Algebraic Reconstruction Technique for Diffusion NMR Experiments. Application to the Molecular Weight Prediction of Polymers

Most of the algorithms employed in diffusion NMR are optimization methods based on diverse regularized methods such as Tikhonov's, which decomposes the multiexponential detected signal attenuation as a sum of mono exponential signals. Our approach uses projections over hyperplanes of the Hilbert space using a Laplace transform kernel, which is a special case of projection onto convex sets. This new application of an algebraic reconstruction technique for diffusion NMR experiments (dART) has been applied for the first time in both simulated and real systems, and then compared with established methods such as ITAMeD and TRAIn. The new algorithm provides excellent results in systems with overlapped signals and more importantly performs more rapidly than any other one assayed. One of the main advantages is that the reported method does not need a regularization parameter, which allows one to explore the largest spaces. In addition, we have provided the calibration curve for weight-average M-w prediction of poly(propylene) polymers with no dependence on the solvent used.