The polychromatic nature of the x-ray beams and their effects on the reconstructed image are often disregarded during standard image reconstruction. This leads to cupping and beam hardening artifacts inside the reconstructed volume. To correct for a general cupping, methods like water precorrection exist. They correct the hardening of the spectrum during the penetration of the measured object only for the major tissue class. In contrast, more complex artifacts like streaks between dense objects need other techniques of correction. If using only the information of one single energy scan, there are two types of corrections. The first one is a physical approach. Thereby, artifacts can be reproduced and corrected within the original reconstruction by using assumptions in a polychromatic forward projector. These assumptions could be the used spectrum, the detector response, the physical attenuation and scatter properties of the intersected materials. A second method is an empirical approach, which does not rely on much prior knowledge. This so-called empirical beam hardening correction (EBHC) and the previously mentioned physical-based technique are both relying on a segmentation of the present tissues inside the patient. The difficulty thereby is that beam hardening by itself, scatter, and other effects, which diminish the image quality also disturb the correct tissue classification and thereby reduce the accuracy of the two known classes of correction techniques. The herein proposed method works similar to the empirical beam hardening correction but does not require a tissue segmentation and therefore shows improvements on image data, which are highly degraded by noise and artifacts. Furthermore, the new algorithm is designed in a way that no additional calibration or parameter fitting is needed.