Imprecise k-space sampling and central brightening

In real-world sampling of k-space data, one generally makes a stochastic error not only in the value of the sample but in the effective position of the drawn sample. We refer to the latter as imprecise sampling and apply this concept to the fourier-based acquisition of magnetic resonance data. The analysis shows that the effect of such imprecisely sampled data accounts for contributions to noise, blurring, and intensity-bias in the image. Under general circumstances, the blur and the bias may depend on the scanned specimen itself. We show that for gaussian distributed imprecision of k-vector samples the resulting intensity inhomogeneity can be explicitly computed. The presented mechanism of imprecise k-space sampling (IKS) provides a complementary explanation for the phenomenon of central brightening in high-field magnetic resonance imaging. In computed experiments, we demonstrate the adequacy of the IKS effect for explaining central brightening. Furthermore, the experiments show that basic properties of IKS can in principle be inferred from real MRI data by the analysis on the basis of bias fields in magnitude images and information contained in the phase-images.