DE-PAKE-ING OF NMR POWDER SPECTRA BY NONNEGATIVE LEAST-SQUARES ANALYSIS WITH TIKHONOV REGULARIZATION

A new de-Pake-ing method is presented to calculate NMR spectra of oriented samples from the NMR spectra of the corresponding powder samples. This task involves the numerical solution of a Fredholm integral equation of the first kind, i.e., a strongly ill-posed problem. The Tikhonov regularization technique has been proved to be a powerful method for the treatment of such integral equations. For the first time, this technique is applied to the de-Pake-ing procedure. The improvement concerning stability and reliability of the new de-Pake-ing algorithm in comparison with the already known methods is demonstrated. Furthermore, a new technique to consider additional orientation-independent line broadening in the de-Pake-ing procedure is introduced. (C) 1995 Academic Press, Inc.