A Rapid NMR T 2 Inversion Method Based on Norm Smoothing

Norm smoothing is commonly used in nuclear magnetic resonance (NMR) T 2 inversion and the choice of a suitable regularization parameter is a key step for obtaining a satisfactory inversion result, which is usually achieved by repeating T 2 inversion multiple times. However, a greater number of inversions result in a slower speed for the inversion process. In this paper, we propose a rapid norm smoothing T 2 inversion method achieved using a new selection method for the regularization parameter. First, the singular value decomposition (SVD) method is used to calculate singular values of the kernel matrix to compress the echo train data. Subsequently, a suitable regularization parameter is calculated based on the signal-to-noise ratio (SNR) of the echo train and the maximum singular value of the kernel matrix, which avoids the repetitions of the T 2 inversion. Finally, a rapid T 2 inversion is obtained using the Butler–Reeds–Dawson (BRD) method. Numerical simulation and logging data inversion results show that the new method can rapidly provide reasonable T 2 spectra for data with different SNRs and is insensitive to the amount of the compressed data.