Spectral fitting of NMR spectra using an alternating optimization method with a priori knowledge

As alternatives to the fast Fourier transform, advanced parametric methods based on the damped sinusoidal data model have been devised to better quantify the nuclear magnetic resonance (NMR) spectroscopy time-domain data. Previously, linear prediction (LP) fitting methods using Householder triangularization and singular value decomposition (SVD) techniques have been applied to the NMR spectroscopy data analysis. In this paper, we propose an alternating optimization method to quantify the time-domain NMR spectroscopy data. The proposed algorithm uses the a priori knowledge of the possible frequency intervals of the damped sinusoids to obtain more accurate parameter estimates when the NMR spectroscopy data are obtained under low signal-to-noise ratio conditions and the peaks are close together. None of the LP and SVD type of methods can use such approximate a priori knowledge. We have shown with measured NMR spectroscopy data that the proposed algorithm can be used to obtain accurate parameter estimates of frequencies, amplitudes, and damping ratios of the damped sinusoids and therefore the ultimate fit of the spectrum by using the a priori knowledge about the possible frequency intervals of the damped sinusoids.