  Recently, a tensor factorization based method for a low tubal rank tensor
completion problem of a third order tensor was proposed, which performed better
than some existing methods. Tubal rank is only defined on one mode of third
order tensor without low rank structure in the other two modes. That is, low
rank structures on the other two modes are missing. Motivated by this, we first
introduce multi-tubal rank, and then establish a relationship between
multi-tubal rank and Tucker rank. Based on the multi-tubal rank, we propose a
novel low rank tensor completion model. For this model, a tensor factorization
based method is applied and the corresponding convergence anlysis is
established. In addition, spatio-temporal characteristics are intrinsic
features in video and internet traffic tensor data. To get better performance,
we make full use of such features and improve the established tensor completion
model. Then we apply tensor factorization based method for the improved model.
Finally, numerical results are reported on the completion of image, video and
internet traffic data to show the efficiency of our proposed methods. From the
reported numerical results, we can assert that our methods outperform the
existing methods.
