Reconstruction of bremsstrahlung spectra from attenuation data using generalized simulated annealing

The throughout knowledge of a X-ray beam spectrum is mandatory to assess the quality of its source device. Since the techniques to directly measurement such spectra are expensive and laborious, the X-ray spectrum reconstruction using attenuation data has been a promising alternative. However, such reconstruction corresponds mathematically to an inverse, nonlinear and ill-posed problem. Therefore, to solve it the use of powerful optimization algorithms and good regularization functions is required. Here, we present a generalized simulated annealing algorithm combined with a suitable smoothing regularization function to solve the X-ray spectrum reconstruction inverse problem. We also propose an approach to set the initial acceptance and visitation temperatures and a standardization of the objective function terms to automatize the algorithm to address with different spectra range. Numerical tests considering three different reference spectra with its attenuation curve are presented. Results show that the algorithm provides good accuracy to retrieve the reference spectra shapes corroborating the central importance of our regularization function and the performance improvement of the generalized simulated annealing compared to its classical version.