  Minimizing the nuclear norm of a matrix has been shown to be very efficient
in reconstructing a low-rank sampled matrix. Furthermore, minimizing the sum of
nuclear norms of matricizations of a tensor has been shown to be very efficient
in recovering a low-Tucker-rank sampled tensor. In this paper, we propose to
recover a low-TT-rank sampled tensor by minimizing a weighted sum of nuclear
norms of unfoldings of the tensor. We provide numerical results to show that
our proposed method requires significantly less number of samples to recover to
the original tensor in comparison with simply minimizing the sum of nuclear
norms since the structure of the unfoldings in the TT tensor model is
fundamentally different from that of matricizations in the Tucker tensor model.
