Improvement of measurement precision in absorption spectra by apodization

In in vivo MR spectroscopy studies, it is desirable to determine metabolite peak parameters with good precision and to estimate the uncertainties. How to achieve optimal precision for an apodized MR spectrum by using a weighted least squares estimator is discussed and demonstrated. Analytic methods for calculating the uncertainties of all parameters obtained from least squares estimators are described. The time domain apodization before Fourier transformation can substantially decrease the minimum variance bound in parameters obtained from the frequency domain absorption spectrum. A weighted least squares estimation is needed to reach the Cramer-Rao lower bound. When an unweighted least squares estimation is performed, the time domain apodization also leads to improvement in precision.