Deconvolution of nuclear spectra of low counts

Abstract

Conventional methods of spectrum deconvolution usually fail when spectra of extremely low count numbers have to be evaluated. Such spectra carry much more information than used by these conventional methods. To keep all information and to obtain the best possible results low count spectra should be approached with a special philosophy: instead of dividing the spectrum into well-defined areas regarded as single peaks, the counts in all channels have to be allocated to the peaks by all possible divisions into two sets. The probability of each division can be determined using the probability distributions of the single peaks (peak shapes). Probabilities of all those distributions which belong to the same values of peak areas are added together. The distribution of the highest probability can be regarded as the final result. The confidence level of the deconvolution is described by the corresponding probability. The method is suitable for determining small peak areas on a high background, for decomposing overlapping peaks and for deconvoluting the whole spectrum or its one section.