Reconstruction of bremsstrahlung spectra from attenuation data using generalized simulated annealing

Abstract

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.

Sobre a possibilidade de determinar espectros de energia de fótons contaminantes a partir da fórmula Schiff e o algoritmo de recozimento simulado generalizado

“…A terceira etapa está relacionada com o uso da fórmula analítica de Schiff [11][12][13] dada pela Equação 1 A variável é o número atómico efetivo dos materiais atenuantes, é a energia total dos elétrons incidentes no alvo em MeV, é a espessura hipotética do alvo em cm e ( ) é o coeficiente de atenuação linear dos materiais do alvo em cm -1 .…”

Reconstrução de Espectros de Raios X de Aceleradores Lineares Clínicos usando o Método de Recozimento Simulado Generalizado

“…O GSA 8, 12 é um método estocástico que permite encontrar o mínimo de função de custo f(Φ trial ) como a equação (2), mediante o resfriamento controlado da temperatura fazendo um ciclo iterativo baixando a temperatura (esquema de esfriamento) até o sistema alcançar seu estado cristalino de mínima energia. O método consiste em supor uma solução inicial para a fluência Φ trial e encontrar novas soluções validadas pelo critério de Metropolis 7,10 .…”

Spectral reconstruction of kilovoltage photon beams using generalized simulated annealing

“…Mathematical methods usually derive the spectrum from experimental transmission curves of the X-rays by a given material (Chen et al, 2012;Hill et al, 2014). Some difficulties of experimental and computational approaches are related to the cost of the spectrometer, specific information about the geometry and materials of the X-ray equipment for use in the Monte Carlo modelling (Baird, 1981;Hill et al, 2014) and expertise (Menin et al, 2016). Furthermore, softwares as SpekCalc only allow calculations for a fixed source-detector distance (Poludniowski et al, 2009).…”