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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]

As in the case of NMR-CT, it is some- times required that an image with a high resolution is obtained from the limited number of data because of the long data acquisition time due to the spin-lattice relaxation time. This paper attempts to cope with such a requirement, and proposes a reconstruction method for NMR image with improved resolution from a limited number of data. The proposed image reconstruction method first models the observed signal sequence by a multidimensional complex stochastic system with a matrix state probability variable. Then the state probability variable is estimated using a complex Kalman filter. To demonstrate the usefulness of the proposed method, an image is reconstructed from 128 × 128 data acquired from the cross section of the human head using NMR-CT of 0.1 [T]. The result is compared with the NMR image reconstructed by the traditional two-dimensional discrete-Fourier transform. It is shown as a result that the proposed method not only improves the image resolution but also emphasizes the edge of the image and realizes an enlargement of the image. Furthermore, it is shown that an image emphasizing the contrast due to the spin-spin relaxation time can be obtained. [ABSTRACT FROM AUTHOR]