A variational approach to Gibbs artifacts removal in MRI

Gibbs ringing is a feature of MR images caused by the finite sampling of the acquisition space (k-space). It manifests itself with ringing patterns around sharp edges which become increasingly significant for low-resolution acquisitions. In this paper, we model the Gibbs artefact removal as a constrained variational problem where the data discrepancy, represented in denoising and convolutive form, is balanced to sparsity-promoting regularization functions such as Total Variation, Total Generalized Variation and L1 norm of the Wavelet transform. The efficacy of such models is evaluated by running a set of numerical experiments both on synthetic data and real acquisitions of brain images. The Total Generalized Variation penalty coupled with the convolutive data discrepancy term yields, in general, the best results both on synthetic and real data.