Exact analytic reconstruction in x-ray fluorescence CT and approximated versions.

X-ray fluorescence computed tomography (XFCT) is a relatively new synchrotron-based imaging modality aiming at reconstructing the distribution of nonradiative elements within a sample irradiated with high-intensity monochromatic x-rays. In a recent paper La Rivière (2004 Phys. Med. Biol. 49 2391-405) presented an approximated inversion method based on reducing the problem to the inversion of the exponential radon transform. In this paper we compare La Rivière's results with recently derived 'exact' analytic formulae for the generalized attenuated radon transform. We present numerical experiments with real and simulated data.