TY  - EJOU
AU  - Chen, Yiguo 
AU  - Feng, Congjun 
AU  - He, Yonghong 
AU  - Chen, Zhijun 
AU  - Fan, Xiaowei 
AU  - Wang, Chao 
AU  - Ge, Xinmin 

TI  - A Novel Method to Enhance the Inversion Speed and Precision of the NMR T<sub>2</sub> Spectrum by the TSVD Based Linearized Bregman Iteration
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2023
VL  - 136
IS  - 3
SN  - 1526-1506

AB  - The low-field nuclear magnetic resonance (NMR) technique has been used to probe the pore size distribution and the fluid composition in geophysical prospecting and related fields. However, the speed and accuracy of the existing numerical inversion methods are still challenging due to the ill-posed nature of the first kind Fredholm integral equation and the contamination of the noises. This paper proposes a novel inversion algorithm to accelerate the convergence and enhance the precision using empirical truncated singular value decompositions (TSVD) and the linearized Bregman iteration. The L1 penalty term is applied to construct the objective function, and then the linearized Bregman iteration is utilized to obtain fast convergence. To reduce the complexity of the computation, empirical TSVD is proposed to compress the kernel matrix and determine the appropriate truncated position. This novel inversion method is validated using numerical simulations. The results indicate that the proposed novel method is significantly efficient and can achieve quick and effective data solutions with low signal-to-noise ratios.
KW  - Low field nuclear magnetic resonance; linearized bregman iteration; truncated singular value decomposition; numerical simulations

DO  - 10.32604/cmes.2023.021145