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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.
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Keywords:
- lowfield nuclear magnetic resonance /
- T2 spectrum inversion /
- sparse representation /
- L1-norm minimization constraint
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[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
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[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 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 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 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 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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[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 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 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 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 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 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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