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基于L1范数的低场核磁共振T2谱稀疏反演方法

蒋川东 常星 孙佳 李天威 田宝凤

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基于L1范数的低场核磁共振T2谱稀疏反演方法

蒋川东, 常星, 孙佳, 李天威, 田宝凤

Sparse inversion method of T2 spectrum based on the L1 norm for low-field nuclear magnetic resonance

Jiang Chuan-Dong, Chang Xing, Sun Jia, Li Tian-Wei, Tian Bao-Feng
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  • 低场核磁共振技术(LF-NMR)以其无损、非侵入、原位和绿色等优势被广泛应用在食品、农业、能源和化工等行业,尤其是在食品安全监管领域发挥着越来越重要的作用.在油品品质检测中,常规非负奇异值分解(SVD)弛豫(T2)谱反演方法,只能反映光滑模型的T2谱,对于稀疏模型的反演结果存在较大差异,从而导致T2谱反演分辨率低和品质分析不准确的问题.针对这一问题,本文提出基于L1范数最小化约束的T2谱稀疏反演算法,建立NMR回波曲线的稀疏模型表达式,利用截断牛顿内点法求解L1范数最小化问题,得到稀疏模型的T2谱反演结果.通过构造光滑模型的T2谱、以及不同峰值数和信噪比的稀疏模型的T2谱,对比非负SVD算法和L1稀疏算法的反演效果,得到当信噪比大于20 dB时,L1稀疏算法能精确反演多峰T2谱,峰值幅度和峰位置均优于非负SVD算法结果.最后通过多组煎炸油样品进行低场核磁共振检测实验和不同信噪比数据的反演结果对比,验证了L1范数稀疏反演算法的准确性和优越性.
    The technology of low-field nuclear magnetic resonance (LF-NMR) is commonly used in food, agriculture, energy and chemical sectors due to its non-destructive, non-invasive, in situ, green and other advantages. Recently, this technology played an increasingly large role in the field of food-safety supervision especially. In oil product quality testing, conventional T2 spectrum inversion methods such as the non-negative singular value decomposition (SVD) algorithm can only reflect T2 spectrum in a smooth model. However, for a sparse model, the inversion result of non-negative SVD algorithm is expected to be very glossy, leading to low resolution of T2 spectrum and inaccurate analysis of sample property. To solve this problem, we propose a sparse T2 spectrum inversion algorithm based on the L1 norm minimization constraint. In this paper, we establish the sparse model expression of NMR echo curve, and obtain the T2 sparse spectrum inversion results based on the inner truncated Newton-point method. Furthermore, the effectiveness of L1 sparse inversion algorithm is examined by the synthetic data of the smooth model and the spare model which have different peak numbers and signaltonoise ratios (SNRs). Synthetic results show that compared with the non-negative SVD algorithm, the L1 sparse algorithm is appropriate for both the smooth model and the sparse model with higher inversion accuracy. When the number of T2 peaks in a sparse model changes from a single peak to a quad peak, the L1 sparse algorithm can still obtain accurate inversion results, while the SVD algorithm results in a gradual deterioration, and cannot even determine the peak number. Under the sparse model, when the SNR of the measured NMR curve is gradually changed from 5 dB to 50 dB, the L1 sparse algorithm at 20 dB or more can obtain accurate inversion results which have less than 10% peak error and less than 5% peak position error and amplitude average error. However, the non-negative SVD algorithm cannot obtain accurate results at each SNR. Finally, multiple sets of frying oil samples are utilized to prove the accuracy and robustness of L1 sparse inversion algorithm. Inversion results of seven sets of frying oil samples show that the L1 sparse algorithm prefers the non-negative SVD algorithm. The obtained T2 spectrum by the L1 sparse algorithm shows three peaks obviously, and the T21 peak area ratio S21 and the single component relaxation time T2w are higher linear with respect to frying time than the results by non-negative SVD algorithm, which is useful for detecting the frying oil quality change. The inversion results of the T2 spectrum at different SNRs are consistent with the synthetic results, i.e., when the SNR is reduced, the T2 spectrum inversion results from the L1 sparse algorithm are better than those from the non-negative SVD algorithm when SNR is greater than 20 dB.
      通信作者: 田宝凤, tianbf@jlu.edu.cn
    • 基金项目: 国家重大科学仪器设备开发和应用专项项目(批准号:2011YQ030133);国家自然科学基金青年科学基金(批准号:41604083,41204079,41504086);吉林省自然科学基金(批准号:20160101281JC)和吉林大学大学生创新创业训练项目(批准号:2015651016)资助的课题.
      Corresponding author: Tian Bao-Feng, tianbf@jlu.edu.cn
    • Funds: Project supported by the National Key Foundation for Exploring Scientific Instrument (Grant No.2011YQ030133),the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos.41604083,41204079,41504086),the Natural Science Foundation of Jilin Province,China (Grant No.20160101281JC),and the College Students' Innovation and Entrepreneurship Training Project of Jilin University,China (Grant No.2015651016).
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    Lin F, Wang Z W, Liu Q H, Ding Y, Li C C 2009 J. Jilin Univ. (Earth Sci. Ed) 39 1150 (in Chinese)[林峰, 王祝文, 刘菁华, 丁阳, 李长春 2009吉林大学学报(地球科学版)39 1150]

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    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]

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    Wu L, Chen F, Huang C Y, Ding G H, Ding Y M 2016 Acta Phys. Sin. 65 107601 (in Chinese)[吴量, 陈方, 黄重阳, 丁国辉, 丁义明 2016 物理学报 65 107601]

