A deconvolution method for scintillator gamma-ray spectrum analysis based on convex optimization

Abstract A deconvolution method based on convex optimization is developed and applied to gamma-ray spectrum deconvolution of simulated complicated spectra of NaI(Tl) measurements. The gamma-ray deconvolution problem is transformed into a minimization problem with inequality constraints. Then the Lagrange dual method is applied to transform the primal Lagrange problem into the dual problem. The interior-point method is applied and the logarithm barrier function is applied to construct the Newton system for iteration search. PCG (Preconditioned Conjugate Gradient) is applied to do the inexact search of the Newton system. The proposed method is applied to deconvolution of 4 typical gamma-ray spectra: (a) characteristic gamma-ray spectrum of 137Cs; (b) characteristic gamma-ray spectrum of 60Co; (c) characteristic gamma-ray spectrum of 152Eu; (d) mixed fission products in the primary loop of PWR (Pressurized Water Reactor), including the isotopes of Kr, Xe, I and Cs. Compared with the ML-EM method, improved accuracies and high resolution can be obtained with the proposed method. Moreover, the proposed method costs about 1/3 computational time of the ML-EM method.