基于总体最小二乘-旋转不变算法的地表核磁共振信号参数估计

于晓辉; 冯海; 田宝凤; 孙海欣; 孙晓东

doi:10.11999/JEIT230102

基于总体最小二乘-旋转不变算法的地表核磁共振信号参数估计

doi: 10.11999/JEIT230102

1.
吉林大学通信工程学院长春 130022
2.
吉林大学仪器科学与电气工程学院/地球信息探测仪器教育部重点实验室长春 130026
3.
长春大学电子信息学院长春 130022

基金项目: 国家自然科学基金(42074217)

详细信息

作者简介:
于晓辉：女，硕士生导师，主要研究方向为自动控制、信号处理

冯海：男，硕士生，主要研究方向为核磁信号处理

田宝凤：女，硕士生导师，主要研究方向为核磁共振探测方法、数字信号处理技术

孙海欣：女，副教授，主要研究方向为微弱信号处理和时频分析

孙晓东：男，副教授，硕士生导师，主要研究方向为微弱信号检测和信号侦查理论

通讯作者:
孙晓东　sunxd@jlu.edu.cn

中图分类号: P631
计量
- 文章访问数: 266
- HTML全文浏览量: 113
- PDF下载量: 32
- 被引次数: 0
出版历程
- 收稿日期: 2023-02-24
- 修回日期: 2023-07-12
- 网络出版日期: 2023-07-20
- 刊出日期: 2024-02-29

Parameter Estimation of Surface Nuclear Magnetic Resonance Signals Based on Total Least Squares-Estimation of Signal Parameters via Rotational Invariance Technique

1.
School of Communication Engineering, Jilin University, Changchun 130022, China
2.
College of Instrumentation & Electrical Engineering/Key Laboratory of Geo-Exploration Instrumentation, Ministry of Education, Jilin University, Changchun 130026, China
3.
School of Electronic and Information Engineering, Changchun University, Changchun 130022, China

Funds: The National Natural Science Foundation of China (42074217)

摘要

摘要: 在地表核磁共振(SNMR)找水系统中，根据SNMR信号的参数能够预估地下含水层的储水量、导电性以及孔隙结构等信息。然而在实际应用中探测现场采集的SNMR信号十分微弱，易受到环境噪声干扰，导致无法直接获取SNMR信号的参数。针对这一问题，该文提出基于总体最小二乘-旋转不变法(TLS-ESPRIT)的地表核磁共振信号参数估计方法。基于谐波噪声与SNMR信号的相似信号特征构成一个由多个正弦衰减信号叠加的混合信号模型，使用TLS-ESPRIT将混合信号参数提取问题转换为旋转不变矩阵的广义特征值求解，从而获得SNMR信号的拉莫尔频率和弛豫时间，并结合最小二乘法求得其初始振幅和相位。仿真信号和实测信号实验结果表明此方法能够估计出混有随机噪声和工频谐波噪声的SNMR信号的参数，相比传统的谐波建模方法，在参数提取精度上效果更好。
- 地表核磁共振 /
- 总体最小二乘-旋转不变法 /
- 谐波噪声
Abstract: In the Surface Nuclear Magnetic Resonance (SNMR) water searching system, the parameters of SNMR signals can be used to predict the water storage, electrical conductivity, pore structure of underground aquifer. However, the SNMR signals collected on site are very weak in practical application, which is easy to be interfered by environmental noise, resulting in the inability to directly obtain the parameters of SNMR signal. To solve this problem, an estimation method of SNMR signal parameters based on Total Least Squares-Estimation of Signal Parameters via Rotational Invariance Technique (TLS-ESPRIT) is proposed in this paper. Based on the similar signal characteristics of harmonic noise and SNMR signals, a mixed signal model consisting of multiple sinusoidal attenuation signals is constructed. TLS-ESPRIT is used to transform the problem of extracting mixed signal parameters into a generalized eigenvalue solution of a rotation invariant matrix, in order to obtain the Lamor frequency and the relaxation time of the SNMR signal, and its initial amplitude and phase are obtained by combining the least squares method. The experimental results of simulated signal and measured signal show that the proposed method can estimate the parameters of SNMR signal mixed with random noise and power frequency harmonic noise. Compared with the traditional harmonic modeling method, the parameter extraction accuracy is better.

