After publishing this ICIP paper, we noticed that a very similar approach has already been proposed by the paper "Artifact-Free Decompression and Zooming of JPEG Compressed Images with Total Generalized Variation" in the proceedings of VISAPP2012 (as well as in Springer, Computer Vision, Images and Computer Graphics, CCIS).
http://link.springer.com/chapter/10.1007/978-3-642-38241-3_16
We also note that the sentence in our paper "...this primal definition of TGV is first introduced by Setzer et al. in [11]." is somehow misleading, because the primal formulation also appeared in [10].
We apologize for any confusion this may have caused.
Thanks to Dr. Martin Holler for pointing out.