An analytical method for quantitative reconstruction of X-ray fluorescence computed tomography with attenuation correction

X-ray fluorescence computed tomography (XFCT) can perform elemental imaging of an object, but its results often suffer from attenuation due to the low-energy nature of X-ray fluorescence. Here we propose an analytical reconstruction method based on solving a partial differential equation precisely describing a forward-scattering XFCT system. This method is able to carry out fast quantitative reconstruction with arbitrary attenuation correction for both source and fluorescence simultaneously. It incorporates the prior knowledge of the attenuation of scanned object, thus demands an extra scan. However, this can be avoided if the attenuation of source is similar to that of fluorescence or the attenuation is not significant. Monte Carlo simulation results show that this method is capable of providing more accurate quantitative results than traditional algorithms such as filtered backprojection or some simple attenuation compensation techniques.