An Iterative Truncated Singular Value Decomposition (TSVD)-Based Inversion Methods for 2D NMR

Chinese Journal of Magnetic Resonance

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An Iterative Truncated Singular Value Decomposition (TSVD)-Based Inversion Methods for 2D NMR

ZHOU Xiao-long1，NIE Sheng-dong1*，WANG Yuan-jun1，ZHANG Ying-li2，YANG Pei-qiang2

1. Institute of Medical Imaging Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China;
2. Shanghai Niumag Corporation, Shanghai 200333, China

Received:2013-04-07 Revised:2013-05-04 Online:2013-12-05 Published:2013-12-05
About author:*Corresponding author: Nie Sheng-dong, Tel: 021-55271172, E-mail:nsd4647@163.com.
Supported by:
国家自然科学基金资助项目（60972122）, 上海市教育委员会科研创新项目(13YZ069、14ZZ135)，国家重大科学仪器设备开发专项资助项目(2013YQ17046303).

Abstract

Abstract:

Truncated singular value decomposition (TSVD)-based methods are often used for two-dimensional inversion, but can suffer from drawbacks such as failure to locate an appropriate truncating position, sensitivity to noise, and generation of artificial signals. In this paper, we proposed an improved TSVDbased inversion method for 2D NMR. First, an accurate locating method using a progressive refinement regional searching algorithm was employed to find the largest preserving number of singular values. Then we calculated the minimum preserving number according to the clustering level of singular values. Lastly, an iterative TSVD method was implemented. The results on simulated and actual data set were reported. Compared with the existing TSVD-based methods, the proposed iterative TSVD method was shown to be more robust, and capable of producing spectra with higher resolution.

Key words: nuclear magnetic resonance, 2D inversion, D-T₂, T₁-T₂

CLC Number:

TP391.9

ZHOU Xiao-long1，NIE Sheng-dong1*，WANG Yuan-jun1，ZHANG Ying-li2，YANG Pei-qiang2 . An Iterative Truncated Singular Value Decomposition (TSVD)-Based Inversion Methods for 2D NMR[J]. Chinese Journal of Magnetic Resonance.

References

[1] Akkurt R，Bachman H N，Minh C C, et al. New nuclear magnetic resonance comes out of its shell[J]. Oilfield Review，2008，20（4）: 4-23.

[2] Mitchell J, Chandrasekera T C, Gladden L F. Numerical estimation of relaxation and diffusion distributions in two dimensions[J]. Prog Nucl Magn Reson Spectrosc, 2012, 62: 34-50.

[3] Gu Zhao-bin(顾兆斌), Liu Wei(刘卫). The Inversion of Two-dimensional NMR Map(核磁共振二维谱反演)[J]. Chinese J Magn Reson(波谱学杂志), 2007, 24(3): 311-319.

[4] Tan M J, Zou Y L, Zhou C C. A new inversion method for (T₂, D) 2D NMR logging and fluid typing[J]. Comput Geosci, 2013, 51: 366-380.

[5] Li Xin-jun(李新军), Nie Sheng-dong(聂生东), Wang Yuan-jun(王远军), et al. A Low-field NMR diffusion-transverse relaxation two-dimensional inversion algorithm (低场核磁共振扩散-横向弛豫二维反演算法)[J]. Chinese J Magn Reson(波谱学杂志). 2013, 30(3): 322-335.

[6] Venkataramanan L, Song Y Q, Hurlimann M D. Solving fredholm integrals of the first kind with tensor product structure in 2 and 2.5 dimensions[J]. IEEE T Signal Proces, 2002, 50(5): 1 017-1 026.

[7] Chouzenoux , Moussaoui S, Idier J, et al. Efficient maximum entropy reconstruction of nuclear magnetic resonance T₁-T₂ Spectra[J]. IEEE T Signal Proces, 2010, 58(12): 6 040-6 051.

[8] Zhou Xiao-long(周小龙), Nie Sheng-dong(聂生东), Wang Yuan-jun(王远军), et al. 2D NMR inversion method: A review(核磁共振二维谱反演技术综述)[J]. Chinese J Magn Reson(波谱学杂志). 2013, 30(2): 293-305.

[9] Warsa, Grandis H. Sensitivity study of 3-D modeling for multi D inversion of surface NMR[J]. AIP Conf Proc, 2012,1 454: 130-133.

[10] Hansen P C, O'Leary D P. The use of the L-curve in the regularization of discrete ill-posed problems[J]. Siam J Sci Comput, 1993, 14: 1 487-1 503.

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An Iterative Truncated Singular Value Decomposition (TSVD)-Based Inversion Methods for 2D NMR

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