In a method and apparatus for the correction of artifacts in magnetic resonance images (MR) acquired with an MR pulse sequence in which gradients are switched simultaneously during the radiation of at least one non-selective excitation pulse, measurement data acquired with the pulse sequence in k-space are loaded into a processor, in which a perturbation matrix is determined on the basis of spatial and k-space point data of the acquired measurement data and the gradients used during the excitation. A corrected image is calculated from the acquired measurement data in k-space and the perturbation matrix, with the calculation of the corrected image including a matrix inversion of the perturbation matrix. The corrected image is then stored or displayed.