A method for the reduction of streak artifacts in an image data set reconstructed from projection images of an X-ray device is provided. The method includes determining a first interim data set by applying a non-linear low-pass filter to pixels that satisfy a selection condition. A second non-linear, high-pass-filtered interim data set is determined by pixel-by-pixel subtraction of the first interim data set from the image data set. The second interim data set is Fourier transformed in order to obtain a spatial frequency data set. Frequency portions attributable to artifacts in the spatial frequency data set are removed, and the processed spatial frequency data set is inverse Fourier transformed, such that a third interim data set is obtained. An artifact-reduced result data set is determined by addition of the third interim data set and the first interim data set.
