In CSCT, an exact reconstruction of a scattering function for each voxel is not known for polychromatic primary radiation. According to an exemplary embodiment of the present invention, a beam hardening compensation is performed prior to reconstruction allowing to perform a quasi-exact reconstruction on the basis of the primary radiation mean attenuation values are determined, from which an equivalent water thickness is derived. From the equivalent water thickness an energy shift is calculated, which is used to correct the initial mean energy of the scatter radiation. Furthermore, a CT reconstruction may be performed prior to a CSCT reconstruction allowing for a beam-hardening correction. Advantageously, this may allow for an improved image quality and an improved resolution of the scatter function.