A Signal-Enhancement Algorithm for the Quantification of NMR Data in the Time Domain

Abstract

A new enhancement algorithm is presented for cleaning up NMR data before estimating signal parameters using a subspace-based method. The proposed algorithm is based on the minimum variance estimation method, which starts from a very rectangular (instead of a square) Hankel structured data matrix in order to make the corresponding signal-only data matrix orthogonal to the noise, then computes an estimate of the signal-only data matrix, and finally restores the Hankel structure of the computed estimate. This algorithm has remarkable practical advantages over Cadzow′s and nonenhanced algorithms in both resolution performance and computational efficiency that make it well suited to the quantitative time-domain analysis of NMR measurement data. The convergence of the enhancement procedure is found to be redundant when followed by an SVD-based estimator such as HTLS, offering drastic reduction in the computational cost. Extensive computer simulations on NMR signals with overlapping peaks have been carried out to evaluate the new algorithm after one iteration, its convergence, and its combination with Cadzow′s method. The enhancement algorithms are applied to the parameter estimation of real-world NMR measurement data as well. In particular, the newly proposed algorithm is recommended for estimating the parameters of overlapping peaks when the signal-to-noise ratio is low and prior knowledge is hardly available.