基于迭代TSVD的NMR二维谱反演算法

An Iterative Truncated Singular Value Decomposition(TSVD)-Based Inversion Methods for 2D NMR

针对现有基于TSVD的二维反演算法中截断位置判断不准确、容易产生虚假峰等问题,提出了一种改进的方法.首先,通过逐步求精的方法对L曲线上的拐角位置进行定位,得到迭代的最大截断位置;然后,根据反演核奇异值的集中程度获取迭代的最小截断位置;最后,在给定的截断位置范围内从小到大进行TSVD,每次迭代都以上一次迭代的结果为依据.对仿真数据和实验数据的反演结果表明,该算法都能够得到比较好的二维反演效果.与现有基于TSVD的方法相比,该算法具有更高的鲁棒性,能够得到更清晰的二维谱,可满足实际应用需求.

Truncated singular value decomposition （TSVD）-based methods are often used for two-dimensional inversion,but can suffer from drawbacks such as failure to locate an appropriate truncating position,sensitivity to noise,and generation of artificial signals.In this paper,we proposed an improved TSVD-based inversion method for 2D NMR.First,an accurate locating method using a progressive refinement regional searching algorithm was employed to find the largest preserving number of singular values.Then we calculated the minimum preserving number according to the clustering level of singular values.Lastly,an iterative TSVD method was implemented.The results on simulated and actual data set were reported.Compared with the existing TSVD-based methods,the proposed iterative TSVD method was shown to be more robust,and capable of producing spectra with higher resolution.