Multi-exponential inversion of T-2 spectrum in NMR based on improved nonlinear fitting

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	Multi-exponential inversion of T-2 spectrum in NMR based on improved nonlinear fitting
	Wu Liang 1,2; Chen Fang 1; Huang Chong-Yang 1; Ding Guo-Hui 1,2; Ding Yi-Ming 1
刊名	ACTA PHYSICA SINICA
	2016-05-20
卷号	65 期号:10
关键词	nuclear magnetic resonance multi-exponential inversion nonlinear fitting differential evolution
英文摘要	Multi-exponential inversion algorithm of nuclear magnetic resonance (NMR) T-2 spectrum is an important mathematical tool for the NMR relaxation study of complicated samples. The popular algorithm usually obtains the T-2 spectrum by linear fitting under the prescribed distribution of T-2. When the T-2 spectrum is dispersed, such a procedure is inaccurate because of the lack of adaptive prescription and the limit of linear method. Nonlinear fitting method does not fix the T-2 distribution, and it provides the positions and the weights of T-2 simultaneously via the nonlinear fitting of multi-exponential function. In this case, the problem of multi-exponential inversion is transformed into a nonlinear optimization problem with non-negative constraints. The optimization objective function is the residual sum of squares (or residual sum of squares with regularization). The nonlinear optimization problem can usually be solved by Levenberg-Marquardt algorithm and evolutionary algorithm. But the results of Levenberg-Marquardt algorithm are dependent on initial values, and the calculation of evolutionary algorithm is complicated. We provide an optimal model for the nonlinear fitting in the inversion of dispersed T-2 spectrum based on the linear regression and least-squares. The key idea is that the optimal weights of T-2 can be calculated by least square when the positions of T-2 are fixed, although the positions of T-2 are adjusted adaptively. So we can relate the positions to weights appropriately to improve the popular nonlinear fitting algorithms. Such an improvement can reduce the searching inversion parameters, speed up its convergence and reduce the dependence on initial value. Incorporating it into the Levenberg-Marquardt algorithm or evolutionary algorithm can improve the inversion accuracy and make the algorithm more robust. The validity of our improvement is demonstrated by the inversions of simulation data and practical NMR data by combining Levenberg-Marquardt algorithm and differential evolution algorithm with our improvement. The inversion results of simulation data show that for dispersed T-2 spectrum, the algorithm using this improvement can obtain more accurate T-2 spectrum than previous ones, especially in the case of low signal-to-noise ratio (SNR) cases. The inversion results also indicate that the improvement can reduce the dependence on initial value of Levenberg-Marquardt algorithm, and can accelerate the convergence of differential evolution algorithm. The inversion results of practical NMR data show that the algorithm using the improvement can obtain more accurate T-2 spectrum than the widely used CONTIN program in the case of low signal-to-noise ratio (SNR). The inversion results of oil-water mixture sample NMR data also demonstrate that the relaxation time T-2 is independent of dispersion degree of immiscible system components.
WOS标题词	Science & Technology ; Physical Sciences
类目[WOS]	Physics, Multidisciplinary
研究领域[WOS]	Physics
关键词[WOS]	UNIFORM-PENALTY INVERSION ; INTEGRAL-EQUATIONS ; RELAXATION DATA ; DECAY DATA ; REGULARIZATION ; ALGORITHM
收录类别	SCI
语种	英语
WOS记录号	WOS:000380363900039
内容类型	期刊论文
源URL	[http://ir.wipm.ac.cn/handle/112942/9474]
专题	武汉物理与数学研究所_数学物理与应用研究部
作者单位	1.Chinese Acad Sci, State Key Lab Magnet Resonance & Atom & Mol Phys, Key Lab Magnet Resonance Biol Syst, Natl Ctr Magnet Resonance Wuhan,Wuhan Inst Phys &, Wuhan 430071, Peoples R China 2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Wu Liang,Chen Fang,Huang Chong-Yang,et al. Multi-exponential inversion of T-2 spectrum in NMR based on improved nonlinear fitting[J]. ACTA PHYSICA SINICA,2016,65(10).
APA	Wu Liang,Chen Fang,Huang Chong-Yang,Ding Guo-Hui,&Ding Yi-Ming.(2016).Multi-exponential inversion of T-2 spectrum in NMR based on improved nonlinear fitting.ACTA PHYSICA SINICA,65(10).
MLA	Wu Liang,et al."Multi-exponential inversion of T-2 spectrum in NMR based on improved nonlinear fitting".ACTA PHYSICA SINICA 65.10(2016).