Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Multi-exponential inversion of T2 spectrum in NMR based on improved nonlinear fitting

Wu Liang Chen Fang Huang Chong-Yang Ding Guo-Hui Ding Yi-Ming

Citation:

Multi-exponential inversion of T2 spectrum in NMR based on improved nonlinear fitting

Wu Liang, Chen Fang, Huang Chong-Yang, Ding Guo-Hui, Ding Yi-Ming
PDF
Get Citation

(PLEASE TRANSLATE TO ENGLISH

BY GOOGLE TRANSLATE IF NEEDED.)

  • Multi-exponential inversion algorithm of nuclear magnetic resonance (NMR) T2 spectrum is an important mathematical tool for the NMR relaxation study of complicated samples. The popular algorithm usually obtains the T2 spectrum by linear fitting under the prescribed distribution of T2. When the T2 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 T2 distribution, and it provides the positions and the weights of T2 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 T2 spectrum based on the linear regression and least-squares. The key idea is that the optimal weights of T2 can be calculated by least square when the positions of T2 are fixed, although the positions of T2 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 T2 spectrum, the algorithm using this improvement can obtain more accurate T2 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 T2 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 T2 is independent of dispersion degree of immiscible system components.
      Corresponding author: Chen Fang, chenfang@wipm.ac.cn;ding@wipm.ac.cn ; Ding Yi-Ming, chenfang@wipm.ac.cn;ding@wipm.ac.cn
    • Funds: Project supported by the National Basic Research Program of China (Grant No. 2013CB910200) and the National Natural Science Foundation of China (Grant No. 11405264).
    [1]

    Wang W M, Li P, Ye C H 2001 Sci. China A 31 730 (in Chinese) [王为民, 李培, 叶朝辉 2001 中国科学A 31 730]

    [2]

    Xu F, Huang Y R 2002 Acta Phys. Sin. 51 415 (in Chinese) [许峰, 黄永仁 2002 物理学报 51 415]

    [3]

    Zheng S K, Chen Z, Chen Z W, Zhong J H 2001 Chin. Phys. 10 558

    [4]

    Borgia G C, Brown R J S, Fantazzini P 1998 J. Magn. Res. 132 65

    [5]

    Borgia G C, Brown R J S, Fantazzini P 2000 J. Magn. Res. 147 273

    [6]

    Butler J P, Reeds J A, Dawson S V 1981 SIAM J. Numer. Anal. 18 381

    [7]

    Dunn K J, LaTorraca G A, Warner J L, Bergman D J 1994 SPE 69th Annual Techoical Conference and Exhibition New Orleans, Louisiana September25-28, 1994 SPE28367 45

    [8]

    Wang Z D, Xiao L Z, Liu T Y 2003 Sci. China G 33 323 (in Chinese) [王忠东, 肖立志, 刘堂宴 2003 中国科学G 33 323]

    [9]

    Lawson C L, Hanson R J 1974 Solving Least Square Problems (Englewood Cliffs, New Jersey: Prentice-Hall) p158

    [10]

    Bro R, De Jong S 1997 J. Chemom. 11 393

    [11]

    Liao G Z, Xiao L Z, Xie R H, Fu J J 2007 Chinese J. Geophys. 50 932 (in Chinese) [廖广志, 肖立志, 谢然红, 付娟娟 2007 地球物理学报 50 932]

    [12]

    Berman P, Levi O, Parmet Y, Saunders M, Wiesman Z 2013 Concepts in Magnetic Resonance Part A 42 72

    [13]

    Tikhonov A N 1963 Soviet Mathematics 4 1035

    [14]

    Provencher S W 1982 Comput. Phys. Commun. 27 229

    [15]

    Moody J B, Xia Y 2004 J. Magn. Res. 167 36

    [16]

    Prange M, Song Y Q 2009 J. Magn. Res. 196 54

    [17]

    Prange M, Song Y Q 2010 J. Magn. Res. 204 118

    [18]

    Lin F, Wang Z W, Li J Y, Zhang X A, Jiang Y L 2011 Appl. Geophys. 8 233

    [19]

    Wang H, Li G Y 2005 Acta Phys. Sin. 54 1431 (in Chinese) [王鹤, 李鲠颖 2005 物理学报 54 1431]

    [20]

    Pan K J, Chen H, Tan Y J 2008 Acta Phys. Sin. 57 5956 (in Chinese) [潘克家, 陈华, 谭永基 2008 物理学报 57 5956]

    [21]

    Chen H, Pan K J, Tan Y J 2009 Well Logging Technol. 33 37 (in Chinese) [陈华, 潘克家, 谭永基 2009 测井技术 33 37]

    [22]

    Tan M J, Shi Y L, Xie G B 2007 Well Logging Technol. 31 413 (in Chinese) [谭茂金, 石耀霖, 谢关宝 2007 测井技术 31 413]

    [23]

