Methods for deconvolving sparse positive delta function series

Sparse delta function series occur as data in many chemical analysis and seismic methods. This original data is often sufficiently degraded by the recording instrument response that the individual delta function peaks are difficult to distinguish and measure. A method, which has been used to measure these peaks, is to fit a parameterized model by a nonlinear least squares fitting algorithm. The deconvolution approaches described here have the advantage of not requiring a parameterized point spread function, nor do they expect a fixed number of peaks. Two new methods will be presented. The maximum power technique will be reviewed. A maximum a posteriori technique will be introduced. Results on both simulated and real data by the two methods will be presented. The characteristics of the data can determine which method gives superior results.