Use of an iterative convolution approach for qualitative and quantitative peak analysis in low resolution gamma-ray spectra

In many applications, low resolution gamma-ray spectrometers, such as sodium iodide scintillation detectors, are widely used primarily due to their relatively low cost and high detection efficiency. There is widespread interest in improved methods for analyzing spectral data acquired with such devices, using inverse analysis. Peak means and peak areas in gamma- and X-ray spectra are needed for both qualitative and quantitative analysis. This paper introduces the PEAKSI code package that was developed at the Center for Engineering Applications of Radioisotopes (CEAR). The basic approach described here is to use accurate forward models and iterative convolution instead of direct deconvolution. Rather than smoothing and differentiation a combination of linear regression and non-linear searching is used to minimize the reduced chi-square, since this approach retains the capability of establishing uncertainties in the estimated peak parameters. The PEAKSI package uses a Levenberg–Marquardt (LM) non-linear search method combined with multiple linear regression (MLR) to minimize the reduced chi-square value for fitting single or multiple overlapping peaks to determine peak parameters, including peak means, peak standard deviations or full width at half maximum (FWHM), net peak counts, and background counts of peaks in experimental gamma-ray spectra. This approach maintains the natural error structure so that parameter uncertainties can be estimated. The plan is to release this code to the public in the near future.