HTML全文

图 1 基于TLS-ESPRIT算法的SNMR信号参数估计的流程图

下载: 全尺寸图片幻灯片

图 2 不同噪声水平下初始振幅统计

下载: 全尺寸图片幻灯片

图 3 不同噪声水平下弛豫时间统计

下载: 全尺寸图片幻灯片

图 4 不同噪声水平下拉莫尔频率统计

下载: 全尺寸图片幻灯片

图 5 不同噪声水平下初始相位统计

下载: 全尺寸图片幻灯片

图 6 不同$ T_2^* $下初始振幅统计

下载: 全尺寸图片幻灯片

图 7 不同$ T_2^* $下弛豫时间统计

下载: 全尺寸图片幻灯片

图 8 不同$ T_2^* $下拉莫尔频率统计

下载: 全尺寸图片幻灯片

图 9 不同$ T_2^* $下初始相位统计

下载: 全尺寸图片幻灯片

图 10 初始振幅RMSE

下载: 全尺寸图片幻灯片

图 11 弛豫时间RMSE

下载: 全尺寸图片幻灯片

图 12 实测信号和SNMR信号时频域图

下载: 全尺寸图片幻灯片

表 1 SNMR信号参数实际值以及使用TLS-ESPRIT算法求得的参数估计值

	SNMR信号参数实际值			TLS-ESPRIT算法的估计值
	$ {E_0} $(nV)	$ T_2^* $(s)	$ {f_L} $(Hz)	$ {E_0} $(nV)	$ T_2^* $(s)	$ {f_L} $(Hz)
1	400	0.05	2355	382.71	0.0524	2354.853
2	400	0.1	2355	368.22	0.1079	2354.967
3	400	0.2	2355	442.45	0.2007	2355.061
4	400	0.3	2355	363.39	0.2936	2355.036
5	400	0.4	2355	424.78	0.4280	2355.026

下载: 导出CSV

参考文献(20)

