Simultaneous segmentation and beam-hardening correction in computed microtomography of rock cores

We propose a post-reconstruction correction procedure for the beam-hardening artifact that neither requires knowledge of the X-ray spectrum nor of the attenuation coefficients in multi-mineral geologic samples. The beam-hardening artifact in polychromatic X-ray computer tomography (CT) hampers segmentation of the phase assemblage in geologic samples. We show that in cylindrically shaped samples like rock cores, the X-ray attenuation value for a single phase depends mainly on the distance from the center of the cylinder. This relationship could be easily extracted from the CT data for every phase and used to infer the presence of these phases at all positions in the sample. Our new approach enables simple segmentation of the phases for further analysis. Additionally, we propose a simple mathematical exercise for parallel beam geometry to show how recent experimentally observed deviations from Beer's law could be incorporated to model the beam-hardening artifact and simultaneously be used for its removal.