拉斯反演变换; 深度学习

本文引用格式

杨钰 , 陈博 , 吴柳滨 , 林恩平 , 黄玉清 , 陈忠 . Laplace NMR谱图重建——从经典正则化到深度学习[J]. 波谱学杂志, 2024 , 41(2) : 191 -208 . DOI: 10.11938/cjmr20233079

Abstract

Laplace NMR can provide information on diffusion coefficients or relaxation time, serving as a powerful technology for studying molecular structure, dynamics, and interactions in samples. Generally, the applicability of Laplace NMR is subject to the performance of signal processing and reconstruction algorithms associated with the inverse Laplace transform. In this paper, we first discuss the ill-posed nature of the spectrum reconstruction problem for Laplace NMR, then revisit the classic regularization-based reconstruction algorithms and introduce the state-of-the-art deep-learning-based methods. In conclusion, the advantages and disadvantages of these algorithms are summarized, and future improvements for Laplace NMR signal processing methods are prospected.

Key words： Laplace NMR; diffusion NMR; DOSY (diffusion ordered spectroscopy); ILT (inverse Laplace transform); deep learning

参考文献

[1]	TELKKI V V. Hyperpolarized Laplace NMR[J]. Magn Reson Chem, 2018, 56(7): 619-632.
[2]	CHANDRA K, SCHLAGNITWEIT J, WOHLSCHLAGER C, et al. Spin-noise-detected two-dimensional Fourier-transform NMR spectroscopy[J]. J Phys Chem Lett, 2013, 4(22): 3853-3856.
[3]	KING J N, LEE V J, AHOLA S, et al. Ultrafast multidimensional Laplace NMR using a single-sided magnet[J]. Angew Chem Int Ed, 2016, 55(16): 5040-5043.
[4]	MANKINEN O, ZHIVONIKO V V, SELENT A, et al. Ultrafast diffusion exchange nuclear magnetic resonance[J]. Nat Commun, 2020, 11(1): 3251.
[5]	MORRIS K F, JOHNSON C S JR. Diffusion-ordered two-dimensional nuclear magnetic resonance spectroscopy[J]. J Am Chem Soc, 1992, 114(8): 3139-3141.
[6]	PRICE W S. NMR studies of translational motion: Principles and applications[M]. Cambridge University Press, 2009.
[7]	CALLAGHAN P T. Translational dynamics and magnetic resonance: principles of pulsed gradient spin echo NMR[M]. Oxford University Press, 2011.
[8]	LV J, SHAN L, TU G Z. The integrated DOSY acquisition/processing module for Topspin NMR software[J]. Chinese J Magn Reson, 2008, 25(1): 133-143.
	吕娟, 单璐, 涂光忠. TopSpin核磁共振软件中集成的DOSY采集/处理模块DOSYm-(TM)[J]. 波谱学杂志, 2008, 25(1): 133-143.
[9]	MA H, PEDERSEN C M, ZHAO Q, et al. Utilizing 3D DOSY NMR in the characterization of organic compounds in coal chemical wastewater[J]. Magn Reson Lett, 2022, 2(2): 69-79.
[10]	WANG L, AMELUNG W, WILLBOLD S. Diffusion-ordered nuclear magnetic resonance spectroscopy (DOSY-NMR): A novel tool for identification of phosphorus compounds in soil extracts[J]. Environ Sci Technol, 2017, 51(22): 13256-13264.
[11]	BUSSE F, REHORN C, KUPPERS M, et al. NMR relaxometry of oil paint binders[J]. Magn Reson Chem, 2020, 58(9): 830-839.
[12]	SONG Y-Q, KAUSIK R. NMR application in unconventional shale reservoirs - A new porous media research frontier[J]. Prog Nucl Magn Reson Spectrosc, 2019, 112-113: 17-33.
[13]	MENG K, WANG S J, XUE Z A, et al. Quantitative evaluation of shale pore structure using nuclear magnetic resonance data[J]. Chinese J Magn Reson, 2021, 38(2): 215-226.
	孟昆, 王胜建, 薛宗安, 等. 利用核磁共振资料定量评价页岩孔隙结构[J]. 波谱学杂志, 2021, 38(2): 215-226.
[14]	CHAO F A, BYRD R A. Protein dynamics revealed by NMR relaxation methods[J]. Emerging topics in life sciences, 2020, 2(1): 93-105.
[15]	STEJSKAL E O, TANNER J E. Spin diffusion measurements: spin echoes in the presence of a time-dependent field gradient[J]. J Chem Phys, 1965, 42(1): 288-292.
[16]	PRANG M, SONG Y Q. Understanding NMR T₂spectral uncertainty[J]. J Magn Reson, 2010, 204(1): 118-123.
