Deconvolution of positron annihilation coincidence Doppler broadening spectra using an iterative projected Newton method with non-negativity constraints

Abstract

A generalized least-square method with Tikonov-Miller regularization and non-negativity constraints has been developed for deconvoluting two-dimensional coincidence Doppler broadening spectroscopy ͑CDBS͒ spectra. A projected Newton algorithm is employed to solve the generalized least-square problem. The algorithm has been tested on Monte Carlo generated spectra to find the best regularization parameters for different simulated experimental conditions. Good retrieval of the underlying positron-electron momentum distributions in the low momentum region is demonstrated. The algorithm has been successfully used to deconvolute experimental CDBS data from aluminum.

CDBTools - Evaluate Positron Annihilation Coincidence Doppler Broadening Spectrum

“…Last version of the program with program sources should be downloaded from the project webpage [5]. This software use averaging data filtering, for more accurate results spectra deconvolution like [8], based on Tikonov-Miller regularization is appropriate.…”

Positronium as a probe of small free volumes in crystals, polymers and porous media

“…the plot in the coordinates S vs. W allows to identify the defects in the sample structure. The attempts to improve the deconvolution method are continued till now [46].…”

A Primal-Dual Active-Set Method for Non-Negativity Constrained Total Variation Deblurring Problems

“…The semi-smooth Newton's update for (28)- (30) is given by the following system: (32) Here, denotes a diagonal matrix such that and denotes a matrix such that…”

“…For example, in applications such as gamma ray spectral analysis [31], astronomical imaging and spectroscopy [32], the physical characteristics of the problem require the recovered data to be non-negative. An intuitive approach to ensuring non-negativity is to solve the unconstrained problem first, followed by setting the negative components of the resulting output to zero.…”