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首页> 外文期刊>Geoscience and Remote Sensing Letters, IEEE >An Inversion of NMR Echo Data Based on a Normalized Iterative Hard Thresholding Algorithm
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An Inversion of NMR Echo Data Based on a Normalized Iterative Hard Thresholding Algorithm

机译：基于归一化迭代硬阈值算法的NMR回波数据反演

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摘要

The inversion of nuclear magnetic resonance (NMR) echo data requires solving the discrete Fredholm integral equation of the first kind, which is an ill-posed problem. In this letter, a surrogate objective function of an NMR inversion without an explicit regularization term based on least-squares fitting is introduced to avoid the process of choosing a regularization parameter, and a normalized iterative hard thresholding algorithm is proposed to solve the surrogate objective function. Furthermore, the invertedn$T_{2}$nspectra of the proposed method, the truncated singular value decomposition method, the Butler–Reeds–Dawson method, and the least-squares QR decomposition method are compared using numerical simulation examples. The results show that the proposed method is superior to the other methods because the peaks of the invertedn$T_{2}$nspectra with a shorter relaxation time are the most similar to the model at a low signal-to-noise ratio and the root-mean-square errors of the invertedn$T_{2}$nspectra are the lowest. Finally, we process the NMR experimental data of tight sandstone using the four methods and verify the effectiveness of the proposed method for solving the NMR echo data inversion problem.
机译：核磁共振（NMR）回波数据的反演需要求解第一种离散的Fredholm积分方程，这是一个不适定的问题。为了避免选择正则化参数的过程，引入了不具有基于最小二乘拟合的显式正则项的NMR反演的替代目标函数，提出了一种归一化的迭代硬阈值算法来求解该替代目标函数。 。此外，invertedn $ T_ {2} $ 使用数值模拟实例比较了所提出方法的 n谱，截断奇异值分解方法，Butler-Reeds-Dawson方法和最小二乘QR分解方法。结果表明，所提出的方法优于其他方法，因为反相n $ T_ {2} $ n光谱，松弛时间较短，在低信噪比和均方根下与模型最相似 $ T_ {2} $ 的错误 nspectra最低。最后，我们用这四种方法处理了致密砂岩的NMR实验数据，并验证了所提方法解决NMR回波数据反演问题的有效性。

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