Formalism for hypercomplex multidimensional NMR employing partial-component subsampling

Journal of Magnetic Resonance

Volumn 227, Issue , 2013, Pages 20-24

  Schuyler, Adam D ^a   MacIejewski, Mark W ^a   Stern, Alan S ^b   Hoch, Jeffrey C ^a  

^a UNIVERSITY OF CONNECTICUT HEALTH CENTER   (United States)

^b HARVARD UNIVERSITY   (United States)

Author keywords

Aliasing; Compressed sensing; Convolution; Discrete Fourier transform (DFT); Point spread function (PSF)

Indexed keywords

ALIASING; COMPRESSIVE SENSING; DATA POINTS; DATA SETS; HYPERCOMPLEX NUMBER; MULTIDIMENSIONAL NMR; NONUNIFORM SAMPLING; ONE DIMENSION; PHASE-SENSITIVE DETECTION; POINT-SPREAD FUNCTION; POINT-SPREAD FUNCTIONS; SAMPLED DATA;

DISCRETE FOURIER TRANSFORMS; NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY;

CONVOLUTION;

ALGORITHM; ARTICLE; METHODOLOGY; NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY; SAMPLE SIZE; SIGNAL PROCESSING;

ALGORITHMS; MAGNETIC RESONANCE SPECTROSCOPY; SAMPLE SIZE; SIGNAL PROCESSING, COMPUTER-ASSISTED;

EID: 84870779499     PISSN: 10907807     EISSN: 10960856     Source Type: Journal    
DOI: 10.1016/j.jmr.2012.11.019     Document Type: Article

References (24)

1. I.I. Rabi, J.R. Zacharias, S. Millman, and P. Kusch A new method of measuring nuclear magnetic moment Physical Review 53 1938 318
2. F. Bloch Nuclear induction Physical Review 70 7-8 1946 460 474
3. F. Bloch, W.W. Hansen, and M. Packard The nuclear induction experiment Physical Review 70 7-8 1946 474 485
4. E.M. Purcell, H.C. Torrey, and R.V. Pound Resonance absorption by nuclear magnetic moments in a solid Physical Review 69 1-2 1946 37 38
5. R.R. Ernst, and W.A. Anderson Application of Fourier transform spectroscopy to magnetic resonance Review of Scientific Instruments 37 1 1966 93 102
6. Luciano Müller, Anil Kumar, and R.R. Ernst Two-dimensional carbon-13 NMR spectroscopy Journal of Chemical Physics 63 1975 5490 5491
7. Geoffrey Bodenhausen, and R.R. Ernst The accordion experiment, a simple approach to three-dimensional NMR spectroscopy Journal of Magnetic Resonance 45 1981 367 373
8. Jennifer C.J. Barna, Ernest D. Laue, Michael R. Mayger, John Skilling, and Simon J.P. Worrall Reconstruction of phase-sensitive two-dimensional nuclear-magnetic resonance spectra using maximum entropy Biochemical Society Transactions 14 1986 1262 1263
9. D.J. States, R.A. Haberkorn, and D.J. Ruben A two-dimensional nuclear Overhauser experiment with pure absorption phase in four quadrants Journal of Magnetic Resonance (1969) 48 2 1982 286 292
10. Marc A. Delsuc Spectral representation of 2D NMR spectra by hypercomplex numbers Journal of Magnetic Resonance (1969) 77 1 1988 119 124
11. Mark W. Maciejewski, Mehdi Mobli, Adam D. Schuyler, Alan S. Stern, and Jeffrey C. Hoch Data sampling in multidimensional NMR: fundamentals and strategies Topics in Current Chemistry 316 2012 49 78
12. Brian E. Coggins, and Pei Zhou Sampling of the NMR time domain along concentric rings Journal of Magnetic Resonance 184 2 2007 207 221
13. Sven G. Hyberts, Koh Takeuchi, and Gerhard Wagner Poisson-gap sampling and forward maximum entropy reconstruction for enhancing the resolution and sensitivity of protein NMR data Journal of the American Chemical Society 132 7 2010 2145 2147
14. Adam D. Schuyler, Mark W. Maciejewski, Haribabu Arthanari, and Jeffrey C. Hoch Knowledge-based nonuniform sampling in multidimensional NMR Journal of Biomolecular NMR 50 3 2011 247 262
15. David Rovnyak, Mark Sarcone, and Ze Jiang Sensitivity enhancement for maximally resolved two-dimensional NMR by nonuniform sampling Magnetic Resonance in Chemistry 49 8 2011 483 491
16. J.C. Hoch, and A.S. Stern Maximum entropy reconstruction, spectrum analysis and deconvolution in multidimensional nuclear magnetic resonance Methods in Enzymology 338 2001 159 178
17. Alan S. Stern, Kuo-Bin Li, and Jeffrey C. Hoch Modern spectrum analysis in multidimensional NMR spectroscopy: comparison of linear-prediction extrapolation and maximum-entropy reconstruction Journal of the American Chemical Society 124 9 2002 1982 1993
18. Seho Kim, and Thomas Szyperski GFT NMR, a new approach to rapidly obtain precise high-dimensional NMR spectral information Journal of the American Chemical Society 125 5 2003 1385 1393
19. Ēriks Kupče, and Ray Freeman Projection-reconstruction of three-dimensional NMR spectra Journal of the American Chemical Society 125 46 2003 13958 13959
20. Mark W. Maciejewski, Matthew Fenwick, Adam D. Schuyler, Alan S. Stern, Vitaliy Gorbatyuk, and Jeffrey C. Hoch Random phase detection in multidimensional NMR Proceedings of the National Academy of Sciences of the United States of America 108 40 2011 16640 16644
21. Todd Anthony Ell Quaternion-Fourier transforms for analysis of two-dimensional linear time-invariant partial differential systems Proceedings of the 32nd IEEE Conference on Decision and Control 2 1993 1830 1841
22. Todd A. Ell, and Stephen J. Sangwine Hypercomplex Fourier transforms of color images IEEE Transactions on Image Processing 16 1 2007 22 35
23. Stephen J. Sangwine, Todd A. Ell, Complex and Hypercomplex Discrete Fourier Transforms Based on Matrix Exponential form of Euler's Formula, 2010, arXiv:1001.4379.
24. Michael Lustig, David Donoho, and John M. Pauly Sparse MRI: the application of compressed sensing for rapid MR imaging Magnetic Resonance in Medicine 58 6 2007 1182 1195