In a method as well as a magnetic resonance tomography apparatus for implementation of such a method for improved sensitivity-encoded magnetic resonance imaging using a two-dimensional or three-dimensional acquisition coil array, two-dimensional or three-dimensional undersampling of k-space is undertaken by measurement of a number N of basic partial trajectories τn in k-space that in their entirety form a geometric arrangement of source points, a number M of different operators Cm(Δ km) are determined, with each operator representing an algebraic transformation with which unmeasured target points at an interval Δ km from one of the measured source points are synthesized from a number of measured source points, the operators Cm(Δ km) are applied to at least one subset of the measured source points for at least partial completion of the magnetic resonance data set, and a largely artifact-free image is reconstructed in three-dimensional space on the basis of the measured source points and the synthesized data points.