In a method for magnetic resonance imaging using a partial parallel acquisition technique with a non-Cartesian occupation of k-space, a number of antennas disposed around an imaging volume for reception of magnetic resonance signals and the magnetic resonance signals in the imaging volume are spatially coded by magnetic gradient fields, such that k-space for each antenna is only incompletely occupied with magnetic resonance signals with at least one trajectory proceeding around the origin of k-space. From the reception signals of each antenna, missing sample values of the trajectory that lie on a straight-line segment extending from the origin are determined in k-space according to a weighting with weighting factors from sample values of the trajectory that likewise lie on the straight lines, such that each k-space is completely occupied. A partial image of the imaging area is generated from each completely occupied k-space by means of a Fourier transformation. An image of the imaging volume is generated from the partial images.