Trust-region algorithm for the inversion of molecular diffusion NMR data

Diffusion NMR experiments are very useful in studying structural and dynamical properties of molecules and in sorting out components from mixtures. A number of numerical approaches have been developed for the processing of diffusion NMR data. In this paper, numerical problems of the direct regularization methods such as CONTIN, MaxEnt, and the newly proposed ITAMeD approach are illustrated by analyzing simulated and experimental data. It allows us to further develop a new method to calculate the distribution of diffusion coefficients. Therefore, we present here an iterative regularization method based on the Trust-Region Algorithm for the Inversion (TRAIn) of molecular diffusion NMR data. It is demonstrated in this paper that our approach overcomes major numerical difficulties of the direct regularization methods mentioned above. Besides, this method reconstructs more reliable diffusion coefficient distributions, especially for real world samples of which the diffusion coefficients are nonsymmetrically distributed.