Two-dimensional NMR inversion based on fast norm smoothing method

Abstract

Two-dimensional (2D) nuclear magnetic resonance (NMR) inversion operates with massive echo train data and is an ill-posed problem. It is very important to select a suitable inversion method for the 2D NMR data processing. In this study, we propose a fast, robust, and effective method for 2D NMR inversion that improves the computational efficiency of the inversion process by avoiding estimation of some unneeded regularization parameters. Firstly, a method that combines window averaging (WA) and singular value decomposition (SVD) is used to compress the echo train data and obtain the singular values of the kernel matrix. Subsequently, an optimum regularization parameter in a fast manner using the signal-to-noise ratio (SNR) of the echo train data and the maximum singular value of the kernel matrix are determined. Finally, we use the Butler-Reeds-Dawson (BRD) method and the selected optimum regularization parameter to invert the compressed data to achieve a fast 2D NMR inversion. The numerical simulation results indicate that the proposed method not only achieves satisfactory 2D NMR spectra rapidly from the echo train data of different SNRs but also is insensitive to the number of the final compressed data points.