k‐Space interpretation of the Rose Model: Noise limitation on the detectable resolution in MRI

Noise limitation on the detected spatial resolution, described by the Rose Model, is well known in X-ray imaging and routinely used in designing X-ray imaging protocols. The purpose of this article is to revisit the Rose Model in the context of MRI where image data are acquired in the spatial frequency domain. A k-space signal-to-noise ratio (kSNR) is introduced to measure the relative signal and noise powers in a circular annulus in k-space. It is found that the kSNR diminishes rapidly with k-space radius. The Rose criterion that the voxel SNR approximately 4 is translated to kSNR cutoff values was tested using theoretical derivation and experimental histogram analysis. Experiments demonstrate that data acquisition beyond this cutoff k-space radius adds little or no information to the image. In order to reduce the noise limit on spatial resolution, the signal strength must be improved through means such as increasing the coil sensitivity, contrast enhancement, and signal averaging. This finding implies that the optimal k-space volume to be sampled or the optimal scan time in MRI should be matched to the relative SNR level.