Nishiyama K, Mita T
IEEE Trans Biomed Eng. 1989 Feb;36(2):222-31. doi: 10.1109/10.16469.
When the DFT (discrete Fourier transform) is used as a method for obtaining NMR (nuclear magnetic resonance) spectrum, resolution of the obtained NMR spectrum depends clearly on spin-spin relaxation times of the nucleus and the sampled number of NMR signal. That is, the NMR spectrum is affected by decay of NMR signal due to the relaxation times and errors associated with discrete approximation of NMR spectrum. As a results, its resolution is degraded and the spectrum disagrees with the density distribution of the nucleus. In the present paper, we propose a new NMR spectrum estimation method for reducing their effects, demonstrating a high resolution NMR spectrum which is closer to the density distribution than that of the DFT. The proposed method is derived from applying the Kalman filter or the recursive least-square method to a NMR signal model based on Bloch equation. Under various conditions, the proposed method is compared with the DFT using a proton 1H NMR signal observed from mayonnaise in a 2 [T] static magnetic field. The results show that if spin-spin relaxation times are known previously, the proposed method can provide a higher resolution NMR spectrum than the DFT. In addition, it is shown that the method can reduce the discrete approximation errors of NMR spectrum. Finally, we demonstrate that if frequency components of sources of NMR signal are present in a limited range in frequency domain of interest, the method can magnify NMR spectrum with a sampling time and interval fixed.
当离散傅里叶变换（DFT）用作获取核磁共振（NMR）谱的方法时，所获得的NMR谱的分辨率明显取决于原子核的自旋 - 自旋弛豫时间以及NMR信号的采样数量。也就是说，NMR谱会受到由于弛豫时间导致的NMR信号衰减以及与NMR谱离散近似相关的误差的影响。结果，其分辨率会降低，并且谱与原子核的密度分布不一致。在本文中，我们提出了一种新的NMR谱估计方法以减少这些影响，展示了一种比DFT更接近密度分布的高分辨率NMR谱。所提出的方法是通过将卡尔曼滤波器或递归最小二乘法应用于基于布洛赫方程的NMR信号模型而推导出来的。在各种条件下，使用在2 [T]静磁场中从蛋黄酱观察到的质子1H NMR信号，将所提出的方法与DFT进行比较。结果表明，如果事先知道自旋 - 自旋弛豫时间，所提出的方法可以提供比DFT更高分辨率的NMR谱。此外，结果表明该方法可以减少NMR谱的离散近似误差。最后，我们证明如果NMR信号源的频率分量存在于感兴趣的频域中的有限范围内，该方法可以在采样时间和间隔固定的情况下放大NMR谱。
