低场核磁共振二维谱反演技术应用研究

目的：二维相关谱是低场核磁共振时域分析技术中最为前沿的技术之一。从一维向三维推进也是低场核磁共振设备发展的必然趋势。但是从采样数据中反演得到二维谱的问题是一个典型的病态问题．求解存在很多困难。首先二维反演需要处理的数据规模非常大，其次问题本身具有很大的条件数。会因极小的采样误差引起反演结果的巨大变化。为了稳定求解低场核磁共振二维谱，提出了一种全新的通用反演算法框架。方法：首先从采样数据中分离出噪声并对其进行估计，然后进行数据压缩使在普通计算机上进行处理成为，接着对原始问题进行正则化处理．最后通过变量替换的方式转化为无约束的凸规划进行求解，求解以Newton法等迭代寻优的方式进行。结果：通过将这种二维反演框架应用到造影剂浓度选择、种子含油率测定、食用明胶与工业明胶鉴别等不同行业的不同实验中．取得了与经验信息一致的结果，验证了该二维反演算法的可靠性和实用性。结论：低场核磁共振二维谱反演技术能够满足不同领域中的组分区分和定量分析的要求，是一种可靠的新工具。

Research on the Applications of Two Dimensional NMR Relaxometry Technology in Low Field

Objective： Two dimensional correlations is one of the most advanced techniques in the field of time-domain Nuclear Magnetic Resonance （NMR） analysis. And giving information of more dimensional is an inevitablo trend of development of NMR equipment. But it is a typical ill-posed problem to inverting spectrum from sampling data. Firstly, the scale of the data is too large for ordinary computers to handle. Secondly, a small change in sampling will cause a giant distortion in spectrum. In order to solve the two dimensional NMR inversion problem stably, a new inverting algorithm for general use is proposed. Methods： The proposal method consists of some main steps： Firstly, the noises are isolated from measurements and the noise level is estimated. Secondly, data compressing is implemented to make it small enough for ordinary computers. Then the primary problem is regularized. Next, a proper latent variable is involved to transform the original constrained optimization problem to an unconstrained convex one. At last, the convex optimization problem is solved iteratively. Results： The inversion method was applied to various experimental data. These experiments consist of searching an optimal concentration of metal ion doped contrast agents, measuring of oils in seeds and distinguishing between edible and industrial gelatins. The results showed its practicality and reliability. Conclusions： In Conclusion, the proposed method gives a new approach to exactly quantitative analysis and it could meet the needs of different applications.