The C-13-1 NMR peak in proton-decoupled spectra of liver glycogen solution was quantitatively analyzed by three types of model-function fitting algorithms: iterative line-fitting in the frequency domain (MDCON); iterative least-squares fitting (VARPRO) in the time domain; and noniterative singular value decomposition-based analysis (HTLS), also in the time domain, Quantification results were compared with manual integration values, Performance of the algorithms was tested at different signal-to-noise ratios (S/N) of the glycogen C-1 peak, This was achieved by varying the number of scans summed prior to analysis, Since T-2 relaxation in glycogen has been shown to be multiexponential [Overloop, K. et al. Magn, Reson. Med. 36, 45-51 (1996], the exact quantification of the C-1 glycogen signal requires a model function comprising a sum of Lorentzian components, each with a different broadening at the glycogen frequency, This paper focuses on the performances of the above methods to fit such a multicomponent resonance line, In the frequency domain, line fitting with two Lorentz lines gives good results at sufficiently high S/N, In the time domain, VARPRO performs better than HTLS because fixed values can be imposed to the linewidth of the components at the common C-1 frequency, thereby reducing convergence problems at low S/N. (C) 1997 by John Wiley & Sons, Ltd.

Many parameter-estimation algorithms have been developed for the accurate quantification of NMR data modeled as a sum ofKexponentially damped sinusoids. Some well-known time-domain techniques based on subspace estimation and the singular value decomposition are Kumaresan and Tuft's linear prediction method and Kunget al.’s method based on state–space modeling, etc. All these methods do not use prior knowledge, except the formulation of the data model and the model order estimateK. The best accuracy is obtained with a variant of Kung's method, called HTLS, using the total least-squares principle. In this paper, the HTLS method is extended to the HTLS-PK method, which has the capability to accommodate prior knowledge of some known signal poles. Simulated and real-world NMR signals are processed using the HTLS and HTLS-PK methods to demonstrate the advantage of the new method.

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.

This paper shows how the total-least-squares method improves the signal parameter estimates of HSVD, a noniterative black-box method for time-domain NMR data quantification. The algorithm, called HTLS, is presented and discussed. Experiments, performed on simulated and in vivo NMR signals, show the benefits in parameter accuracy that can be obtained from the use of total least squares as compared to ordinary least squares. In particular, the damping factor estimates of spectral components at low signal-to-noise ratios improve substantially, thereby also improving the accuracy of the amplitudes and phases.

A time series of 16 31P NMR spectra of rat liver perfused with 2,5-anhydro-D-mannitol has been quantitatively analyzed by two types of model function fitting algorithms in the time domain: an iterative least-squares fitting procedure (VARPRO) and a noniterative singular-value-decomposition-based method, combined with minimum-variance preprocessing (MV-HTLS). MV-HTLS, which does not allow the incorporation of prior knowledge, is unreliable for the quantification of overlapping peaks at low signal-to-noise ratio. Although the overall fit is good, i.e., the residue is small, the fitted parameters do not accurately represent the individual components. The incorporation of prior knowledge about the model parameters results in a significant gain in precision of VARPRO.