  Higher-order low-rank tensors naturally arise in many applications including
hyperspectral data recovery, video inpainting, seismic data recon- struction,
and so on. We propose a new model to recover a low-rank tensor by
simultaneously performing low-rank matrix factorizations to the all-mode ma-
tricizations of the underlying tensor. An alternating minimization algorithm is
applied to solve the model, along with two adaptive rank-adjusting strategies
when the exact rank is not known.
  Phase transition plots reveal that our algorithm can recover a variety of
synthetic low-rank tensors from significantly fewer samples than the compared
methods, which include a matrix completion method applied to tensor recovery
and two state-of-the-art tensor completion methods. Further tests on real-
world data show similar advantages. Although our model is non-convex, our
algorithm performs consistently throughout the tests and give better results
than the compared methods, some of which are based on convex models. In
addition, the global convergence of our algorithm can be established in the
sense that the gradient of Lagrangian function converges to zero.
