X-ray attenuation models to account for beam hardening in computed tomography

We introduce a beam-hardening correction method for lab-based X-ray computed tomography (CT) by modifying existing iterative tomographic reconstruction algorithms. Our method simplifies the standard Alvarez-Macovski X-ray attenuation model [Phys. Med. Biol.21, 733 (1976)] and is compatible with conventional (i.e., single-spectrum) CT scans. The sole modification involves a polychromatic projection operation, which is equivalent to applying a weighting that more closely matches the attenuation of polychromatic X-rays. Practicality is a priority, so we only require information about the X-ray spectrum and some constants relating to material properties. No other changes to the experimental setup or the iterative algorithms are necessary. Using reconstructions of simulations and several large experimental datasets, we show that this method is able to remove or reduce cupping, streaking, and other artefacts from X-ray beam hardening and improve the self-consistency of projected attenuation in CT. When the assumptions made in the simplifications are valid, the reconstructed tomogram can even be quantitative.