A novel detection-estimation scheme for noisy NMR signals: Applications to delayed acquisition data

Many potentially interesting and useful classes of NMR experiments generate data for which conventional spectral estimation and quantification aa the Fourier transform are unsatisfactory. In particular, recently introduced solid-state NMR experiments which involve long delays before data acquisition fall into this category, as the free induction decays are heavily ''truncated'' and have low signal-to-noise ratios. A novel detection-estimation scheme is introduced in order to analyze data from such experiments and others where the sensitivity is low and/or the data record is strongly damped or truncated, Based on the assumption of exponential data modeling, the number of signals present is first detected using criteria derived from information theory and the spectral parameters are then estimated using the matrix pencil method, Monte Carlo simulations and experimental. applications are carried out to demonstrate its superior statistical and computational performances and its general applicability to delayed acquisition data. Over the range of note levels investigated, it is found that this approach is essentially near-optimal in the sense that the estimated spectral parameters have biases almost equal to zero and variances very close to their theoretical Cramer-Rao lower bounds. Compared to the popular method of linear prediction with singular value decomposition, this method not only improves the estimation accuracy (by a factor of 2-4) with a lower ''break-down'' signal-to-noise threshold (approximate to 1.5 dB), but also reduces the computational cost by about an order of magnitude, It also holds great promise in effectively reducing truncation artifacts. It is concluded that this approach not only facilitates the analysis of delayed acquisition data, but can also become a valuable tool in the routine quantification of general NMR spectra, ia listing of programs is also included in the Appendix. (C) 1997 Academic Press.