A method for establishing and/or reducing artifacts that arise when reconstructing (R) an MPI overall image data record from MPI signal data and an appended system matrix (SMapp(r,f)), wherein the appended system matrix (SMapp(r,f)) includes system matrices of different particle classes (P1, P2). The method includes setting a selection region (cvn(r)) of a reconstructed MPI overall image data record (cn(r)), producing virtual signal data (sn(f)) by inverse transformation of the selection region, reconstructing a virtual overall image data record (c′vn(r)) from the virtual signal data and the appended system matrix, setting an artifact region (cartifact_n(r)) within the reconstructed virtual overall image data record so that the artifact region has only voxels lying outside of the selection region, and assigning the image data present in the artifact region as artifact image data (cartifact_n(r)). This permits ghost artifacts to be corrected.