[17]	BARJAT H, MORRIS G A, SMART S, et al. High-resolution diffusion-ordered 2D spectroscopy (HR-DOSY) - a new tool for the analysis of complex mixtures[J]. J Magn Reson, Series B, 1995, 108(2): 170-172.
[18]	MORRIS K F, JOHNSON C S. Resolution of discrete and continuous molecular size distributions by means of diffusion-ordered 2D NMR spectroscopy[J]. J Am Chem Soc, 1993, 115(10): 4291-4299.
[19]	NILSSON M, CONNELL M A, DAVIS A L, et al. Biexponential fitting of diffusion-ordered NMR data:? Practicalities and limitations[J]. Anal Chem, 2006, 78(9): 3040-3045.
[20]	LAGARIAS J C, REEDS J A, WRIGHT M H, et al. Convergence properties of the Nelder-Mead simplex method in low dimensions[J]. SIAM J Optim, 1998, 9(1): 112-147.
[21]	MORE J J. The Levenberg-Marquardt algorithm: Implementation and theory[C]// Numerical Analysis, 1978 Berlin, Heidelberg: 105-116.
[22]	LAWSON C L, HANSON R J. Solving least squares problems[M]. Society for Industrial and Applied Mathematics, 1995.
[23]	ANTALEK B, WINDIG W. Generalized rank annihilation method applied to a single multicomponent pulsed gradient spin echo NMR data set[J]. J Am Chem Soc, 1996, 118(42): 10331-10332.
[24]	WINDIG W, ANTALEK B. Direct exponential curve resolution algorithm (DECRA): A novel application of the generalized rank annihilation method for a single spectral mixture data set with exponentially decaying contribution profiles[J]. Chemometr Intell Lab Syst, 1997, 37(2): 241-254.
[25]	WINDIG W, ANTALEK B. Resolving nuclear magnetic resonance data of complex mixtures by three-way methods: Examples of chemical solutions and the human brain[J]. Chemometr Intell Lab Syst, 1999, 46(2): 207-219.
[26]	ANTALEK B. Using pulsed gradient spin echo NMR for chemical mixture analysis: How to obtain optimum results[J]. Concepts Magn Reson, 2002, 14(4): 225-258.
[27]	STILBS P, PAULSEN K. Global least-squares analysis of large, correlated spectral data sets and application to chemical kinetics and time-resolved fluorescence[J]. Rev Sci Instrum, 1996, 67(12): 4380-4386.
[28]	STILBS P, PAULSEN K, GRIFFITHS P C. Global least-squares analysis of large, correlated spectral data sets: Application to component-resolved FT-PGSE NMR spectroscopy[J]. J Phys Chem, 1996, 100(20): 8180-8189.
[29]	GRIFFITHS P C, STILBS P, PAULSEN K, et al. FT-PGSE NMR study of mixed micellization of an anionic and a sugar-based nonionic surfactant[J]. J Phys Chem B, 1997, 101(6): 915-918.
[30]	NILSSON M, MORRIS G A. Speedy component resolution: An improved tool for processing diffusion-ordered spectroscopy data[J]. Anal Chem, 2008, 80(10): 3777-3782.
[31]	VAN CORKOM L C M, HANCEWICZ T M. Analysis of DOSY and GPC-NMR experiments on polymers by multivariate curve resolution[J]. J Magn Reson, 1998, 130(1): 125-130.
[32]	COLBOURNE A A, MEIER S, MORRIS G A, et al. Unmixing the NMR spectra of similar species-vive la différence[J]. Chem Comm, 2013, 49(89): 10510.
[33]	PROVENCHER S W. A constrained regularization method for inverting data represented by linear algebraic or integral equations[J]. Comput Phys Commun, 1982, 27(3): 213-227.
[34]	BECK A, TEBOULLE M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems[J]. SIAM J Imaging Sci, 2009, 2(1): 183-202.
[35]	URBANCZYK M, BERNIN D, KOZMINSKI W, et al. Iterative thresholding algorithm for multiexponential decay applied to PGSE NMR data[J]. Anal Chem, 2013, 85(3): 1828-1833.
[36]	BOYD S. Distributed optimization and statistical learning via the alternating direction method of multipliers[J]. Found Trends Mach Learn, 2010, 3(1): 1-122.
[37]	GIAMPOURAS P V, THEMELIS K E, RONTOGIANNIS A A, et al. Simultaneously sparse and low-rank abundance matrix estimation for hyperspectral image unmixing[J]. IEEE Trans Geosci Remote Sens, 2016, 54(8): 4775-4789.
