A method for generating an image data set of an image area located in a measurement volume of a magnetic resonance system, the magnetic resonance system comprising a gradient system and an RF transmission/reception system, the method comprising: - reading out k-space corresponding to the imaging area, by: (a) activating a frequency encoding gradient in a predetermined spatial direction and with a predetermined strength G 0 by means of said gradient system, (b) after the activated frequency encoding gradient achieves its strength G 0, radiating a non-slice-selective RF excitation pulse by means of said RF transmission/reception system, (c) after a transmit-receive switch time Δt TR following the radiated excitation pulse, acquiring FID signals with said RF transmission/reception system and storing said FID signals as raw data points in k-space along a radial k-space trajectory that is predetermined by the direction and strength G 0 of the frequency encoding gradient, (d) repeating (a) through (c) with respectively different frequency encoding gradient directions in each repetition until the k-space region corresponding to the image area is read out in an outer region of k-space along radial k-space trajectories, said radial k-space trajectories each having the same radially innermost limit k gap which depends on said switch time Δt TR, (e) reading out a remainder of the k-space region corresponding to the imaging area, said remainder being an inner region of k-space not being filled by said first region and including at least a center of k-space, in a read out procedure that is different from the one defined in steps (a) through (d), and storing all the raw data points thus obtained; and - reconstructing image data from the read out data points in k-space by implementing a reconstruction algorithm; characterized in that the inner k-space region is subdivided into a core region and at least one radially adjacent shell region with raw data points in the core region being acquired as Cartesian raw data, and raw data points in the shell region being acquired along radial k-space trajectories using a gradient strength G that is smaller than the gradient strength G 0. - reading out k-space corresponding to the imaging area, by: (a) activating a frequency encoding gradient in a predetermined spatial direction and with a predetermined strength G 0 by means of said gradient system, (b) after the activated frequency encoding gradient achieves its strength G 0, radiating a non-slice-selective RF excitation pulse by means of said RF transmission/reception system, (c) after a transmit-receive switch time Δt TR following the radiated excitation pulse, acquiring FID signals with said RF transmission/reception system and storing said FID signals as raw data points in k-space along a radial k-space trajectory that is predetermined by the direction and strength G 0 of the frequency encoding gradient, (d) repeating (a) through (c) with respectively different frequency encoding gradient directions in each repetition until the k-space region corresponding to the image area is read out in an outer region of k-space along radial k-space trajectories, said radial k-space trajectories each having the same radially innermost limit k gap which depends on said switch time Δt TR, (e) reading out a remainder of the k-space region corresponding to the imaging area, said remainder being an inner region of k-space not being filled by said first region and including at least a center of k-space, in a read out procedure that is different from the one defined in steps (a) through (d), and storing all the raw data points thus obtained; and (a) activating a frequency encoding gradient in a predetermined spatial direction and with a predetermined strength G 0 by means of said gradient system, (b) after the activated frequency encoding gradient achieves its strength G 0, radiating a non-slice-selective RF excitation pulse by means of said RF transmission/reception system, (c) after a transmit-receive switch time Δt TR following the radiated excitation pulse, acquiring FID signals with said RF transmission/reception system and storing said FID signals as raw data points in k-space along a radial k-space trajectory that is predetermined by the direction and strength G 0 of the frequency encoding gradient, (d) repeating (a) through (c) with respectively different frequency encoding gradient directions in each repetition until the k-space region corresponding to the image area is read out in an outer region of k-space along radial k-space trajectories, said radial k-space trajectories each having the same radially innermost limit k gap which depends on said switch time Δt TR, (e) reading out a remainder of the k-space region corresponding to the imaging area, said remainder being an inner region of k-space not being filled by said first region and including at least a center of k-space, in a read out procedure that is different from the one defined in steps (a) through (d), and storing all the raw data points thus obtained; and - reconstructing image data from the read out data points in k-space by implementing a reconstruction algorithm;