Comparison of Different Sampling Schemes in Compressed Sensing Reconstruction for DQ-SQ experiments

  • ZHENG Hui ,
  • HAN Ming-yue ,
  • HU Bing-wen* ,
  • YANG Guang*
Expand
  • Shanghai key Laboratory of Magnetic Resonance, Department of Physics, East China Normal University, Shanghai 200062, China
*Corresponding author:YANG Guang, Tel: 021-62233873, E-mail: gyang@phy.ecnu.edu.cn; HU Bing-wen, Tel: 021-62233633, E-mail: bwhu@phy.ecnu.edu.cn.s.

Received date: 2014-02-21

  Revised date: 2014-10-27

  Online published: 2014-12-05

Supported by

上海市科委资助项目(08DZ1900700).

Abstract

To increase the speed of acquisition of two-dimensional solid-state DQ-SQ spectrum, a compressed sensing algorithm which makes use of the self-sparsity of the spectrum to construct under-sampled data. The energy function used in optimization is l1 norm together with the finite difference term. In the finite different term, we used different weights for the horizontal and vertical finite differences. Different sampling schemes were compared and pseudo-random sampling combined with compressed sensing reconstruction was found to yield the best results. Furthermore, we found that the extreme case of
pseudo-random sampling, that is, t1-cutoff sampling may be the best choice.the best results. Furthermore, we found that the extreme case of pseudo-random sampling, that is, t1-cutoff sampling may be the best choice.

Cite this article

ZHENG Hui , HAN Ming-yue , HU Bing-wen* , YANG Guang* . Comparison of Different Sampling Schemes in Compressed Sensing Reconstruction for DQ-SQ experiments[J]. Chinese Journal of Magnetic Resonance, 2014 , 31(4) : 535 -547 . DOI: 10.11938/cjmr20140408

References

[1] Jaravine V I I, Orekhov V Y. Removal of a time barrier for high-resolution multidimensional NMR spectroscopy[J]. Nature Methods, 2006, 3(8): 605―607.

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

[3] Hu B W, Zhou P, Noda I, et al. An NMR approach applicable to biomolecular structrue characterization[J]. Anal Chem, 2005, 77(23): 7 534―7 538.

[4] Barna J C J, Laue E D, Mayger M R, et al. Exponential sampling, an alternative method for sampling in two-dimemsional NMR experiments[J]. J Magn Reson, 1987, 73(1): 69―77.

[5] Jeffrey C, Hoch A S S. Maximum entropy reconstruction, spectrum analysis and deconvolution in multidimensional nuclear magnetic resonance[J]. Method Enzymol, 2002, 338: 159―178.

[6] Kazimierczuk K, Orekhov V Y. Accelerated NMR spectroscopy by using compressed sensing[J]. Angew Chem Int Ed, 2011, 50(24): 5 556―5 559.

[7] 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.

[8] Kazimierczuk K, Kozminski W, Zhukov I. Two-dimensional Fourier transform of arbitrarily sampled NMR data sets[J]. J Magn Reson, 2006, 179(2): 323―328.

[9] Kazimierczuk K, Zawadzka A, Kozminski W, et al. Random sampling of evolution time space and fourier transform processing[J]. J Biomol NMR, 2006, 36(3): 157―168.

[10] Emmanuel J C, Justin R, Member L, et al. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information[J]. IEEE T Inf Theory, 2006, 52(2): 489―509.

[11] David L, Donoho M. Ieee Compressed Sensing[J]. IEEE T Inf Theory, 2006, 52(4): 1 289―1 306.

[12] Emmanuel C, Justin R, Tao T. Stable signal recovery from incomplete and inaccurate measurements[J]. Commun Pure Appl Math, 2006, 59(8): 1 207―1 223.

[13] 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.

[14] Qu 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.

[15] Kutyniok G. Theory and applications of compressed sensing[J]. GAMM-Mitteilungen, 2013, 36(1): 79―101.

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

[17] Liu Y P, Wan Q. Anti-sampling-distortion compressive wideband spectrum sensing for cognitive radio[J]. International Journal of Mobile Communications(IJMC), 2011, 9(6): 604―618.

[18] Yu S, Shaharyar Khwaja A, Ma J. Compressed sensing of complex-valued data[J]. Signal Process, 2012, 92(2): 357―362.

[19] Smith D S, Gore J C, Yankeelov T E, et al. Real-time compressive sensing MRI reconstruction using GPU computing and split bregman methods[J]. Int J Biomed Imaging, 2012, 2012(864827).

[20] Hu S, Lustig M, Chen A P, et al. Compressed sensing for resolution enhancement of hyperpolarized 13C flyback 3D-MRSI[J]. J Magn Reson, 2008, 192(2): 258―264.

[21] Duarte M F, Davenport M A, Takhar D, et al. Single-pixel imaging via compressive sampling[J]. IEEE Signal Process Mag, 2008, 25(2): 83―91.

[22] Li Shu-Tao(李树涛), Wei Dan(魏丹). A survey on compressive sensing[J]. Acta Automatica Sinica(自动化学报), 2009, 35(11): 1 369―1 377.

[23] Holland D J, Bostock M J, Gladden L F, et al. Fast multidimensional NMR spectroscopy using compressed sensing[J]. Angew Chem Int Ed, 2011, 50(29): 6 548―6 551.

[24] Bostock M J, Holland D J, Nietlispach D. Compressed sensing reconstruction of undersampled 3D NOESY spectra: application to large membrane proteins[J]. J Biomol NMR, 2012, 54(1): 15―32.

[25] Maciejewski M W, Qui H Z, Rujan I, et al. Nonuniform sampling and spectral aliasing[J]. J Magn Reson, 2009, 199(1): 88―93.

Outlines

/