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

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)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 Riviere (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 Riviere's results with recently derived 'exact' analytic formulae for the generalized attenuated radon transform. We present numerical experiments with real and simulated data.55410071024Nuclear Instrumentation Laboratory Group (Federal University of Rio de Janeiro), BrazilBrazilian Synchrotron Light Laboratory (LNLS)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)FAPESP [06/00356-6]CNPq [304820/2006-7