The invention concerns a method and magnetic resonance apparatus for acquisition and generation of a time-resolved image series of an anatomical organ with a quasi-periodical movement in a subject, k-space is sampled in segments with a number of partial data sets, with the sampling points of each partial data set corresponding to grid points of a Cartesian sampling grid of a k-space segment, and the Cartesian sampling grids of the k-space segments being rotated relative to one another. A series of sub-data sets is incompletely acquired for each partial data set using alternating sampling schemes. Each incomplete sub-data set is associated with one of the individual images. For at least some of the partial data sets, complete sub-data sets are reconstructed from the incomplete sub-data sets. For the reconstruction of the individual images, in each of the individual images, at least some of the complete sub-data sets that are associated with this individual image are used.