1. A method for PPA magnetic resonance tomography imaging with radio data acquisition, comprising the steps of: (1) under-scanning k-space by acquiring a plurality of projections φ of magnetic resonance data with a coil array of M component coils; (2) determining a shift operator C(±nΔk) for a projection φ i dependent on acquired magnetizations along a projection φ i ±α 0 that encompasses φ i and an angle α 0 , with n=1, 2,. .. , m−1; (3) applying said shift operator C(±nΔk) to individual points of the projection φ i to obtain calculated projection points, thereby purely computationally completing the projection φ i ; (4) repeating steps (2) and (3) for all projections φ; and (5) reconstructing an image in the spatial domain from said purely computationally completed projection φ.