[38]	LIN E, CHEN B, NI Z, et al. A generally regularized inversion for NMR applications and beyond[J]. IEEE Trans on Instrum Meas, 2023, 72: 1-11.
[39]	KIM S-J, KOH K, LUSTIG M, et al. An interior-point method for large-scale L₁-regularized least squares[J]. IEEE J Sel Top Signal Process, 2007, 1(4): 606-617.
[40]	LIN E, TELKKI V-V, LIN X, et al. High-resolution reconstruction for multidimensional Laplace NMR[J]. J Phys Chem Lett, 2021, 12(21): 5085-5090.
[41]	DELSUC M A, MALLIAVIN T E. Maximum entropy processing of DOSY NMR spectra[J]. Anal Chem, 1998, 70(10): 2146-2148.
[42]	DAY I J. On the inversion of diffusion NMR data: Tikhonov regularization and optimal choice of the regularization parameter[J]. J Magn Reson, 2011, 211(2): 178-185.
[43]	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.
[44]	LIN E, YANG Y, HUANG Y, et al. High-resolution reconstruction for diffusion-ordered NMR spectroscopy[J]. Anal Chem, 2020, 92(1): 634-639.
[45]	LIN E, ZOU N, HUANG Y, et al. Neural network method for diffusion-ordered NMR spectroscopy[J]. Anal Chem, 2022, 94(6): 2699-2705.
[46]	YANG Y, ZOU N, LIN E, et al. A neural network method for nonconvex optimization and its application on parameter retrieval[J]. IEEE Trans Signal Process, 2021, 69: 3383-3398.
[47]	CASTANAR L, POGGETTO G D, COLBOURNE A A, et al. The GNAT: A new tool for processing NMR data[J]. Magn Reson Chem, 2018, 56(6): 546-558.
[48]	NILSSON M. The DOSY toolbox: A new tool for processing PFG NMR diffusion data[J]. J Magn Reson, 2009, 200(2): 296-302.
[49]	DOSY Toolbox, Manchester NMR methodology group[EB/OL]. https://www.nmr.chemistry.manchester.ac.uk/?q=node/340.
[50]	QU X, HUANG Y, LU H, et al. Accelerated nuclear magnetic resonance spectroscopy with deep learning[J]. Angew Chem Int Ed, 2020, 132(26): 10383-10386.
[51]	LIU Q, YANG Q, CHENG H, et al. Highly undersampled magnetic resonance imaging reconstruction using autoencoding priors[J]. Magn Reson Med, 2020, 83(1): 322-336.
[52]	PARASRAM T, DAOUD R, XIAO D. T₂ analysis using artificial neural networks[J]. J Magn Reson, 2021, 325: 106930.
[53]	LUO G, XIAO L, LUO S, et al. A study on multi-exponential inversion of nuclear magnetic resonance relaxation data using deep learning[J]. J Magn Reson, 2023, 346: 107358.
[54]	CHEN B, WU L, CUI X, et al. High-quality reconstruction for Laplace NMR based on deep learning[J]. Analy Chem, 2023, 95(31): 11596-11602.
[55]	BUTLER J P, REEDS J A, DAWSON S V. Estimating solutions of first kind integral equations with nonnegative constraints and optimal smoothing[J]. SIAM J Numer Anal, 1981, 18(3): 381-397.
[56]	VASWANI A, SHAZEER N, PARMAR N, et al. Attention is all you need[J]. Adv Neural Inf Process Syst, 2017, 30: 5998-6008.
[57]	CHEN J J, HURLIMANN M, PAULSEN J, et al. Dispersion of T₁ and T₂ nuclear magnetic resonance relaxation in crude oils[J]. Chem Phys Chem, 2014, 15(13): 2676-2681.
[58]	SONG Y-Q, XIAO L. Optimization of multidimensional MR data acquisition for relaxation and diffusion[J]. NMR Biomed, 2020, 33(12): e4238.
[59]	ZHANG R, WANG W, GAO Y, et al. Sensitivity analysis of T₂-T₁ 2D NMR measurement parameters in shale oil reservoirs[J]. Chinese J Magn Reson, 2023, 40(2): 122-135.
	张融, 王伟, 高怡, 等. 页岩油储层T₂-T₁二维核磁共振测量参数敏感性分析[J]. 波谱学杂志, 2023, 40(2): 122-135.
[60]	KENDALL A, GAL Y. What uncertainties do we need in Bayesian deep learning for computer vision?[C]// Adv Neural Inf Process Syst, 2017, 30: 5580-5590.
[61]	GLANG F, DESHMANE A, PROKUDIN S, et al. DeepCEST 3 T: Robust MRI parameter determination and uncertainty quantification with neural networks-application to CEST imaging of the human brain at 3 T[J]. Magn Reson Med, 2020, 84(1): 450-466.

Options

文章导航

模态框（Modal）标题

摘要

本文引用格式

Abstract

参考文献