基于奇异值分解的核磁共振T_2谱反演研究

Study on T_2 Spectrum Inversion of Nuclear Magnetic Resonance based on Singular Value Decomposition

在介绍奇异值分解的基本原理基础上,实现了基于奇异值分解的核磁共振T2谱反演。给出了T2谱反演的线性方程组,并利用奇异值分解法求解该线性方程组的解。此SVD法能够获得连续性较好的反演T2谱,算法较稳定,收敛性好,非负约束条件容易实现。反演T2谱与构造T2谱吻合性较高。且由NMR实验室反演效果可知,该方法可以应用于实验室岩心的T2谱反演。

Based on the fundamentals of singular value decomposition, the thesis accomplished T2 spectrum inversion of NMR. Gave linear equations of T2 Spectrum Inversion, and solved it with singular value decomposition. The SVD will obtain better continuity of T2 spectrum inversion. The algorithm is stable and easy to realize the condition of nonnegative constraints with good convergence. Inverse T2 spectrum is well coincide with construct T2 spectrum. The inversion results from NMR laboratory data indicated that this method can be applied to T2 spectrum inversion of laboratory core.