A Novel Method to Enhance the Inversion Speed and Precision of the NMR T2 Spectrum by the TSVD Based Linearized Bregman Iteration

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