低场核磁共振扩散-横向弛豫二维反演算法

An Improved Two-Dimensional Inversion Algorithm for Low-Field NMR Diffusion-Transverse Relaxation Correlation Data

针对低场核磁共振一维反演中无法分辨一维谱中重叠组分和目前报道的扩散-横向弛豫二维反演算法计算量大、计算耗时长的问题,提出了一种计算量小、计算效率高、耗时短的扩散-横向弛豫二维反演算法.首先对扩散系数D和横向弛豫时间T2进行布点;其次根据信号采集条件计算出两个核心矩阵,并分别进行奇异值分解;然后,由所采集信号计算出两个核心矩阵的奇异值截断值,分别对两个核心矩阵的奇异值矩阵进行截断并求其逆矩阵;最后计算出初始反演结果,并添加非负约束经过多次迭代得到最终反演结果.实验结果证明,提出的扩散-横向弛豫二维反演算法在不影响反演结果准确性的基础上,能极大提高计算效率.

NMR spectra acquired at low field often show severe signal overlap. Under such circumstance, two-dimensional （2D） diffusion-transverse relaxation （D-T2） correlation data are useful to differentiate signals from different components in the sample. The currently available inversion algorithms for D-T2 correlation data are time- and memory-consuming. To overcome this problem, we developed an improved 2D D-T2 inversion algorithm, which is more effective and consumes less memory and time than the traditional inversion algorithms. In brief, the logarithm values of discrete diffusion coefficient and transverse relaxation time were first obtained and used to construct two core matrices according to the signal collection conditions. Singular value decomposition was then carried out for the two matrices, followed by application of a cutoff value to remove negligible values. The inverse matrices of the thresholded core matrices were calculated and used to derive the initial inversion result. Finally, the initial inversion results were iterated with non-negative constraints to derived the final inversion results.