Viewing the effective k-space coverage of MR images: phantom experiments with fast Fourier transform

The purpose of this experimental study was to evaluate whether the effective k-space coverage of MR images can in principle be viewed after multidimensional Fourier transform back to k-space. A water-soaked sponge phantom providing homogeneous k-space pattern was imaged with different standard MR sequences, utilizing elliptic acquisitions, partial-Fourier acquisitions and elliptic filtering as imaging examples. The resulting MR images were Fourier-transformed to the spatial frequency domain (the k-space) to visualize their effective k-space coverage. These frequency domain images are named "backtransformed k-space images." For a quantitative assessment, the sponge phantom was imaged with three-dimensional partial-Fourier sequences while varying the partial acquisition parameters in slice and phase direction. By linear regression analysis, the k-space coverage as expected from the sequence menu parameters was compared to the effective k-space coverage as observed in the backtransformed k-space images. The k-space coverage of elliptic and partial-Fourier acquisitions became visible in the backtransformed k-space images, as well as the effect of elliptic filtering. The expected and the observed k-space coverage showed a highly significant correlation (r=.99, P<.001). In conclusion, the effective k-space coverage of MR images becomes visible when Fourier-transforming MR images of a sponge phantom back to k-space. This method could be used for several purposes including sequence parameter optimization, basic imaging research, and to enhance a visual understanding of k-space, especially in three-dimensional MR imaging.