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

Abstract

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.

Fast and Robust 2D Inverse Laplace Transformation of Single-Molecule Fluorescence Lifetime Data

“…Regularization. An alternative approach has been developed in NMR spectroscopy based on SVD based data compression and Tikhonov regularization (28)(29)(30) . This approach differs from MEM in several ways.…”

“…Lastly, it provides a method for choosing an appropriate regularization constant scaled with the noise variance of the data. The outline of the method follows what is presented in references (28,30).…”

“…Work by L. Venkataramanan and coworkers (28) outlined an efficient algorithm for Laplace inversion in NMR relaxometry data that leveraged singular-valued decomposition (SVD) and Tikhonov regularization. Subsequent improvements of this approach have been reported (29,30) . In this paper, we adopt this general approach for application to single-molecule fluorescence spectroscopy analysis.…”

Analysis of Multicomponent Exponential Magnetic Resonance Relaxation Data: Automatable Parameterization and Interpretable Display Protocols

“…Their use accelerated following the publication of a rapid 2D Inverse Laplace Transform method (Song et al, 2002), and they are now widely applied. An incomplete list of a few of the many current research topics related to two-dimensional relaxation measurements include development of processing algorithms (Su et al, 2019) (Fricke et al, 2020), classification of food products (Greer et al, 2018), porous media characterization (Silletta et al, 2018), and investigations of biomaterials like cartilage (Mailhiot et al, 2018). There does not appear to be widespread agreement on the best methods for processing or for parameterizing the information content of 2D measurements.…”