[1]	TRUSHKIN D V, SHUSHAKOV O A, and LEGCHENKO A V. The potential of a noise-reducing antenna for surface NMR groundwater surveys in the earth’s magnetic field[J]. Geophysical Prospecting, 1994, 42(8): 855–862. doi: 10.1111/j.1365-2478.1994.tb00245.x.
[2]	RANGEL R C, PARSEKIAN A D, FARQUHARSON L M, et al. Geophysical observations of Taliks below drained lake basins on the arctic coastal plain of Alaska[J]. Journal of Geophysical Research:Solid Earth, 2021, 126(3): e2020JB020889. doi: 10.1029/2020JB020889.
[3]	LI Mengna, ZENG Yijian, LUBCZYNSKI M W, et al. A first investigation of hydrogeology and hydrogeophysics of the Maqu catchment in the Yellow River source region[J]. Earth System Science Data, 2021, 13(10): 4727–4757. doi: 10.5194/essd-13-4727-2021.
[4]	LU Kai, LI Fan, PAN Jianwei, et al. Using electrical resistivity tomography and surface nuclear magnetic resonance to investigate cultural relic preservation in Leitai, China[J]. Engineering Geology, 2021, 285: 106042. doi: 10.1016/J.ENGGEO.2021.106042.
[5]	BEHROOZMAND A A, KEATING K, and AUKEN E. A review of the principles and applications of the NMR technique for near-surface characterization[J]. Surveys in Geophysics, 2015, 36(1): 27–85. doi: 10.1007/s10712-014-9304-0.
[6]	KEATING K, WALSH D O, and GRUNEWALD E. The effect of magnetic susceptibility and magnetic field strength on porosity estimates determined from low-field nuclear magnetic resonance[J]. Journal of Applied Geophysics, 2020, 179: 104096. doi: 10.1016/j.jappgeo.2020.104096.
[7]	KREMER T, IRONS T, MÜLLER-PETKE M, et al. Review of acquisition and signal processing methods for electromagnetic noise reduction and retrieval of surface nuclear magnetic resonance parameters[J]. Surveys in Geophysics, 2022, 43(4): 999–1053. doi: 10.1007/S10712-022-09695-3.
[8]	LEGCHENKO A and VALLA P. A review of the basic principles for proton magnetic resonance sounding measurements[J]. Journal of Applied Geophysics, 2002, 50(1/2): 3–19. doi: 10.1016/S0926-9851(02)00127-1.
[9]	COSTABEL S and MÜLLER-PETKE M. Despiking of magnetic resonance signals in time and wavelet domains[J]. Near Surface Geophysics, 2014, 12(2): 185–198. doi: 10.3997/1873-0604.2013027.
[10]	万玲, 张扬, 林君, 等. 基于能量运算的磁共振信号尖峰噪声抑制方法[J]. 地球物理学报, 2016, 59(6): 2290–2301. doi: 10.6038/cjg20160631. WAN Ling, ZHANG Yang, LIN Jun, et al. Spikes removal of magnetic resonance sounding data based on energy calculation[J]. Chinese Journal of Geophysics, 2016, 59(6): 2290–2301. doi: 10.6038/cjg20160631.
[11]	LEGCHENKO A and VALLA P. Removal of power-line harmonics from proton magnetic resonance measurements[J]. Journal of Applied Geophysics, 2003, 53(2/3): 103–120. doi: 10.1016/S0926-9851(03)00041-7.
[12]	LARSEN J J, DALGAARD E, and AUKEN E. Noise cancelling of MRS signals combining model-based removal of powerline harmonics and multichannel Wiener filtering[J]. Geophysical Journal International, 2014, 196(2): 828–836. doi: 10.1093/gji/ggt422.
[13]	田宝凤, 朱慧, 易晓峰, 等. 基于谐波建模和自相关的磁共振信号消噪与提取方法研究[J]. 地球物理学报, 2018, 61(2): 767–780. doi: 10.6038/cjg2018L0091. TIAN Baofeng, ZHU Hui, YI Xiaofeng, et al. Denoising and extraction method of magnetic resonance sounding signal based on adaptive harmonic modeling and autocorrelation[J]. Chinese Journal of Geophysics, 2018, 61(2): 767–780. doi: 10.6038/cjg2018L0091.
[14]	庄双勇, 赵伟, 赵东芳, 等. 一种基于滑窗TLS-ESPRIT算法的超谐波动态分析方法[J]. 计量学报, 2020, 41(4): 475–483. doi: 10.3969/j.issn.1000-1158.2020.04.014. ZHUANG Shuangyong, ZHAO Wei, ZHAO Dongfang, et al. A supraharmonics dynamic analysis method based on sliding-window TLS-ESPRIT algorithm[J]. Acta Metrologica Sinica, 2020, 41(4): 475–483. doi: 10.3969/j.issn.1000-1158.2020.04.014.
[15]	CHEN Jian, JIN Tao, MOHAMED M A, et al. An adaptive TLS-ESPRIT algorithm based on an S-G filter for analysis of low frequency oscillation in wide area measurement systems[J]. IEEE Access, 2019, 7: 47644–47654. doi: 10.1109/ACCESS.2019.2908629.
[16]	SAMAL S K and SUBUDHI B. New signal subspace approach to estimate the inter-area oscillatory modes in power system using TLS-ESPRIT algorithm[J]. IET Generation, Transmission & Distribution, 2019, 13(18): 4123–4140. doi: 10.1049/iet-gtd.2018.6401.
[17]	张硕, 杨君, 葛鹏程, 等. 基于Hankel矩阵改进的TLS-ESPRIT多频带融合处理[J]. 电光与控制, 2022, 29(9): 90–95. doi: 10.3969/j.issn.1671-637X.2022.09.018. ZHANG Shuo, YANG Jun, GE Pengcheng, et al. TLS-ESPRIT multiband fusion processing based on hankel matrix improvement[J]. Electronics Optics &Control, 2022, 29(9): 90–95. doi: 10.3969/j.issn.1671-637X.2022.09.018.
[18]	张小宽, 郑舒予, 奚之飞, 等. 基于改进LS-ESPRIT算法的GTD模型参数估计与RCS重构[J]. 电子与信息学报, 2020, 42(10): 2493–2499. doi: 10.11999/JEIT190747. ZHANG Xiaokuan, ZHENG Shuyu, XI Zhifei, et al. GTD model parameters estimation and RCS reconstruction based on the improved LS-ESPRIT algorithm[J]. Journal of Electronics &Information Technology, 2020, 42(10): 2493–2499. doi: 10.11999/JEIT190747.
[19]	GRUNEWALD E, KNIGHT R, and WALSH D. Advancement and validation of surface nuclear magnetic resonance spin-echo measurements of T₂[J]. Geophysics, 2014, 79(2): EN15–EN23. doi: 10.1190/geo2013-0105.1.
[20]	SRIVASTAVA A K, TIWARI A N, and SINGH S N. Harmonic/interharmonic estimation using standard deviation assisted ESPRIT method[J]. COMPEL:The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 2021, 40(6): 1067–1083. doi: 10.1108/COMPEL-03-2021-0108.