1. A magnetic resonance imaging (MRI) apparatus configured to acquire nuclear magnetic resonance (NMR) signal data for a periodically rotated data acquisition region in k-space that includes a plurality of data acquisition loci therewithin, said apparatus comprising: a data acquisition controller configured to acquire NMR signal data for a periodically rotated data acquisition region in k-space that includes a plurality of data acquisition loci therewithin defined by phase-encoding magnetic gradient pulses and read-out magnetic gradient pulses having orthogonal resultant directions which change for different rotational orientations of the region, said loci defining data acquisition regions having a width dimension that is larger at a point disposed further away from k-space origin than the width dimension of said region at a point nearer the origin of k-space thereby reducing or avoiding gaps in the coverage of k-space with acquired NMR data between different rotated positions of the data acquisition region; and an image reconstruction unit configured to reconstruct an image based on said acquired NMR signal data in k-space.