An evaluation of algorithms for the deconvolution of Doppler broadening positron annihilation radiation spectroscopy spectra

Two least squares minimization methods for the deconvolution of 1D Doppler Broadening Annihilation Radiation Spectroscopy (DBARS) spectra have been tested with spectra generated by Monte Carlo simulation according to the following functional forms: inverted triangle, inverted parabola, Laplace, Lorentz and a model DBARS spectrum for a metal composed of an inverted parabola and a Gaussian function. These reference spectra were firstly convoluted with a Gaussian broadening factor and then restored to its original form with the algorithms. The method with Tikhonov regularizer and non-negativity constraint still failed to restore the sharp features of these spectral functions although the negative signal found in an earlier study was removed. On the other hand, the method with the Huber regularizer was successful. Optimization of the deconvolution in terms of regularization parameters is necessary to achieve good deconvolution. The optimization of the deconvolution was checked with visual matching and a quality factor which takes into account the number of counts in the spectrum.