Improved Butler–Reeds–Dawson Algorithm for the Inversion of Two-Dimensional NMR Relaxometry Data

Two-dimensional (2D) NMR relaxometry has been widely used as a powerful new tool for identifying and characterizing molecular dynamics. Various inversion algorithms have been introduced to obtain the versatile relaxation information conveyed by spectra. The inversion procedure is especially challenging because the relevant data are huge in 2D cases and the inversion problem is ill-posed. Here, we propose a new method to process the 2D NMR relaxometry data. Our approach varies from Tikhonov regularization, known previously in CONTIN and Maximum Entropy (MaxEnt) methods, which need additional efforts to compute an appropriate regularization factor. This variety improves Butler–Reeds–Dawson algorithm to optimize the Tikhonov regularization problem and the regularization factor is calculated alongside. The calculation is considerably faster than the mentioned algorithms. The proposed method is compared with some widely used methods on simulated datasets, regarding algorithm efficiency and noise vulnerability. Also, the result of the experimental data is presented to test the practical utility of the proposed algorithm. The results suggest that our approach is efficient and robust. It can meet different application requirements.