Incorporating Bias in Multi-Penalty Regularization for Improved LF-NMR Data Inversion

Low-field nuclear magnetic resonance (LF-NMR) detection technology is widely used in the fields of petroleum, materials, etc. due to its advantages such as precision, stability, and non-destructiveness. The collected LF-NMR signal can obtain the relaxation time distribution through inversion technology, realizing sample identification and component analysis at the molecular level. Although the existing regularization method can improve the accuracy of the inversion results to a certain extent, it is not effective in dealing with the problem of data baseline offset. The baseline offset will cause the algorithm to mistakenly believe that the signal has not been completely attenuated, thereby erroneously introducing ultra-long relaxation components. In order to solve this problem, we add a bias term to the traditional regularization term. In the experimental part, we use simulated data and real LF-NMR data to test the proposed method. The results show that the regularization method with the addition of a bias term improves the accuracy of the inversion results while maintaining computational efficiency. Especially in dealing with baseline offset problems, erroneous ultra-long relaxation components can be effectively eliminated.