Laplace NMR谱图重建——从经典正则化到深度学习

doi:10.11938/cjmr20233079

摘要/Abstract

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

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

中图分类号:

O657.61

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.

YANG Yu, CHEN Bo, WU Liubin, LIN Enping, HUANG Yuqing, CHEN Zhong. Spectrum Reconstruction for Laplace NMR: From Handcraft Regularization to Deep Learning[J]. Chinese Journal of Magnetic Resonance, 2024, 41(2): 191-208.

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	P	3	5	8
GSP	计算时间/s	11	110	650
	收敛步数	91	906	4847
QGC	计算时间/s	50	244	1988
	收敛步数	101	435	3389

样品	LRSpILT参数设置			CoMeF参数设置			单次运行时间（单位/s）
样品	λ₁	λ₂	迭代次数	β	成分数	迭代次数	LRSpILT	CoMeF	DRECT
QGC	0.005	0.0005	1500	0.1	3	30000	106	562	5
GSP	0.01	0.1	1500	0.8	3	30000	131	152	3
M6	0.7	33	1500	0.1	10	100000	123	357	3