Constructing low-rank Tucker tensor approximations using generalized completion

The projected gradient method for matrix completion is generalized towards the higher-dimensional case of low-rank Tucker tensors. It is shown that an operation order rearrangement in the common projected gradient approach provides a complexity improvement. An even better algorithm complexity can be obtained by replacing the completion operator by a general operator that satisfies restricted isometry property; however, such a replacement transforms the completion algorithm into an approximation algorithm.