核磁共振T2谱奇异值分解反演改进算法

Improved algorithm for singular value decomposition inversion of T2 spectrum in nuclear magnetic resonance

介绍了核磁共振T2谱传统奇异值分解(SVD)反演算法,从向量空间的角度对算法进行了分析,提出了一种新的实现非负约束的迭代方案,并根据这个方案改进了传统的SVD反演算法。数值模拟实验和实际应用表明,改进的SVD反演算法具有解算速度快和T2谱分布连续等优点,解决了传统SVD反演算法在实际应用中存在的计算量大和T2谱分布不连续的问题,可以满足核磁共振岩心分析和核磁共振测井工作的需求。

The nonnegative constraint inversion problem of nuclear magnetic resonance （NMR） was analyzed by the multi-exponential model. The common ways of singular value decomposition （SVD） algorithm is to reduce the coefficient matrix and diminish the negative components iteratively. Such procedure may result in a large amount of computation and discontinuity of T2 spectrum. The common SVD algorithm was briefly discussed and analyzed on the basis of vector space, and a new iterative scheme was proposed to a- chieve the nonnegative constraint. Based on this scheme, the SVD inversion algorithm was improved. The numerical simulations and laboratory application indicated that the improved SVD algorithm could reduce the amount of computation greatly and keep the continuity of T2 spectrum. This algorithm overcomes the faults of the common SVD algorithm and can be applicable in NMR core analysis and NMR logging.