A model-based correction method for beam hardening artefacts in X-ray tomography

The absorption law of Lambert-Beer gives rise to the linear relationship between the attenuation and the thickness of the material. However, this law is only true for a monochromatic beam. For polychromatic sources used in medical computer tomography (CT) and microtomography, this linear relationship no longer holds, which leads to beam hardening. When the beam hardening effect is not accounted for, the reconstructed images will be corrupted by cupping artefacts. Here, a bimodal energy model for the energy spectrum is presented and applied to correct the beam hardening effect in different materials. In essence, this correction method is a linearization technique based on a physical model, where no a priori knowledge about the spectrum of the source is required. 1 The bimodal energy model The bimodal energy model is based on the assumption that the detected energy spectrum is characterized by two dominant energies, E1 and E2. This may be justified by inspecting the peak energies of the tungsten source and the gadox detector. As shown in [1], this particular combination of source and scintillator material gives rise to two bands in the energy spectrum, which led to the proposition of a bimodal form for the detected energy distribution. Suppose the incident and outcoming intensity of the X-ray beam is given as I0 and I , respectively. Then, the model can be written as follows: