平滑的
稳健性(进化)
算法
放松(心理学)
谱线
计算机科学
低分辨率
数学优化
残余物
数学
应用数学
生物系统
化学
物理
高分辨率
统计
天文
地质学
心理学
社会心理学
生物化学
遥感
生物
基因
作者
Sihui Luo,Lizhi Xiao,Jiangfeng Guo,Yan Jin,Xiaobo Qu,Zhangren Tu,Gang Luo,Can Liang
标识
DOI:10.1016/j.petsci.2022.10.020
摘要
In this paper, we proposed a novel method for low-field nuclear magnetic resonance (NMR) inversion based on low-rank and sparsity restraint (LRSR) of relaxation spectra, with which high quality construction is made possible for one- and two-dimensional low-field and low signal to noise ratio NMR data. In this method, the low-rank and sparsity restraints are introduced into the objective function instead of the smoothing term. The low-rank features in relaxation spectra are extracted to ensure the local characteristics and morphology of spectra. The sparsity and residual term are contributed to the resolution and precision of spectra, with the elimination of the redundant relaxation components. Optimization process of the objective function is designed with alternating direction method of multiples, in which the objective function is decomposed into three subproblems to be independently solved. The optimum solution can be obtained by alternating iteration and updating process. At first, numerical simulations are conducted on synthetic echo data with different signal-to-noise ratios, to optimize the desirable regularization parameters and verify the feasibility and effectiveness of proposed method. Then, NMR experiments on solutions and artificial sandstone samples are conducted and analyzed, which validates the robustness and reliability of the proposed method. The results from simulations and experiments have demonstrated that the suggested method has unique advantages for improving the resolution of relaxation spectra and enhancing the ability of fluid quantitative identification.
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