Doppler broadening of annihilation radiation spectroscopy study using Richardson‐Lucy, Maximum Entropy and Huber methods

Abstract

The Richardson-Lucy, Maximum Entropy and Huber regularization methods are popularly used in solving ill-posed inverse problems. This paper considers the use of these three methods in the deconvoluting DBARS (Doppler Broadening of Annihilation Radiation Spectroscopy) data. As DBARS data have a constant background on the high-energy side and a long exponential tail on the low-energy side, we check the different deconvolution schemes paying specific attention to the quality of the deconvolution at the peak and tail positions. Comparison of the three methods is made by testing on Monte-Carlo simulated data both in terms of the deconvoluted quality and computational resources required. Finally, we apply these methods to experimental DBARS data taken on polycrystalline metal samples.

Iterative Methods of Richardson-Lucy-Type for Image Deblurring

“…It is a nonlinear iterative method, whose convergence may be quite slow. Nevertheless, the method is popular; see, e.g., [1,3,[16][17][18][19] for a variety of recent applications. Richardson-Lucy iteration also is applied to solve blind deconvolution problems; see [2,5].…”