A magnetic resonance imaging apparatus includes a plurality of radio frequency coils (34) that acquire variable density sensitivity encoded data that is undersampled at least away from the center of k-space. A reconstruction processor (52) for each coil reconstructs: a regularization image reconstructed from a higher density portion of the variable density sensitivity encoded data disposed at or near a center of k-space acquired by that coil; and a folded image reconstructed from the variable density sensitivity encoded data acquired by that coil. An unfolding processor (66) unfolds the folded images. The unfolding is regularized by the regularization images.