一种面向核磁共振短弛豫弱信号的反演方法

Inversion method for NMR weak signals with short relaxation time

针对具有短弛豫分量的核磁共振弱信号的反演难题,提出了一种适用于低信噪比核磁共振弛豫信号的反演方法,通过结合SVD方法和Tikhonov方法,选择更加合适的滤波因子进行反演.与现有的反演方法相比,该方法获得的弛豫时间分布图谱更接近于核磁共振模拟信号的原始谱,尤其是信号较弱时的短弛豫分量.通过计算反演结果的不确定度,证明了该方法在不同信噪比下的可靠性.此外,通过实验测量和多弛豫分量样品的反演分析,表明该方法能够获得精确的弛豫时间.最后,将该方法应用于水泥水化过程核磁共振弛豫信号的分析,通过对短弛豫弱信号的有效辨识,准确发现了水泥水化过程中各组分的变化规律.证明了该方法能够有效分辨弛豫时间较短的核磁共振弱信号,对寻找样品关键成分和表征其物理性质具有重要作用,从而促进了核磁共振弛豫技术的应用.

An improved inversion method for nuclear magnetic resonance(NMR)relaxation signals with a low signal-to-noise ratio(SNR)is proposed to solve the inversion problem of weak NMR signals with short relaxation components.This method selects a suitable filter factor for inversion by combining the singular-value decomposition and Tikhonov methods.Compared with existing inversion methods,the relaxation-time spectrum based on the proposed method is closer to the original spectrum of the NMR simulation signal,especially in short relaxation components when the signal is weak.The reliability of the proposed method under different SNRs was proven by calculating the uncertainty of the solutions.The ability to obtain precise relaxation times was proven by experimental measurement and inversion analysis of samples with multiple relaxation components.The changing pattern of the components in a cement-hydration process found by identifying the weak signal with short relaxation components was validated.In conclusion,the proposed inversion method can effectively distinguish a weak NMR signal with short relaxation times,which plays an important role in determining the key components of a sample and in characterizing its physical properties,thus promoting the application of NMR relaxation technology.