1. A magnetic resonance imaging method including acquisition of datasets in bins of magnetic resonance data from an object, applying a respiratory navigator to decide which bins to be filled in time so that each binned dataset relates to a motion state of the object, at least some of the datasets being undersampled in k-space in a defined, bin-specific manner by way of an appropriate k-space sampling scheme such that some of the bins contain incomplete data, a complete sampling of the centre of k-space is obtained and k-space is sampled in a variable density random fashion, each dataset relating to a motion state of the object, reconstruction of images from the magnetic resonance data in each of the bins of datasets by way of a compressed sensing reconstruction, application of a motion correction to the reconstructed images relative to a selected motion state, so as to generate motion corrected images and derivation of a diagnostic image for the selected motion state from the motion corrected images.