物理学报2017，Vol.66Issue(4)：263-275,13.DOI:10.7498/aps.66.047601
基于L1范数的低场核磁共振T2谱稀疏反演方法
Sparse inversion method of T2 sp ectrum based on the L1 norm for low-field nuclear magnetic resonance
摘要
Abstract
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 tech-nology 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 mini-mization 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.关键词
低场核磁共振/T2谱反演/稀疏模型/L1范数最小化约束Key words
lowfield nuclear magnetic resonance/T2 spectrum inversion/sparse representation/L1-norm minimization constraint引用本文复制引用
蒋川东,常星,孙佳,李天威,田宝凤..基于L1范数的低场核磁共振T2谱稀疏反演方法[J].物理学报,2017,66(4):263-275,13.基金项目
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). 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. （Grant No. 2011YQ030133）
