The invention relates to a method for correcting truncation artifacts in reconstructing computer tomography recordings. The projection images of the computer tomography recordings are extended by extrapolation. An equivalent body is determined which in the peripheral region of the projection image attenuates the radiation emanating from a radiation source of the computer tomography according to the object to be examined, and the attenuation is determined outside the projection image for extrapolated image points. A smoothing of the signal of a projection data line is effected with a digital polynomial filter to reduce the noise portion of the signal. The truncated portion of the projection data line is computed from the smoothed signal of the projection data line by an extrapolation method.