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    Chen W C, Wang W, Gao J H, Jiang C F, Lei J L 2013 Chin. J. Geophys. 56 2771 (in Chinese)[陈文超, 王伟, 高静怀, 姜呈馥, 雷江莉 2013 地球物理学报 56 2771]

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    Mallat S G, Zhang Z 1993 IEEE Trans. Signal Proces. 41 3397

    [19]

    Zhou W 2013 M. S. Thesis (Guangzhou:South China University of Technology) (in Chinese)[周巍 2013 硕士论文 (广州:华南理工大学)]

    [20]

    Zhang L Q, Wang J Y 2008 Chin. J. Eng. Geophys. 5 509 (in Chinese)[张丽琴, 王家映 2008 工程地球物理学报 5 509]

    [21]

    Wei H, Sasaki H, Kubokawa J, Yokoyama R 1998 IEEE Trans. Power Syst. 13 870

    [22]

    Koh K, Kim S J, Boyd S 2007 J. Mach. Learn. Res. 8 1519

    [23]

    Stern A S, Donoho D L, Hoch J C 2007 J. Mag. Res. 188 295

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    Berman P, Levi O, Parmet Y, Saunders M, Wiesman Z 2013 Concept Mag. Res. A 42 72

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    Karmarkar N 1984 Combinatorica 4 373

  • [1]

    Marcone M F, Wang S, Albabish W, Nie S, Somnarain D, Hill A 2013 Food Res. Int. 51 729

    [2]

    Li X, Xiao L Z, Liu H B, Zhang Z F, Guo B X, Yu H J, Zong F R 2013 Acta Phys. Sin. 62 147602 (in Chinese)[李新, 肖立志, 刘化冰, 张宗富, 郭葆鑫, 于慧俊, 宗芳荣 2013 物理学报 62 147602]

    [3]

    Wang S, Munro R A, Shi L, Kawamura I, Okitsu T, Wada A, Kim S Y, Jung K H, Brown L S, Ladizhansky V 2013 Nat. Methods 10 1007

    [4]

    Dalitz F, Cudaj M, Maiwald M, Guthausen G 2012 Prog Nucl. Mag. Res. Sp. 60 52

    [5]

    Shen Y G, Xiao Z Q, Chen S S, Zhang Y L, Jiang W, Lai K Q 2013 J. Food Sci. Technol. 31 37 (in Chinese)[申云刚, 肖竹青, 陈舜胜, 张英力, 蒋伟, 赖克强 2013 食品科学技术学报 31 37]

    [6]

    Wang Y W, Wang X, Liu B L, Shi R, Yang P Q 2012 Food Sci. 33 171 (in Chinese)[王永巍, 王欣, 刘宝林, 史然, 杨培强 2012 食品科学 33 171]

    [7]

    Zhang Q, Saleh A M, Shen Q 2012 Food Bioprocess Technol. 6 2562

    [8]

    Zhu W, Wang X, Chen L 2017 Food Chem. 216 268

    [9]

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

    [10]

    Butler J P, Dawson S V 1981 Siam J. Numer. Anal. 18 381

    [11]

    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]

    [12]

    Chen S S, Wang H Z, Yang P Q, Zhang X L 2014 J. Biomed. Eng. 31 682 (in Chinese)[陈珊珊, 汪红志, 杨培强, 张学龙 2014 生物医学工程学杂志31 682]

    [13]

    Li P J, Ge C, Sun G P, Chen X, Wang Y K 2010 Well Logging Technol. 34 215 (in Chinese)[李鹏举, 葛成, 孙国平, 陈新, 王彦凯 2010测井技术34 215]

    [14]

    Lin F, Wang Z W, Liu Q H, Ding Y, Li C C 2009 J. Jilin Univ. (Earth Sci. Ed) 39 1150 (in Chinese)[林峰, 王祝文, 刘菁华, 丁阳, 李长春 2009吉林大学学报(地球科学版)39 1150]

    [15]

    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]

    [16]

    Wu L, Chen F, Huang C Y, Ding G H, Ding Y M 2016 Acta Phys. Sin. 65 107601 (in Chinese)[吴量, 陈方, 黄重阳, 丁国辉, 丁义明 2016 物理学报 65 107601]

    [17]

    Chen W C, Wang W, Gao J H, Jiang C F, Lei J L 2013 Chin. J. Geophys. 56 2771 (in Chinese)[陈文超, 王伟, 高静怀, 姜呈馥, 雷江莉 2013 地球物理学报 56 2771]

    [18]

    Mallat S G, Zhang Z 1993 IEEE Trans. Signal Proces. 41 3397

    [19]

    Zhou W 2013 M. S. Thesis (Guangzhou:South China University of Technology) (in Chinese)[周巍 2013 硕士论文 (广州:华南理工大学)]

    [20]

    Zhang L Q, Wang J Y 2008 Chin. J. Eng. Geophys. 5 509 (in Chinese)[张丽琴, 王家映 2008 工程地球物理学报 5 509]

    [21]

    Wei H, Sasaki H, Kubokawa J, Yokoyama R 1998 IEEE Trans. Power Syst. 13 870

    [22]

    Koh K, Kim S J, Boyd S 2007 J. Mach. Learn. Res. 8 1519

    [23]

    Stern A S, Donoho D L, Hoch J C 2007 J. Mag. Res. 188 295

    [24]

    Berman P, Levi O, Parmet Y, Saunders M, Wiesman Z 2013 Concept Mag. Res. A 42 72

    [25]

    Karmarkar N 1984 Combinatorica 4 373

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出版历程
  • 收稿日期:  2016-09-13
  • 修回日期:  2016-11-18
  • 刊出日期:  2017-02-05

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