1. A method to generate a series of magnetic resonance (MR) images in order to monitor a position of an interventional device located in an examination region within an examination subject, comprising: operating an MR data acquisition unit to acquire MR data from an examination region of an examination subject in which an interventional device is located, by: (a) activating at least two phase-coding gradients in respective, different spatial directions with a gradient coil system of said MR data acquisition unit, (b) after the activated phase-coding gradients reach full strength, radiating a non-slice-selective radio-frequency (RF) excitation pulse with an RF transmission antenna of said MR data acquisition unit, (c) following a time t 1 after the radiated RF excitation pulse, acquiring echo signals, resulting from nuclear spins excited by the radiated RF excitation pulse, with an RF reception antenna, and entering raw data points, representing said echo signals, into a memory representing k-space, along a radial k-space trajectory predetermined by the strength of the phase-coding gradients, k-space in said memory comprising an imaging area, corresponding to said examination region, (d) repeating (a) through (c) with respectively different phase-coding gradient until a first region of k-space, dependent on t 1 , within said imaging area is filled with respective raw data points entered along respective radial k-space trajectories, and (e) making data entries into a remainder of said imaging area in k-space, not covered by said first region, and comprising at least a center of k-space, differently than in (a) through (d); in a computer, implementing a Fourier transformation of said raw data points in said first region and in said remainder of k-space to generate image data representing said examination region; repeating said operation of said MR data acquisition unit and said reconstruction of image data to generate multiple MR images of said examination region; and displaying said multiple MR images of said examination region at a monitor to allow visual determination therein of a current position of said interventional device.