In a method for operating a magnetic resonance imaging system to generate a magnetic resonance data file, raw magnetic resonance data are acquired, and k-space is established in a computerized storage medium, with k-space being divided into a contiguous central region and a contiguous region surrounding the central region. In a computerized procedure, the raw data are entered into k-space at a constant sampling rate for both of the central and peripheral regions, while sampling the central region with a first density of sampling points, and sampling the peripheral region at a second density of sampling points that is less than the first sampling density. The set of data points thereby representing sampled k-space is made available in a data file as an output from the computerized procedure, in a form allowing an image to be reconstructed from the contents of the data file.