Fourier-transform analysis of radiopharmaceutical data

A modification of a method of Gardner, which employs Fourier-transform techniques, is used to obtain initial estimates for the number of terms and values of the parameters for data which are represented by a sum of exponential terms. New experimental methods have increased both the amount and accuracy of data from radiopharmaceutical experiments. This in turn allows one to devise specific numerical methods that utilize the better data. The inherent difficulties of fitting exponentials to data, which is an ill-posed problem, cannot be overcome by any method. However, we show that the present accuracy of Fourier methods may be extended by our numerical methods applied to the improved data sets. In many cases the method yields accurate estimates for the parameters; these estimates then are to be used as initial estimates for a nonlinear least-squares analysis of the problem.