Maximum entropy method in nuclear magnetic resonance spectroscopy

Abstract It is shown that the maximum entropy method (MEM) is a powerful method of analyzing free induction decay data which does not introduce more structure into the resulting spectrum than is required to fit the FID. Other techniques in current use either fail to fit the data properly, or are liable to give spectra containing negative number densities, or contain structure for which there is no reliable evidence in the data. To assess MEM in practice, it has been applied to the 'H and 13C NMR spectra of 2-vinylpyridine. Compared with conventional spectra, MEM spectra show considerable suppression of the noise accompanied by significant resolution enhancement, leading to improved visual clarity. MEM is able to distinguish between real peaks arising from the sample and noise peaks of comparable intensity, without loss of resolution. This should be of considerable benefit in analyzing complex and noisy spectra, such as those of complex molecules in biological experiments.

[1]  Sibusiso Sibisi,et al.  Two-dimensional reconstructions from one-dimensional data by maximum entropy , 1983, Nature.

[2]  Rodney W. Johnson,et al.  Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy , 1980, IEEE Trans. Inf. Theory.

[3]  S. Gull,et al.  Image reconstruction from incomplete and noisy data , 1978, Nature.

[4]  J. Lindon,et al.  Digitisation and data processing in Fourier transform NMR , 1980 .

[5]  J. Skilling,et al.  Maximum entropy image reconstruction: general algorithm , 1984 .

[6]  J. Skilling,et al.  Maximum entropy theory , 1985 .

[7]  R. Brereton,et al.  The application of adjustable-parameter sine bell apodization to carbon-13 NMR spectra , 1981 .

[8]  J. Skilling,et al.  Maximum entropy signal processing in practical NMR spectroscopy , 1984, Nature.

[9]  P. Lalanne,et al.  A new scheme for resolution enhancement in fourier transform NMR , 1979 .

[10]  J. Lohman.  A new noise-reduction filter effective in resolution enhancement , 1980 .

[11]  A. J. Shaka,et al.  Separation of chemical shifts and spin coupling in proton NMR: elimination of dispersion signals from two-dimensional spectra , 1984 .

[12]  John Skilling,et al.  Image restoration by a powerful maximum entropy method , 1982, Comput. Vis. Graph. Image Process..

[13]  Christopher M. Dobson,et al.  Resolution enhancement of protein PMR spectra using the difference between a broadened and a normal spectrum , 1973 .

[14]  J. Lindon,et al.  Resolution enhancement in FT NMR through the use of a double exponential function , 1978 .

[15]  M. Guéron.  Line narrowing and line broadening using trigonometric functions , 1978 .

[16]  A. Redfield,et al.  Quadrature fourier NMR detection: Simple multiplex for dual detection and discussion , 1975 .

[17]  K. Wüthrich,et al.  Digital filtering with a sinusoidal window function: An alternative technique for resolution enhancement in FT NMR , 1976 .