Super-Resolution NMR Spectrum Estimation Method.

Several methods have been proposed to determine a high-resolution NNR spectrum from limited data. This paper attempts to improve and extend the NMR spectrum estimation method using a complex Kalman filter, which was pro- posed previously by Nishlyama and Mita. In the proposed NMR spectrum estimation using the Kalman filter, extra data were required in addition to that to be used in the spectrum estimation, in the approximate determination of the spin-spin relaxation time. Hence, the previously reported NMR spectrum estimation is not based strictly on the same condition as that of the discrete Fourier transform. This paper improves this point, and the extra data are obtained by extrapolation by the AR model. This makes it possible to compare the method with the discrete Fourier transform based on the same number of data. It is shown that when the spectrum is limited to a certain frequency band, the proposed method gives an NMR spectrum with twice higher frequency resolution by reducing the effect of the spin-spin relaxation time and the effect of discrete approximation. In the proposed method, the spin-spin relaxation time of the nucleus, corresponding to the frequency resolution that is twice higher than usual, is determined by a linear interpolation of the spin-spin (relaxation time which is obtained approximately by discrete Fourier transform. [ABSTRACT FROM AUTHOR]