Streak artifacts generated by at least one X-ray attenuating object arranged outside a reconstruction volume in a three-dimensional image data set showing the reconstruction volume are reduced. The reconstruction volume is reconstructed from two-dimensional projection images recorded from different projection directions. The object is localized in the projection images showing the object. To determine corrected projection images for the reconstruction of the image data set, the image data of the area of each projection image showing the object is corrected to remove the object. The localization of the object is performed taking into account difference images of the measured projection images and from a reconstruction data set of forward-projected comparative images reconstructed from the measured projection images.
