There is described a method for correction of truncation artifacts in reconstructed tomographic images in a reconstruction method for tomographic images with truncated projection image data in the reconstructed tomographic images, in which divergent radiation is emitted from a radiographic source, an object to be examined is x-rayed with the divergent radiation in different projection directions, the radiation penetrating through the object to be examined is detected by a detector as projection images, with the data of the signal being arranged in a number of projection data rows and projection images detected by the detector being expanded line-by-line through extrapolation of the projection data rows. In this case the signal of a projection data row can be smoothed with a polynomial filter to reduce the noise component of the signal and the truncated proportion of the projection data row can be computed from the smoothed signal of the projection data row by means of an extrapolation method, with the extrapolation widths being derived from a number of rows.