迭代软阈值法压缩感知重建谱峰较宽的二维固体谱

doi:10.11938/cjmr20150401

波谱学杂志 ›› 2015, Vol. 32 ›› Issue (4): 551-562.doi: 10.11938/cjmr20150401

迭代软阈值法压缩感知重建谱峰较宽的二维固体谱

韩明月，郑慧，胡炳文*，杨光*

华东师范大学物理系，上海市磁共振重点实验室，上海 200062

收稿日期:2014-11-24 修回日期:2015-10-24 出版日期:2015-12-05 发布日期:2015-12-05
作者简介:韩明月(1988-)，女，吉林长春人，硕士研究生，无线电物理专业． *通讯联系人：杨光，电话：021-62233873，E-mail：gyang@phy.ecnu.edu.cn；胡炳文，电话：021-62233633，E-mail：bwhu@phy.ecnu.edu.cn.
基金资助:
上海市科委资助项目(08DZ1900700)

Compressed Sensing Reconstruction with Iterative Soft Thresholding for Two-Dimensional Solid-State NMR Spectra with Broad Peaks

HAN Ming-yue，ZHENG Hui，HU Bing-wen*，YANG Guang*

Shanghai Key Laboratory of Magnetic Resonance, Department of Physics, East China Normal University, Shanghai 200062, China

Received:2014-11-24 Revised:2015-10-24 Online:2015-12-05 Published:2015-12-05
About author:*Corresponding author：YANG Guang, Tel: +86-21-62233873, E-mail: gyang@phy.ecnu.edu.cn; HU Bing-wen, Tel: +86-21-62233633, E-mail: bwhu@phy.ecnu.edu.cn.
Supported by:
上海市科委资助项目(08DZ1900700)

摘要/Abstract

摘要：

压缩感知技术可以打破传统奈奎斯特采样定理的限制，利用优化算法对欠采数据进行重建，并获得高质量的结果，因此在核磁共振领域得到了广泛的关注．但是当核磁共振谱的谱峰很宽时，基于共轭梯度方法的压缩感知重建却难以得到令人满意的谱图．因此，该文采用凸优化非线性重建算法，使用基于谱图域软阈值的压缩感知算法重建固体二维宽谱（¹H双量子-单量子谱或MQMAS谱），有效地解决了宽峰在重建时变弱的问题．

关键词: 压缩感知(Compressed Sensing, CS), 固体核磁共振, 软阈值, 随机欠采, 共轭梯度

Abstract:

Conjugate gradient (CG) method has been used previously to reconstruct double quantum-single quantum (DQ-SQ) spectra. However, satisfactory results can be obtained only when the spectra contain only narrow peaks, but not in the case when broad peaks are present. Compressed sensing technology can break the limit of the Nyquist acquisition theorem and reconstruct under-sampled data with high quality. The technology has been applied in the field of nuclear magnetic resonance (NMR). In this paper, we propose to use compressed sensing with iterative soft thresholding (IST) to reconstruct two-dimensional solid-state NMR spectra with broad peaks, such as the spectra obtained in ¹H DQ-SQ and ⁸⁷Rb multiple quantum-magic angle spinning (MQ-MAS) experiments. It was found that, with the IST method, compressed sensing technology could be used to reconstruct high-quality spectra containing broad peaks from under-sampled datasets.

Key words: compressed sensing, solid-state NMR, iterative soft thresholding, pseudo- random sampling, conjugate gradient

中图分类号:

O482.53

韩明月，郑慧，胡炳文*，杨光*. 迭代软阈值法压缩感知重建谱峰较宽的二维固体谱
[J]. 波谱学杂志, 2015, 32(4): 551-562.

HAN Ming-yue，ZHENG Hui，HU Bing-wen*，YANG Guang*. Compressed Sensing Reconstruction with Iterative Soft Thresholding for Two-Dimensional Solid-State NMR Spectra with Broad Peaks[J]. Chinese Journal of Magnetic Resonance, 2015, 32(4): 551-562.

参考文献

[1] Ernst R R, Bodenhausen G, Wokaun A. Principles of Nuclear Magnetic Resonance in One and Two Dimensions[M]. Oxford: Oxford University Press, 1990.

[2] Massiot D, Fayon F, Capron M, et al. Modelling one and two dimensional solid-state NMR spectra[J]. Magn Reson Chem, 2002, 40(1): 70－76.

[3] Kazimierczuk K, Orekhov V Y. A comparison of convex and non-convex compressed sensing applied to multidimensional NMR[J]. J Magn Reson, 2012, 223: 1－10.

[4] Bruschweiler R. Theory of covariance nuclear magnetic resonance spectroscopy[J]. J Chem Phys, 2004, 121(1): 409－414.

[5] Daniell G J, Hore P J. Maximum entropy and NMR—A new approach[J]. J Magn Reson, 1989, 84(3): 515–536.

[6] Coggins B E, Zhou P. High resolution 4-D spectroscopy with sparse concentric shell sampling and FFT-CLEAN[J]. J Biomol NMR, 2008, 42(4): 225－239.

[7] Lustig M, Donoho D, Pauly J M. Sparse MRI: The application of compressed sensing for rapid MR imaging[J]. Magn Reson Med, 2007, 58(6): 1 182－1 195.

[8] Baraniuk R G. Compressive sensing[J]. IEEE Signal Proc Mag, 2007, 24(4): 118－124.

