A variational approach to Gibbs artifacts removal in MRI

Abstract Gibbs ringing is a feature of MR images caused by the finite sampling acquisition space ( k -space). It manifests itself with patterns around sharp edges which become increasingly significant for low-resolution acquisitions. In this paper, we model artefact removal as constrained variational problem where data discrepancy, represented in denoising and convolutive form, balanced to sparsity-promoting regularization functions such Total Variation, Generalized Variation $$L_1$$ L 1 norm Wavelet transform. The efficacy models evaluated running set numerical experiments both on synthetic real acquisitions brain images. penalty coupled discrepancy term yields, general, best results data.