In a method and magnetic resonance (MR) apparatus for reducing artifacts in an image dataset reconstructed from MR raw data that were acquired by radial sampling using different coil elements, for each of at least some of the coil elements, exclusion information is determined that identify MR data from that coil element that are responsible for at least one artifact, by a comparison of a sensitivity map, which defines a spatial reception capability of that coil element, with at least one comparison dataset obtained from at least a portion of the MR data from that coil element. At least the MR data identified from the exclusion information are excluded from the reconstruction of the image dataset.