[9] Foucart S, Rauhut H. A Mathematical Introduction to Compressive Sensing[M]. Berlin: Springer, 2013.

[10] Donoho D L. Compressed sensing[J]. IEEE T Inform Theory, 2006, 152(4): 1 289－1 306.

[11] Xu X B, Guo D, Cao X, et al. Reconstruction of self-sparse 2D NMR spectra from undersampled data in the indirect dimension[J]. Sensors (Basel), 2011, 11(9): 8 888－8 909.

[12] Holland D J, Bostock M J, Gladden L F, et al. Fast multidimensional NMR spectroscopy using compressed sensing[J]. Angewandte Chemie, 2011, 50(29): 6 678－6 681.

[13] Candes E J, Romberg J K, Tao T. Stable signal recovery from incomplete and inaccurate measurements[J]. Commun Pur Appl Math, 2006, 59(8): 1 207－1 223.

[14] Candes E J, Romberg J K, Tao T. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information[J]. IEEE T Inform Theory, 2006, 52(2): 489－509.

[15] Candes E J, Tao T. Near-optimal signal recovery from random projections: Universal encoding strategies?[J]. IEEE T Inform Theory, 2006, 52(12): 5 406－5 425.

[16] Donoho D L. De-noising by soft-thresholding[J]. IEEE T Inform Theory, 1995, 41(3): 613－627.

[17] Blumensath T, Davies M E. Iterative hard thresholding for compressed sensing[J]. Appl Comput Harmon Anal, 2009, 27(3): 265－274.

[18] Fornasier M, Rauhut H. Iterative thresholding algorithms[J]. Appl Comput Harmon Anal, 2008, 25(2): 187－208.

[19] Donoho D L, Johnstone I M. Engineering Advances: New Opportunities for Biomedical Engineers[C]. Baltimore: Proceedings of the 16th Annual International Conference of the IEEE, 1994.

[20] Stern A S, Donoho D L, Hoch J C. NMR data processing using iterative thresholding and minimum l1 norm reconstruction[J]. J Magn Reson, 2007, 188(2): 295－300.

[21] Steidl G, Weickert J, Brox T, et al. On the equivalence of soft wavelet shrinkage, total variation diffusion, total variation regularization, and SIDEs[J]. SIAM J Numer Anal, 2004, 42(2): 686－713.

[22] Beck A, Teboulle M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems[J]. SIAM J Imag Sci, 2009, 2(1): 183－202.

[23] Bruck J R E. On the weak convergence of an ergodic iteration for the solution of variational inequalities for monotone operators in Hilbert space[J]. J Math Anal Appl, 1977, 61(1): 159－164.

[24] Passty G B. Ergodic convergence to a zero of the sum of monotone operators in Hilbert space[J]. J Math Anal Appl, 1979, 72(2): 383－390.

[25] Facchinei F, Pang J S. Finite-Dimensional Variational Inequalities and Complementarity Problems[M]. New York: Springer, 2003.

[26] Candes E J. Compressive sampling[C]. Madrid: Proceedings on the International Congress of Mathematicians, 2006, 1 433－1 452.

[27] Candes E J, Romberg J K. Sparsity and incoherence in compressive sampling[J]. Inverse Probl, 2006, 23(3): 969－985.

[28] Nayak K S, Nishimura D G. Randomized trajectories for reduced aliasing artifact[C]. Proceedings of the 6th Annual Meeting of the International Society for Magnetic Resonance in Medicine (ISMRM'98), 1998, 670.

[29] Tsai C M, Nishimura D G. Reduced aliasing artifacts using variable-density k-space sampling trajectories[J]. Magn Reson Med, 2000, 43(3): 452－458.

[30] Zheng Hui(郑慧), Han Ming-yue(韩明月), Hu Bing-wen(胡炳文), et al. Comparison of different sampling schems in compressed sensing reconstruction for DQ-SQ experiments(不同采样模式的固体DQ-SQ实验的压缩感知重建比较)[J]. Chinese J Magn Reson(波谱学杂志), 2015, 31(4): 535－547.

[31] Lustig M, Donoho D L, Santos J M, et al. Compressed sensing MRI[J]. IEEE Signal Proc Mag, 2008, 25(2): 72－82.

[32] Gamper U, Boesiger P, Kozerke S. Compressed sensing in dynamic MRI[J]. Magn Reson Med, 2008, 59(2): 365－373.

[33] Otazo R, Kim D, Axel L, et al. Combination of compressed sensing and parallel imaging for highly accelerated first‐pass cardiac perfusion MRI[J]. Magn Reson Med, 2010, 64(3): 767－776.

[34] Ung H, Sung K, Nayak K S, et al. k - t FOCUSS: A general compressed sensing framework for high resolution dynamic MRI[J]. Magn Reson Med, 2009, 61(1): 103－116.

[35] Sommer W, Demco D E, Hafner S, et al. Rotation-synchronized homonuclear dipolar decoupling[J]. J Magn Reson A, 1995, 116(1): 36－45.

[36] Trebosc J, Amoureux J P, Gan Z H. Comparison of high-resolution solid-state NMR MQMAS and STMAS methods for half-integer quadrupolar nuclei[J]. Solid State Nucl Magn Reson, 2007, 31(1): 1－9.

迭代软阈值法压缩感知重建谱峰较宽的二维固体谱

Compressed Sensing Reconstruction with Iterative Soft Thresholding for Two-Dimensional Solid-State NMR Spectra with Broad Peaks

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