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 executing a first MR data acquisition procedure that comprises: (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, and (d) repeating (a) through (c) with respectively different phase-coding gradients 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; operating said MR data acquisition unit to also acquire MR data from the examination region of the examination subject in which the interventional device is located, by executing a second MR data acquisition procedure that differs from said first MR data acquisition procedure, and making data entries of the MR data acquired in said second MR data acquisition procedure into a remainder of said imaging area in k-space, not covered by said first region, and comprising the center of k-space; 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.