Extension of the R–L algorithm for [formula omitted]-ray spectra deconvolution and its experimental results

Abstract

The Richardson–Lucy (R–L) algorithm is widely used for γ-ray spectra deconvolution. In this study, we considered the R–L algorithm as an iteration process of an optimization problem and extended it with a universal function. Three iterative formulae are given based on common elementary functions: the exponential R–L algorithm, the logarithmic R–L algorithm, and the power R–L algorithm. Simulated and experimental 152Eu spectra were used to test the effects of the proposed algorithms. Results show that all the three algorithms make the objective function value decrease monotonically with the increase of iteration number. With proper parameters, the extended algorithms achieve faster convergence than the original R–L algorithm and the MAP algorithm. The power R–L algorithm with m less than but close to 2 shows the fastest convergence rate. This indicates the proposed extension is an effective improvement. Also, the method could be used for other objective functions, which provides a new idea for constructing better iterative algorithms for spectrum or image deconvolution, such as chromatography, infrared spectroscopy, Raman spectroscopy, X-ray fluorescence spectroscopy and medical imaging.