  Low-rank tensor completion has been widely used in computer vision and
machine learning. This paper develops a novel multi-modal core tensor
factorization (MCTF) method combined with a tensor low-rankness measure and a
better nonconvex relaxation form of this measure (NC-MCTF). The proposed models
encode low-rank insights for general tensors provided by Tucker and T-SVD, and
thus are expected to simultaneously model spectral low-rankness in multiple
orientations and accurately restore the data of intrinsic low-rank structure
based on few observed entries. Furthermore, we study the MCTF and NC-MCTF
regularization minimization problem, and design an effective block successive
upper-bound minimization (BSUM) algorithm to solve them. This efficient solver
can extend MCTF to various tasks, such as tensor completion. A series of
experiments, including hyperspectral image (HSI), video and MRI completion,
confirm the superior performance of the proposed method.
