一种基于预处理迭代算法的核磁共振T2谱反演

A Preconditioned Iterative Algorithm For Inversing T2 Spectrum of NMR

在求解病态线性方程组时,数值解通常存在不稳定和误差过大等问题,尤其在系数矩阵和右端向量存在扰动时更是如此。针对上述问题,首先设计一个预条件对角阵,叠加在病态方程组上,并推导出一个简单迭代公式。为了确保迭代算法的有效性,对迭该代公式的收敛性进行了证明。最后,分别以希尔伯特病态线性方程组和实验室岩心数据构建的T2谱反演模型为测试实例,对预处理迭代算法进行了验证。实验结果表明,该算法对严重病态线性方程组的求解是有效的。

When an ill-conditioned linear equations is solved,the numerical solutions usually have some problems such as instability and excessive error,espicially there being a disturbance in the coefficient matrix and the right end vector.For the above problems,a preconditioned diagonal matrix is designed,which is superimposed on the original ill-conditioned linear equations,and a simple iteration formula is derived.In order to ensure the validity of the iterative algorithm,the convergence of the iterative formula is proved.Finally,taking Hilbert ill-conditioned linear equations and T2 spectrum inversion model which built by core data in laboratory for test cases,effectiveness of the preconditoned iterative algorithm is verified.Experimental results show that the proposed algorithm is effective for addressing badly ill-conditioned linear equations.