    Hastie T, Tibshirani R, Friedman J 2001 The Elements of Statistical Learning: Data Mining, Inference, and Prediction (New York: Springer) p11

  • [1]

    Wang W M, Li P, Ye C H 2001 Sci. China A 31 730 (in Chinese) [王为民, 李培, 叶朝辉 2001 中国科学A 31 730]

    [2]

    Xu F, Huang Y R 2002 Acta Phys. Sin. 51 415 (in Chinese) [许峰, 黄永仁 2002 物理学报 51 415]

    [3]

    Zheng S K, Chen Z, Chen Z W, Zhong J H 2001 Chin. Phys. 10 558

    [4]

    Borgia G C, Brown R J S, Fantazzini P 1998 J. Magn. Res. 132 65

    [5]

    Borgia G C, Brown R J S, Fantazzini P 2000 J. Magn. Res. 147 273

    [6]

    Butler J P, Reeds J A, Dawson S V 1981 SIAM J. Numer. Anal. 18 381

    [7]

    Dunn K J, LaTorraca G A, Warner J L, Bergman D J 1994 SPE 69th Annual Techoical Conference and Exhibition New Orleans, Louisiana September25-28, 1994 SPE28367 45

    [8]

    Wang Z D, Xiao L Z, Liu T Y 2003 Sci. China G 33 323 (in Chinese) [王忠东, 肖立志, 刘堂宴 2003 中国科学G 33 323]

    [9]

    Lawson C L, Hanson R J 1974 Solving Least Square Problems (Englewood Cliffs, New Jersey: Prentice-Hall) p158

    [10]

    Bro R, De Jong S 1997 J. Chemom. 11 393

    [11]

    Liao G Z, Xiao L Z, Xie R H, Fu J J 2007 Chinese J. Geophys. 50 932 (in Chinese) [廖广志, 肖立志, 谢然红, 付娟娟 2007 地球物理学报 50 932]

    [12]

    Berman P, Levi O, Parmet Y, Saunders M, Wiesman Z 2013 Concepts in Magnetic Resonance Part A 42 72

    [13]

    Tikhonov A N 1963 Soviet Mathematics 4 1035

    [14]

    Provencher S W 1982 Comput. Phys. Commun. 27 229

    [15]

    Moody J B, Xia Y 2004 J. Magn. Res. 167 36

    [16]

    Prange M, Song Y Q 2009 J. Magn. Res. 196 54

    [17]

    Prange M, Song Y Q 2010 J. Magn. Res. 204 118

    [18]

    Lin F, Wang Z W, Li J Y, Zhang X A, Jiang Y L 2011 Appl. Geophys. 8 233

    [19]

    Wang H, Li G Y 2005 Acta Phys. Sin. 54 1431 (in Chinese) [王鹤, 李鲠颖 2005 物理学报 54 1431]

    [20]

    Pan K J, Chen H, Tan Y J 2008 Acta Phys. Sin. 57 5956 (in Chinese) [潘克家, 陈华, 谭永基 2008 物理学报 57 5956]

    [21]

    Chen H, Pan K J, Tan Y J 2009 Well Logging Technol. 33 37 (in Chinese) [陈华, 潘克家, 谭永基 2009 测井技术 33 37]

    [22]

    Tan M J, Shi Y L, Xie G B 2007 Well Logging Technol. 31 413 (in Chinese) [谭茂金, 石耀霖, 谢关宝 2007 测井技术 31 413]

    [23]

    Hastie T, Tibshirani R, Friedman J 2001 The Elements of Statistical Learning: Data Mining, Inference, and Prediction (New York: Springer) p11

