An Inversion of NMR Echo Data Based on a Normalized Iterative Hard Thresholding Algorithm - Guo, Jiangfeng; Xie, Ranhong (IEEE geoscience and remote sensing letters, 2018)
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 inverted T_{2} spectra 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 inverted T_{2} spectra 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 inverted T_{2} spectra 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.