Global Least-Squares Analysis of Large, Correlated Spectral Data Sets:  Application to Component-Resolved FT-PGSE NMR Spectroscopy

A new data processing mode for Fourier Transform Pulsed-Gradient Spin-Echo (FT-PGSE) data sets is described. Unlike conventional analysis methods, it uses all of the significant spectral information of a data set of typically 16 or 32 different magnetic field gradient settings for 10−1000 significant frequency channels out of a 1−16K FT-PGSE data set. The procedure is based on a global least-squares minimization approach at two levels:  an upper level that optimizes the actual global self-diffusion coefficient data and a lower one that optimizes the amplitude(s) of the component(s) for a particular frequency channel. This approach relies on the intrinsic property of FT-PGSE data sets in that the whole bandshape of a particular component attenuates by exactly the same relative amount upon incrementing the field gradient pulse parameters (Stilbs, P. Anal. Chem. 1981, 53, 2135 which was also shown to provide a pathway for separating the spin-echo bandshapes of the constituents of multicomponent systems. As a...