  • [1] Kong Xiang-Yu, Zhu Yuan-Ye, Wen Jing-Wei, Xin Tao, Li Ke-Ren, Long Gui-Lu. New research progress of nuclear magnetic resonance quantum information processing. Acta Physica Sinica, 2018, 67(22): 220301. doi: 10.7498/aps.67.20180754
    [2] Jiang Chuan-Dong, Wang Qi, Du Guan-Feng, Yi Xiao-Feng, Tian Bao-Feng. Characteristics of surface nuclear magnetic off-resonance signal and complex envelope inversion. Acta Physica Sinica, 2018, 67(1): 013302. doi: 10.7498/aps.67.20171464
    [3] Pan Jian, Yu Qi, Peng Xin-Hua. Experimental technique for multi-qubit nuclear magnetic resonance system. Acta Physica Sinica, 2017, 66(15): 150302. doi: 10.7498/aps.66.150302
    [4] Li Xiao-Li, Sun Jian-Gang, Tao Ning, Zeng Zhi, Zhao Yue-Jin, Shen Jing-Ling, Zhang Cun-Lin. Application of nonlinear data fitting method to thermal diffusivity of carbon-carbon composite measured by transmission pulsed thermography. Acta Physica Sinica, 2017, 66(18): 188702. doi: 10.7498/aps.66.188702
    [5] Li Zheng, Zhou Rui, Zheng Guo-Qing. Quantum criticalities in carrier-doped iron-based superconductors. Acta Physica Sinica, 2015, 64(21): 217404. doi: 10.7498/aps.64.217404
    [6] Xu Xin-He, Liu Ying, Gan Yue-Hong, Liu Wen-Miao. A method of retrieving the constitutive parameter matrix of magnetoelectric coupling metamaterial. Acta Physica Sinica, 2015, 64(4): 044101. doi: 10.7498/aps.64.044101
    [7] Tian Bao-Feng, Zhou Yuan-Yuan, Wang Yue, Li Zhen-Yu, Yi Xiao-Feng. Noise cancellation method for full-wave magnetic resonance sounding signal based on independent component analysis. Acta Physica Sinica, 2015, 64(22): 229301. doi: 10.7498/aps.64.229301
    [8] Li Jun, Cui Jiang-Yu, Yang Xiao-Dong, Luo Zhi-Huang, Pan Jian, Yu Qi, Li Zhao-Kai, Peng Xin-Hua, Du Jiang-Feng. Quantum control of nuclear magnetic resonance spin systems. Acta Physica Sinica, 2015, 64(16): 167601. doi: 10.7498/aps.64.167601
    [9] Xie Yu, Zhao Chun-Xia, Zhang Hao-Feng, Yan Xue-Jun, Chen De-Bao. A blending crossover differential evolution approach to camera space manipulation parameter optimization. Acta Physica Sinica, 2015, 64(2): 020701. doi: 10.7498/aps.64.020701
    [10] Wang Yan, Zou Nan, Fu Jin, Liang Guo-Long. Estimation of single hydrophone target motion parameter based on cepstrum analysis. Acta Physica Sinica, 2014, 63(3): 034302. doi: 10.7498/aps.63.034302
    [11] Li Xin, Xiao Li-Zhi, Liu Hua-Bing, Zhang Zong-Fu, Guo Bao-Xin, Yu Hui-Jun, Zong Fang-Rong. Optimization of nuclear magnetic resonance refocusing pulses to enhance signal intensity in gradient B0 field. Acta Physica Sinica, 2013, 62(14): 147602. doi: 10.7498/aps.62.147602
    [12] Yao Xi-Wei, Zeng Bi-Rong, Liu Qin, Mu Xiao-Yang, Lin Xing-Cheng, Yang Chun, Pan Jian, Chen Zhong. Subspace quantum process tomography via nuclear magnetic resonance. Acta Physica Sinica, 2010, 59(10): 6837-6841. doi: 10.7498/aps.59.6837
    [13] Li Shao, Ren Yu-Feng, Wang Ning, Tian Ye, Chu Hai-Feng, Li Song-Lin, Chen Ying-Fei, Li Jie, Chen Geng-Hua, Zheng Dong-Ning. Detection of nuclear magnetic resonance in the microtesla range using a high Tc dc-superconducting quantum interference device. Acta Physica Sinica, 2009, 58(8): 5744-5749. doi: 10.7498/aps.58.5744
    [14] Xu Feng, Liu Tang-Yan, Huang Yong-Ren. Theoretical computation and numerical simulation of the relaxation of sphere-capillary model saturated with oil and water. Acta Physica Sinica, 2008, 57(1): 550-555. doi: 10.7498/aps.57.550
    [15] Pan Ke-Jia, Chen Hua, Tan Yong-Ji. Multi-exponential inversion of T2 spectrum in NMR based on differential evolution algorithm. Acta Physica Sinica, 2008, 57(9): 5956-5961. doi: 10.7498/aps.57.5956
    [16] Xu Feng, Liu Tang-Yan, Huang Yong-Ren. Theoretical description and numerical computation of the relaxation of multi-spin system in the presence of an RF field. Acta Physica Sinica, 2006, 55(6): 3054-3059. doi: 10.7498/aps.55.3054
    [17] Wang He, Li Geng-Ying. Combination of inversion and fitting as an effective method for the analysis of NMR relaxation data. Acta Physica Sinica, 2005, 54(3): 1431-1436. doi: 10.7498/aps.54.1431
    [18] Xu Feng, Huang Yong-Ren. . Acta Physica Sinica, 2002, 51(6): 1371-1376. doi: 10.7498/aps.51.1371
    [19] Xu Feng, Huang Yong-Ren. . Acta Physica Sinica, 2002, 51(11): 2617-2622. doi: 10.7498/aps.51.2617
    [20] . Acta Physica Sinica, 2002, 51(2): 415-419. doi: 10.7498/aps.51.415
Metrics
  • Abstract views:  5426
  • PDF Downloads:  235
  • Cited By: 0
Publishing process
  • Received Date:  24 September 2015
  • Accepted Date:  08 March 2016
  • Published Online:  05 May 2016

/

返回文章
返回