Pixel-by-pixel correction of beam hardening artifacts by bowtie filter in fan-beam CT

Objective. Beam hardening (BH) artifacts in computed tomography (CT) images originate from the polychromatic nature of x-ray photons. In a CT system with a bowtie filter, residual BH artifacts remain when polynomial fits are used. These artifacts lead to worse visuals, reduced contrast, and inaccurate CT numbers. This work proposes a pixel-by-pixel correction (PPC) method to reduce the residual BH artifacts caused by a bowtie filter.Approach. The energy spectrum for each pixel at the detector after the photons pass through the bowtie filter was calculated. Then, the spectrum was filtered through a series of water slabs with different thicknesses. The polychromatic projection corresponding to the thickness of the water slab for each detector pixel could be obtained. Next, we carried out a water slab experiment with a mono energyE= 69 keV to get the monochromatic projection. The polychromatic and monochromatic projections were then fitted with a 2nd-order polynomial. The proposed method was evaluated on digital phantoms in a virtual CT system and phantoms in a real CT machine.Main results. In the case of a virtual CT system, the standard deviation of the line profile was reduced by 23.8%, 37.3%, and 14.3%, respectively, in the water phantom with different shapes. The difference of the linear attenuation coefficients (LAC) in the central and peripheral areas of an image was reduced from 0.010 to 0.003cm-1and 0.007cm-1to 0 in the biological tissue phantom and human phantom, respectively. The method was also validated using CT projection data obtained from Activion16 (Canon Medical Systems, Japan). The difference in the LAC in the central and peripheral areas can be reduced by a factor of two.Significance. The proposed PPC method can successfully remove the cupping artifacts in both virtual and authentic CT images. The scanned object's shapes and materials do not affect the technique.